Dave WilsonSr Industrial Systems Engineer

BLDC Motors and Control

PMSM Motors

In Todayrsquos Exciting Episodehellip

Field Oriented Control

Sensorless FOC

TI Motor Control Solutions

N

STo

rque

Clo

ckw

ise

Cou

nter

-Clo

ckw

ise

θ360deg

Torque in a BLDC Motor

B

B

C

CN

S

A

AC

urre

nt

A

B

C

N

S

Commutating a BLDC Motor

B

B

C

C

N

S

A

ATo

rque

Cur

rent

0deg

A

B

C

A

B

C

0deg

)()4( INBlrTorque =)()( IkT=

Control of a Brushless DC Motor

12 zones in 360 degreesof mechanical rotation

1

2

3

4

5

6

BA

C

s

rtC

ontr

olle

r

110

Source Eastern Air Devices Inc Brushless DC Motor Brochure

120 0 hall spacing is preferred over 60 0

spacing since unpowered or

unconnected sensors produce 111 or 000

codes which can be used for fault

detection

BLDC CommutationQ1

Fault input signal

Q3

Q4

Q5

Q6

Q2

Hall C

Hall B

Hall A

Commutation of a Brushless DC Motor

NS

NS

NN

S

NS

C

C

CC

A

A

A

A

B

B

B

B

N N

S

S

N

N

S S

NS

NS

NS

NS

NNS

S

NN

S

S

N

S

N

S

N

N

S

S

NS

S

N

NN

S

S

N

N

S

S

S

N

S

N

S

N

S

N

NS

SN

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

NS

NS

NS

SN

Sensorless BLDC Control

Con

trol

ler

Source Eastern Air Devices Inc Brushless DC Motor Brochure

Conditioning

Back EMF in a Single Loop of Wire

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

N

S

Uniform airgap flux density

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Uniformwindingdensity

Back EMF in a Multi-turn Winding

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

BLDC Motors and Control

PMSM Motors

In Todayrsquos Exciting Episodehellip

Field Oriented Control

Sensorless FOC

TI Motor Control Solutions

N

STo

rque

Clo

ckw

ise

Cou

nter

-Clo

ckw

ise

θ360deg

Torque in a BLDC Motor

B

B

C

CN

S

A

AC

urre

nt

A

B

C

N

S

Commutating a BLDC Motor

B

B

C

C

N

S

A

ATo

rque

Cur

rent

0deg

A

B

C

A

B

C

0deg

)()4( INBlrTorque =)()( IkT=

Control of a Brushless DC Motor

12 zones in 360 degreesof mechanical rotation

1

2

3

4

5

6

BA

C

s

rtC

ontr

olle

r

110

Source Eastern Air Devices Inc Brushless DC Motor Brochure

120 0 hall spacing is preferred over 60 0

spacing since unpowered or

unconnected sensors produce 111 or 000

codes which can be used for fault

detection

BLDC CommutationQ1

Fault input signal

Q3

Q4

Q5

Q6

Q2

Hall C

Hall B

Hall A

Commutation of a Brushless DC Motor

NS

NS

NN

S

NS

C

C

CC

A

A

A

A

B

B

B

B

N N

S

S

N

N

S S

NS

NS

NS

NS

NNS

S

NN

S

S

N

S

N

S

N

N

S

S

NS

S

N

NN

S

S

N

N

S

S

S

N

S

N

S

N

S

N

NS

SN

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

NS

NS

NS

SN

Sensorless BLDC Control

Con

trol

ler

Source Eastern Air Devices Inc Brushless DC Motor Brochure

Conditioning

Back EMF in a Single Loop of Wire

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

N

S

Uniform airgap flux density

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Uniformwindingdensity

Back EMF in a Multi-turn Winding

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

N

STo

rque

Clo

ckw

ise

Cou

nter

-Clo

ckw

ise

θ360deg

Torque in a BLDC Motor

B

B

C

CN

S

A

AC

urre

nt

A

B

C

N

S

Commutating a BLDC Motor

B

B

C

C

N

S

A

ATo

rque

Cur

rent

0deg

A

B

C

A

B

C

0deg

)()4( INBlrTorque =)()( IkT=

Control of a Brushless DC Motor

12 zones in 360 degreesof mechanical rotation

1

2

3

4

5

6

BA

C

s

rtC

ontr

olle

r

110

Source Eastern Air Devices Inc Brushless DC Motor Brochure

120 0 hall spacing is preferred over 60 0

spacing since unpowered or

unconnected sensors produce 111 or 000

codes which can be used for fault

detection

BLDC CommutationQ1

Fault input signal

Q3

Q4

Q5

Q6

Q2

Hall C

Hall B

Hall A

Commutation of a Brushless DC Motor

NS

NS

NN

S

NS

C

C

CC

A

A

A

A

B

B

B

B

N N

S

S

N

N

S S

NS

NS

NS

NS

NNS

S

NN

S

S

N

S

N

S

N

N

S

S

NS

S

N

NN

S

S

N

N

S

S

S

N

S

N

S

N

S

N

NS

SN

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

NS

NS

NS

SN

Sensorless BLDC Control

Con

trol

ler

Source Eastern Air Devices Inc Brushless DC Motor Brochure

Conditioning

Back EMF in a Single Loop of Wire

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

N

S

Uniform airgap flux density

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Uniformwindingdensity

Back EMF in a Multi-turn Winding

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

B

B

C

CN

S

A

AC

urre

nt

A

B

C

N

S

Commutating a BLDC Motor

B

B

C

C

N

S

A

ATo

rque

Cur

rent

0deg

A

B

C

A

B

C

0deg

)()4( INBlrTorque =)()( IkT=

Control of a Brushless DC Motor

12 zones in 360 degreesof mechanical rotation

1

2

3

4

5

6

BA

C

s

rtC

ontr

olle

r

110

Source Eastern Air Devices Inc Brushless DC Motor Brochure

120 0 hall spacing is preferred over 60 0

spacing since unpowered or

unconnected sensors produce 111 or 000

codes which can be used for fault

detection

BLDC CommutationQ1

Fault input signal

Q3

Q4

Q5

Q6

Q2

Hall C

Hall B

Hall A

Commutation of a Brushless DC Motor

NS

NS

NN

S

NS

C

C

CC

A

A

A

A

B

B

B

B

N N

S

S

N

N

S S

NS

NS

NS

NS

NNS

S

NN

S

S

N

S

N

S

N

N

S

S

NS

S

N

NN

S

S

N

N

S

S

S

N

S

N

S

N

S

N

NS

SN

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

NS

NS

NS

SN

Sensorless BLDC Control

Con

trol

ler

Source Eastern Air Devices Inc Brushless DC Motor Brochure

Conditioning

Back EMF in a Single Loop of Wire

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

N

S

Uniform airgap flux density

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Uniformwindingdensity

Back EMF in a Multi-turn Winding

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

B

B

C

C

N

S

A

ATo

rque

Cur

rent

0deg

A

B

C

A

B

C

0deg

)()4( INBlrTorque =)()( IkT=

Control of a Brushless DC Motor

12 zones in 360 degreesof mechanical rotation

1

2

3

4

5

6

BA

C

s

rtC

ontr

olle

r

110

Source Eastern Air Devices Inc Brushless DC Motor Brochure

120 0 hall spacing is preferred over 60 0

spacing since unpowered or

unconnected sensors produce 111 or 000

codes which can be used for fault

detection

BLDC CommutationQ1

Fault input signal

Q3

Q4

Q5

Q6

Q2

Hall C

Hall B

Hall A

Commutation of a Brushless DC Motor

NS

NS

NN

S

NS

C

C

CC

A

A

A

A

B

B

B

B

N N

S

S

N

N

S S

NS

NS

NS

NS

NNS

S

NN

S

S

N

S

N

S

N

N

S

S

NS

S

N

NN

S

S

N

N

S

S

S

N

S

N

S

N

S

N

NS

SN

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

NS

NS

NS

SN

Sensorless BLDC Control

Con

trol

ler

Source Eastern Air Devices Inc Brushless DC Motor Brochure

Conditioning

Back EMF in a Single Loop of Wire

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

N

S

Uniform airgap flux density

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Uniformwindingdensity

Back EMF in a Multi-turn Winding

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

Control of a Brushless DC Motor

12 zones in 360 degreesof mechanical rotation

1

2

3

4

5

6

BA

C

s

rtC

ontr

olle

r

110

Source Eastern Air Devices Inc Brushless DC Motor Brochure

120 0 hall spacing is preferred over 60 0

spacing since unpowered or

unconnected sensors produce 111 or 000

codes which can be used for fault

detection

BLDC CommutationQ1

Fault input signal

Q3

Q4

Q5

Q6

Q2

Hall C

Hall B

Hall A

Commutation of a Brushless DC Motor

NS

NS

NN

S

NS

C

C

CC

A

A

A

A

B

B

B

B

N N

S

S

N

N

S S

NS

NS

NS

NS

NNS

S

NN

S

S

N

S

N

S

N

N

S

S

NS

S

N

NN

S

S

N

N

S

S

S

N

S

N

S

N

S

N

NS

SN

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

NS

NS

NS

SN

Sensorless BLDC Control

Con

trol

ler

Source Eastern Air Devices Inc Brushless DC Motor Brochure

Conditioning

Back EMF in a Single Loop of Wire

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

N

S

Uniform airgap flux density

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Uniformwindingdensity

Back EMF in a Multi-turn Winding

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

BLDC CommutationQ1

Fault input signal

Q3

Q4

Q5

Q6

Q2

Hall C

Hall B

Hall A

Commutation of a Brushless DC Motor

NS

NS

NN

S

NS

C

C

CC

A

A

A

A

B

B

B

B

N N

S

S

N

N

S S

NS

NS

NS

NS

NNS

S

NN

S

S

N

S

N

S

N

N

S

S

NS

S

N

NN

S

S

N

N

S

S

S

N

S

N

S

N

S

N

NS

SN

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

NS

NS

NS

SN

Sensorless BLDC Control

Con

trol

ler

Source Eastern Air Devices Inc Brushless DC Motor Brochure

Conditioning

Back EMF in a Single Loop of Wire

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

N

S

Uniform airgap flux density

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Uniformwindingdensity

Back EMF in a Multi-turn Winding

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

Commutation of a Brushless DC Motor

NS

NS

NN

S

NS

C

C

CC

A

A

A

A

B

B

B

B

N N

S

S

N

N

S S

NS

NS

NS

NS

NNS

S

NN

S

S

N

S

N

S

N

N

S

S

NS

S

N

NN

S

S

N

N

S

S

S

N

S

N

S

N

S

N

NS

SN

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

C

C

CC

A

A

A

A

B

B

B

B

NS

NS

NS

SN

Sensorless BLDC Control

Con

trol

ler

Source Eastern Air Devices Inc Brushless DC Motor Brochure

Conditioning

Back EMF in a Single Loop of Wire

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

N

S

Uniform airgap flux density

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Uniformwindingdensity

Back EMF in a Multi-turn Winding

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

Sensorless BLDC Control

Con

trol

ler

Source Eastern Air Devices Inc Brushless DC Motor Brochure

Conditioning

Back EMF in a Single Loop of Wire

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

N

S

Uniform airgap flux density

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Uniformwindingdensity

Back EMF in a Multi-turn Winding

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

Back EMF in a Single Loop of Wire

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

N

S

Uniform airgap flux density

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Uniformwindingdensity

Back EMF in a Multi-turn Winding

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Uniformwindingdensity

Back EMF in a Multi-turn Winding

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

PWM 1

PWM 3

PWM 5

PWM 2

PWM 4

PWM 6

Phase R

Phase S

Phase T

0 60 120 180 240 300 360Rotor Electrical Position (Degrees)

Sensorless Commutation

Zero crossings

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

bull In a sensorless BLDC system only two coils are ldquoonrdquo at any moment in time The equivalent circuit of the motor with only two phases ldquoonrdquo is shown below

bull After the inductive flyback associated with Za has extinguished The internal voltages are visible when measuring Va Assuming balanced windings where Zband Zc are equal and Eb and Ec are equal then the voltage at node N = Vdc_link2 Therefore the zero-crossing of Ea occurs when the Va reading is Vdc_link2

Sensorless Control of BLDC Motors

EaEb

Ec

Vdc

_lin

kZb

Zc

Za

Va

I

N

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

96 BLDC Motor Efficiency

Using iron based amorphous core material Japanese researchers at Tokai University break 96 efficiency barrier

asymp 100W

High power output per frame sizeEasy to control with trapezoidal commutationHigh efficiency due to small rotor lossesLow profile designs possibleExcellent high speed performanceStructure inherently allows heat to be removed easier

Slightly more torque ripple than sinusoidal motorsField weakening requires additional currentPermanent magnetic field causes viscous dragPermanent magnets can be demagnetized at high temp

Advantages

Disadvantages

Brushless DC Motor Summary

Brushless DC with Hall Feedback

Stellaris LM3S8971

Torque Ripple from Commutation

0 30 60 90 120 150 180 210 240 270 300 330 360 390

id0

iA

0 30 60 90 120 150 180 210 240 270 300 330 360 390

Torgue

Permanent Magnet AC Motor

bull This motor exhibits a smoothly rotating magnetic field where the magnetic gradient of the stator flux is illustrated by the color shading There is no commutation to cause motor jerking But how do you create such a smoothly rotating magnetic field

Animation by Ken Berringer

Sinusoidal Winding Distribution

Stator winding density is sinusoidally distributedthus creating a sinusoidally distributed flux density

Phase A shown

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Source Mahmoud Riaz ScD Professor of Electrical Engineering Department of Electrical and Computer Engineering University of Minnesota

Flux Resulting from Sinusoidal Current

Pretty cool but no

rotating vector

Adding More PhasesPhase A Phase B Phase C

A

B

C

PMSM Motors Summary

High power output per frame sizeHigh efficiency due to small rotor lossesLow profile designs possibleVery low torque rippleStructure inherently allows heat to be removed easier Zero speed sensorless operation possible with IPM motors

More elaborate control required compared to BLDCHigh rotor angle accuracy required vs BLDC trapezoidalField weakening requires additional currentPermanent magnetic field causes viscous dragPermanent magnets can be demagnetized at high temp (not as much of a problem with IPM motors)

Advantages

Disadvantages

PMSM Load Angle

Animation by Ken Berringer

00s 03s 06s 09s 12s 15s 18s 21s 24s 27s 30s 33s 36s-200V

-150V

-100V

-50V

0V

50V

100V

150V

200VV(treaction)

Simulated Reactance Torque as a function of angle delta

from 2005 Prius Traction Motor

0o 30o 60o 90o 120o 150o 180o-30o-60o-90o-120o-150o-180o

50

100

150

200

0

-50

-100

-150

-200

New

ton-

Met

ers

Maximum torque per amp

Orientation of Field for Max Torque

Source Electric Drives an Integrative Approach by Ned Mohan University of Minn Printing Services 2000

(Reluctance torque assumed to be zero)

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

S

N

+24 V

0015

PWM1

PWM1PWM2

PWM2PWM1

PWM2

PIController

-

+

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor1

Compare the measured current with the desired current and generate an error signal2

Amplify the error signal to generate a correction voltage3

Modulate the correction voltage onto the motor terminals4

Commutator keeps rotor and stator fields

properly aligned

Brush DC Motor

How Do You Control Torqueon a DC Motor

Texas Instruments

DaversquosMotor Control

Center

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Brushless DC with Hall Feedback

Stellaris LM3S8971

Torque Ripple from Commutation

0 30 60 90 120 150 180 210 240 270 300 330 360 390

id0

iA

0 30 60 90 120 150 180 210 240 270 300 330 360 390

Torgue

Permanent Magnet AC Motor

bull This motor exhibits a smoothly rotating magnetic field where the magnetic gradient of the stator flux is illustrated by the color shading There is no commutation to cause motor jerking But how do you create such a smoothly rotating magnetic field

Animation by Ken Berringer

Sinusoidal Winding Distribution

Stator winding density is sinusoidally distributedthus creating a sinusoidally distributed flux density

Phase A shown

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Source Mahmoud Riaz ScD Professor of Electrical Engineering Department of Electrical and Computer Engineering University of Minnesota

Flux Resulting from Sinusoidal Current

Pretty cool but no

rotating vector

Adding More PhasesPhase A Phase B Phase C

A

B

C

PMSM Motors Summary

High power output per frame sizeHigh efficiency due to small rotor lossesLow profile designs possibleVery low torque rippleStructure inherently allows heat to be removed easier Zero speed sensorless operation possible with IPM motors

More elaborate control required compared to BLDCHigh rotor angle accuracy required vs BLDC trapezoidalField weakening requires additional currentPermanent magnetic field causes viscous dragPermanent magnets can be demagnetized at high temp (not as much of a problem with IPM motors)

Advantages

Disadvantages

PMSM Load Angle

Animation by Ken Berringer

00s 03s 06s 09s 12s 15s 18s 21s 24s 27s 30s 33s 36s-200V

-150V

-100V

-50V

0V

50V

100V

150V

200VV(treaction)

Simulated Reactance Torque as a function of angle delta

from 2005 Prius Traction Motor

0o 30o 60o 90o 120o 150o 180o-30o-60o-90o-120o-150o-180o

50

100

150

200

0

-50

-100

-150

-200

New

ton-

Met

ers

Maximum torque per amp

Orientation of Field for Max Torque

Source Electric Drives an Integrative Approach by Ned Mohan University of Minn Printing Services 2000

(Reluctance torque assumed to be zero)

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

S

N

+24 V

0015

PWM1

PWM1PWM2

PWM2PWM1

PWM2

PIController

-

+

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor1

Compare the measured current with the desired current and generate an error signal2

Amplify the error signal to generate a correction voltage3

Modulate the correction voltage onto the motor terminals4

Commutator keeps rotor and stator fields

properly aligned

Brush DC Motor

How Do You Control Torqueon a DC Motor

Texas Instruments

DaversquosMotor Control

Center

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Torque Ripple from Commutation

0 30 60 90 120 150 180 210 240 270 300 330 360 390

id0

iA

0 30 60 90 120 150 180 210 240 270 300 330 360 390

Torgue

Permanent Magnet AC Motor

bull This motor exhibits a smoothly rotating magnetic field where the magnetic gradient of the stator flux is illustrated by the color shading There is no commutation to cause motor jerking But how do you create such a smoothly rotating magnetic field

Animation by Ken Berringer

Sinusoidal Winding Distribution

Stator winding density is sinusoidally distributedthus creating a sinusoidally distributed flux density

Phase A shown

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Source Mahmoud Riaz ScD Professor of Electrical Engineering Department of Electrical and Computer Engineering University of Minnesota

Flux Resulting from Sinusoidal Current

Pretty cool but no

rotating vector

Adding More PhasesPhase A Phase B Phase C

A

B

C

PMSM Motors Summary

High power output per frame sizeHigh efficiency due to small rotor lossesLow profile designs possibleVery low torque rippleStructure inherently allows heat to be removed easier Zero speed sensorless operation possible with IPM motors

More elaborate control required compared to BLDCHigh rotor angle accuracy required vs BLDC trapezoidalField weakening requires additional currentPermanent magnetic field causes viscous dragPermanent magnets can be demagnetized at high temp (not as much of a problem with IPM motors)

Advantages

Disadvantages

PMSM Load Angle

Animation by Ken Berringer

00s 03s 06s 09s 12s 15s 18s 21s 24s 27s 30s 33s 36s-200V

-150V

-100V

-50V

0V

50V

100V

150V

200VV(treaction)

Simulated Reactance Torque as a function of angle delta

from 2005 Prius Traction Motor

0o 30o 60o 90o 120o 150o 180o-30o-60o-90o-120o-150o-180o

50

100

150

200

0

-50

-100

-150

-200

New

ton-

Met

ers

Maximum torque per amp

Orientation of Field for Max Torque

Source Electric Drives an Integrative Approach by Ned Mohan University of Minn Printing Services 2000

(Reluctance torque assumed to be zero)

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

S

N

+24 V

0015

PWM1

PWM1PWM2

PWM2PWM1

PWM2

PIController

-

+

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor1

Compare the measured current with the desired current and generate an error signal2

Amplify the error signal to generate a correction voltage3

Modulate the correction voltage onto the motor terminals4

Commutator keeps rotor and stator fields

properly aligned

Brush DC Motor

How Do You Control Torqueon a DC Motor

Texas Instruments

DaversquosMotor Control

Center

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Permanent Magnet AC Motor

bull This motor exhibits a smoothly rotating magnetic field where the magnetic gradient of the stator flux is illustrated by the color shading There is no commutation to cause motor jerking But how do you create such a smoothly rotating magnetic field

Animation by Ken Berringer

Sinusoidal Winding Distribution

Stator winding density is sinusoidally distributedthus creating a sinusoidally distributed flux density

Phase A shown

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Source Mahmoud Riaz ScD Professor of Electrical Engineering Department of Electrical and Computer Engineering University of Minnesota

Flux Resulting from Sinusoidal Current

Pretty cool but no

rotating vector

Adding More PhasesPhase A Phase B Phase C

A

B

C

PMSM Motors Summary

High power output per frame sizeHigh efficiency due to small rotor lossesLow profile designs possibleVery low torque rippleStructure inherently allows heat to be removed easier Zero speed sensorless operation possible with IPM motors

More elaborate control required compared to BLDCHigh rotor angle accuracy required vs BLDC trapezoidalField weakening requires additional currentPermanent magnetic field causes viscous dragPermanent magnets can be demagnetized at high temp (not as much of a problem with IPM motors)

Advantages

Disadvantages

PMSM Load Angle

Animation by Ken Berringer

00s 03s 06s 09s 12s 15s 18s 21s 24s 27s 30s 33s 36s-200V

-150V

-100V

-50V

0V

50V

100V

150V

200VV(treaction)

Simulated Reactance Torque as a function of angle delta

from 2005 Prius Traction Motor

0o 30o 60o 90o 120o 150o 180o-30o-60o-90o-120o-150o-180o

50

100

150

200

0

-50

-100

-150

-200

New

ton-

Met

ers

Maximum torque per amp

Orientation of Field for Max Torque

Source Electric Drives an Integrative Approach by Ned Mohan University of Minn Printing Services 2000

(Reluctance torque assumed to be zero)

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

S

N

+24 V

0015

PWM1

PWM1PWM2

PWM2PWM1

PWM2

PIController

-

+

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor1

Compare the measured current with the desired current and generate an error signal2

Amplify the error signal to generate a correction voltage3

Modulate the correction voltage onto the motor terminals4

Commutator keeps rotor and stator fields

properly aligned

Brush DC Motor

How Do You Control Torqueon a DC Motor

Texas Instruments

DaversquosMotor Control

Center

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Sinusoidal Winding Distribution

Stator winding density is sinusoidally distributedthus creating a sinusoidally distributed flux density

Phase A shown

Source Electric Drives an Integrative Approachby Ned Mohan University of Minn Printing Services 2000

Source Mahmoud Riaz ScD Professor of Electrical Engineering Department of Electrical and Computer Engineering University of Minnesota

Flux Resulting from Sinusoidal Current

Pretty cool but no

rotating vector

Adding More PhasesPhase A Phase B Phase C

A

B

C

PMSM Motors Summary

High power output per frame sizeHigh efficiency due to small rotor lossesLow profile designs possibleVery low torque rippleStructure inherently allows heat to be removed easier Zero speed sensorless operation possible with IPM motors

More elaborate control required compared to BLDCHigh rotor angle accuracy required vs BLDC trapezoidalField weakening requires additional currentPermanent magnetic field causes viscous dragPermanent magnets can be demagnetized at high temp (not as much of a problem with IPM motors)

Advantages

Disadvantages

PMSM Load Angle

Animation by Ken Berringer

00s 03s 06s 09s 12s 15s 18s 21s 24s 27s 30s 33s 36s-200V

-150V

-100V

-50V

0V

50V

100V

150V

200VV(treaction)

Simulated Reactance Torque as a function of angle delta

from 2005 Prius Traction Motor

0o 30o 60o 90o 120o 150o 180o-30o-60o-90o-120o-150o-180o

50

100

150

200

0

-50

-100

-150

-200

New

ton-

Met

ers

Maximum torque per amp

Orientation of Field for Max Torque

Source Electric Drives an Integrative Approach by Ned Mohan University of Minn Printing Services 2000

(Reluctance torque assumed to be zero)

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

S

N

+24 V

0015

PWM1

PWM1PWM2

PWM2PWM1

PWM2

PIController

-

+

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor1

Compare the measured current with the desired current and generate an error signal2

Amplify the error signal to generate a correction voltage3

Modulate the correction voltage onto the motor terminals4

Commutator keeps rotor and stator fields

properly aligned

Brush DC Motor

How Do You Control Torqueon a DC Motor

Texas Instruments

DaversquosMotor Control

Center

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Source Mahmoud Riaz ScD Professor of Electrical Engineering Department of Electrical and Computer Engineering University of Minnesota

Flux Resulting from Sinusoidal Current

Pretty cool but no

rotating vector

Adding More PhasesPhase A Phase B Phase C

A

B

C

PMSM Motors Summary

High power output per frame sizeHigh efficiency due to small rotor lossesLow profile designs possibleVery low torque rippleStructure inherently allows heat to be removed easier Zero speed sensorless operation possible with IPM motors

More elaborate control required compared to BLDCHigh rotor angle accuracy required vs BLDC trapezoidalField weakening requires additional currentPermanent magnetic field causes viscous dragPermanent magnets can be demagnetized at high temp (not as much of a problem with IPM motors)

Advantages

Disadvantages

PMSM Load Angle

Animation by Ken Berringer

00s 03s 06s 09s 12s 15s 18s 21s 24s 27s 30s 33s 36s-200V

-150V

-100V

-50V

0V

50V

100V

150V

200VV(treaction)

Simulated Reactance Torque as a function of angle delta

from 2005 Prius Traction Motor

0o 30o 60o 90o 120o 150o 180o-30o-60o-90o-120o-150o-180o

50

100

150

200

0

-50

-100

-150

-200

New

ton-

Met

ers

Maximum torque per amp

Orientation of Field for Max Torque

Source Electric Drives an Integrative Approach by Ned Mohan University of Minn Printing Services 2000

(Reluctance torque assumed to be zero)

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

S

N

+24 V

0015

PWM1

PWM1PWM2

PWM2PWM1

PWM2

PIController

-

+

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor1

Compare the measured current with the desired current and generate an error signal2

Amplify the error signal to generate a correction voltage3

Modulate the correction voltage onto the motor terminals4

Commutator keeps rotor and stator fields

properly aligned

Brush DC Motor

How Do You Control Torqueon a DC Motor

Texas Instruments

DaversquosMotor Control

Center

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Adding More PhasesPhase A Phase B Phase C

A

B

C

PMSM Motors Summary

High power output per frame sizeHigh efficiency due to small rotor lossesLow profile designs possibleVery low torque rippleStructure inherently allows heat to be removed easier Zero speed sensorless operation possible with IPM motors

More elaborate control required compared to BLDCHigh rotor angle accuracy required vs BLDC trapezoidalField weakening requires additional currentPermanent magnetic field causes viscous dragPermanent magnets can be demagnetized at high temp (not as much of a problem with IPM motors)

Advantages

Disadvantages

PMSM Load Angle

Animation by Ken Berringer

00s 03s 06s 09s 12s 15s 18s 21s 24s 27s 30s 33s 36s-200V

-150V

-100V

-50V

0V

50V

100V

150V

200VV(treaction)

Simulated Reactance Torque as a function of angle delta

from 2005 Prius Traction Motor

0o 30o 60o 90o 120o 150o 180o-30o-60o-90o-120o-150o-180o

50

100

150

200

0

-50

-100

-150

-200

New

ton-

Met

ers

Maximum torque per amp

Orientation of Field for Max Torque

Source Electric Drives an Integrative Approach by Ned Mohan University of Minn Printing Services 2000

(Reluctance torque assumed to be zero)

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

S

N

+24 V

0015

PWM1

PWM1PWM2

PWM2PWM1

PWM2

PIController

-

+

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor1

Compare the measured current with the desired current and generate an error signal2

Amplify the error signal to generate a correction voltage3

Modulate the correction voltage onto the motor terminals4

Commutator keeps rotor and stator fields

properly aligned

Brush DC Motor

How Do You Control Torqueon a DC Motor

Texas Instruments

DaversquosMotor Control

Center

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

PMSM Motors Summary

High power output per frame sizeHigh efficiency due to small rotor lossesLow profile designs possibleVery low torque rippleStructure inherently allows heat to be removed easier Zero speed sensorless operation possible with IPM motors

More elaborate control required compared to BLDCHigh rotor angle accuracy required vs BLDC trapezoidalField weakening requires additional currentPermanent magnetic field causes viscous dragPermanent magnets can be demagnetized at high temp (not as much of a problem with IPM motors)

Advantages

Disadvantages

PMSM Load Angle

Animation by Ken Berringer

00s 03s 06s 09s 12s 15s 18s 21s 24s 27s 30s 33s 36s-200V

-150V

-100V

-50V

0V

50V

100V

150V

200VV(treaction)

Simulated Reactance Torque as a function of angle delta

from 2005 Prius Traction Motor

0o 30o 60o 90o 120o 150o 180o-30o-60o-90o-120o-150o-180o

50

100

150

200

0

-50

-100

-150

-200

New

ton-

Met

ers

Maximum torque per amp

Orientation of Field for Max Torque

Source Electric Drives an Integrative Approach by Ned Mohan University of Minn Printing Services 2000

(Reluctance torque assumed to be zero)

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

S

N

+24 V

0015

PWM1

PWM1PWM2

PWM2PWM1

PWM2

PIController

-

+

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor1

Compare the measured current with the desired current and generate an error signal2

Amplify the error signal to generate a correction voltage3

Modulate the correction voltage onto the motor terminals4

Commutator keeps rotor and stator fields

properly aligned

Brush DC Motor

How Do You Control Torqueon a DC Motor

Texas Instruments

DaversquosMotor Control

Center

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

PMSM Load Angle

Animation by Ken Berringer

00s 03s 06s 09s 12s 15s 18s 21s 24s 27s 30s 33s 36s-200V

-150V

-100V

-50V

0V

50V

100V

150V

200VV(treaction)

Simulated Reactance Torque as a function of angle delta

from 2005 Prius Traction Motor

0o 30o 60o 90o 120o 150o 180o-30o-60o-90o-120o-150o-180o

50

100

150

200

0

-50

-100

-150

-200

New

ton-

Met

ers

Maximum torque per amp

Orientation of Field for Max Torque

Source Electric Drives an Integrative Approach by Ned Mohan University of Minn Printing Services 2000

(Reluctance torque assumed to be zero)

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

S

N

+24 V

0015

PWM1

PWM1PWM2

PWM2PWM1

PWM2

PIController

-

+

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor1

Compare the measured current with the desired current and generate an error signal2

Amplify the error signal to generate a correction voltage3

Modulate the correction voltage onto the motor terminals4

Commutator keeps rotor and stator fields

properly aligned

Brush DC Motor

How Do You Control Torqueon a DC Motor

Texas Instruments

DaversquosMotor Control

Center

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Orientation of Field for Max Torque

Source Electric Drives an Integrative Approach by Ned Mohan University of Minn Printing Services 2000

(Reluctance torque assumed to be zero)

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

S

N

+24 V

0015

PWM1

PWM1PWM2

PWM2PWM1

PWM2

PIController

-

+

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor1

Compare the measured current with the desired current and generate an error signal2

Amplify the error signal to generate a correction voltage3

Modulate the correction voltage onto the motor terminals4

Commutator keeps rotor and stator fields

properly aligned

Brush DC Motor

How Do You Control Torqueon a DC Motor

Texas Instruments

DaversquosMotor Control

Center

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

+24 V

0015

PWM1

PWM1PWM2

PWM2PWM1

PWM2

PIController

-

+

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor1

Compare the measured current with the desired current and generate an error signal2

Amplify the error signal to generate a correction voltage3

Modulate the correction voltage onto the motor terminals4

Commutator keeps rotor and stator fields

properly aligned

Brush DC Motor

How Do You Control Torqueon a DC Motor

Texas Instruments

DaversquosMotor Control

Center

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

[ ]qsdr IPTorque λ22

3=

Constant (for now)

How Do You Control Torque on a PMSM

Constant

Adjustable

S

N

S

N

S

N

InterruptMeasure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

InterruptMeasure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

A

B

C

AB

C

i b

i c

i a

(implied)

Controllerwith AD

i ai bi c

Measure and From Kirkoffrsquos current law calculate

i a i b i c

A B and C axes are ldquofixedrdquo with respect to the motor housing This reference frame is also called the

ldquostationary framerdquo or ldquostator framerdquo

1 Measure current already flowing in the motor

net current vector

ia

ib

ic

Texas Instruments

DaversquosMotor Control

Center

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

A

B

C

si

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

We must regulate the current vector magnitude AND angle by regulating ia ib and ic

Rotor flux axis

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

N

S

θd

Part A Measure the rotor angle to determine if the net current vector is oriented at 90o with respect to

the rotor flux

This is called the ldquodirectrdquo or ldquodrdquo axis

Usually accomplished with a resolver or encoder

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

αi

βiPart B Convert the three phase

current vectors into two orthogonal vectors that will result in the same net current vector In other words convert the 3-phase motor to a 2-phase motor Then we only have two current values

to regulate instead of three

This is often referred to as the FORWARD CLARK TRANSFORMATION

A

B

C

si

aii 23=α

cb iii 23

23 minus=βia(t) ib(t) ic(t) iβ(t)iα(t)

i b

i c

i a

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

αi

βi

A

B

C

si

ddq

ddd

iii

iii

θθ

θθ

βα

βα

cossin

sincos

+minus=

+=

4 trig calulations7 multiplications3 additions

Total

θdd axis

q axis

rotor flux axis

i q

i d

Part C Jump up on the rotating reference frame

whose x-axis is the rotor flux axis

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Part D and are handled independently Since the comparison is performed in the rotating frame motor AC frequency

is not seen Thus they are DC quantities

i d +

-

error(t)

+

-

error(t)

i q

i q (commanded)

(measured)

can however be used to weaken the field of the machinecontrols amount of torque generated by the motor

i di q

i d i q

(commanded)

i d (measured)

Under normal conditions we have all the d-axis flux we need supplied by the permanent magnets in the rotor

So commanded id is set to zero

This is how much torque we want

2 Compare the measured current (vector) with the desired current (vector) and generate error signals

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

i d

int I

P+ +

+-

error(t)

int I

P+ +

+-

error(t)

(commanded)

i d (measured)

i q

i q (commanded)

(measured)

vd

vq

3 Amplify the error signals to generate correction voltages

The PI regulator is a good choice for current regulation

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Voltage vector

αv

βv

Part A Transfer the voltage vectors back on to the stationary rectangular coordinate system

dqdd

dqdd

vvv

vvv

θθ

θθ

β

α

cossin

sincos

+=

minus=

d axis

q axis

θd

A

B

C

vd

vq

rotor flux axis

4 Modulate the correction voltages onto the motor terminals

We now need to ldquojump offrdquoof the rotating reference

frame

vd (t)

vq(t)

vα (t) vβ (t)

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

αv

βv

A

B

C

v a

v c

v b

βα

βα

α

vvv

vvvvv

c

b

a

31

31

31

31

32

minusminus=

+minus=

=

Part B Next we transform the voltage vectors from the

rectangular coordinate system to three phase vectors

va(t) vb(t) vc(t)vα (t) vβ (t)

Reverse Clark Transformation

4 Modulate the correction voltages onto the motor terminals

Voltage Vector

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom

4 Modulate the correction voltages onto the motor terminals

Over time under steady-state conditions the correction voltagesva vb and vc will be sine waves phase shifted by 120o

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

AC InAC to DCConverter

ThreePhase

Inverter

GateDrivers

DC Bus

GateDriver

PowerSupplies

AnalogConditioning

SerialInterfaceF2803x

12 BitADC

Trig

ger Fa

ult

ePWMModule

Sync

Isolation

eQEPModule

CommandedSpeed

Actual Speed

+-

PIController

FieldOriented

ControllerCommanded iq

Commanded id

PhaseCurrent

Reconstructionicia

SpaceVector

Modulation

Vα

Vβ

ibusBus

Over-Voltage

GPIO or PWM

SpeedCalculation

ibVbus

Mot

or P

WM

s

Ove

rcur

rent

Bus

Cur

rent

Bus

Vol

tage

Processor Ground

θ(t)

θ(t)

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

θθ

Torque

TransmissionController

CAN

Vehi

cle

Spee

d

PowerInverter

PWMs

CurrentFeedback

Motor θ feedback

Encoder IF

torque assist

To steering rack

Essentiallya torque amplifier

PMSM

3

Texas Instruments

DaversquosMotor Control

Center

FOC in Electric Power Steering

resolver

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

( ) ( ) ( ) ( ) ( )

( ) ( )⎟⎠⎞

⎜⎝⎛ minus+minusΔ=Δ

⎟⎠⎞

⎜⎝⎛ minus+Δ+=+

and

andandandand

nynynyny

nynynynyny

β

α

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

( )1+and

ny

( )nyand

( )ny

( )nyand

Δ

y correctionΔy correction ( )nerror

Integrator Integrator

+

^ ^

Tracking Filters

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

αminus1

2minusαminusβ

α+β

minusα

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below

The Tracking FilterhellipUnmasked

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Σ

Σ Σ Σ

Z-1 Z-1

αβ

+

-

++

+ ++

Integrator Integrator

+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the state variables of the system

State Variable Representation

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Observers literally recreate the desired signal mathematically (great noise decoupling)The ldquoguessrdquo is corrected by comparison with an observable signal

Observers are used to ldquoobserverdquo a quantity which is difficult to measureby mathematically modeling the system

Model of H(z)

Integrator Integrator

αβ

Source Motion Controller Employs DSP TechnologyRobert van der Kruk and John Scannell

Phillips Centre for Manufacturing TechnologyPCIM ndash September 1988

By providing an additional feedforward input the tracking filter can make better output estimates It then takes the form of an OBSERVER

Can be designed to have zero (or near

zero) estimation lag

Parameter Estimation with Observers

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed) V(encoder_speed)

V(counts)

0ms 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms-15V

-12V

-9V

-6V

-3V

0V

3V

6V

9V

12V

15V

18V-20V

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V00KV

02KV

04KV

06KV

08KV

10KV

12KV

14KV

16KV

18KV

20KV

22KV

V(i_sampled)

V(speed^)

V(counts)

Servo Performance with Velocity Directly from Encoder vs Observer

Position

Velocity

Current

Velocity from EncoderVelocity from Observer

Velocity from EncoderVelocity from Observer

Actual Velocity

Velocity from EncoderVelocity from Observer

One revolution = 2000 encoder counts

06 NM Load Torque Disturbance

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

sR lsL mL

synEk ω

stator voltage

sL

( )( ) ⎥⎦

⎤⎢⎣

⎡minussdot+⎥

⎦

⎤⎢⎣

⎡sdot+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esynEss k

ii

pLii

Rvv

θθ

ωβ

α

β

α

β

α

cossin

Assuming no saliency stationary frame equations are

Rotor with surface-mount magnetsNon-salient design (magnetically round))

Back EMF component

Sensorless Sinusoidal PMSM Control

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

+

-

Vin

emf

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer

Stationary Frame Back EMF Observer

sRVin

sL i

emf

+

-

Vin

emf

1Rs

LowPassFilter

i

emf

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛minus⎟⎟⎠

⎞⎜⎜⎝⎛ minus=

minusτt

s

in eRtemftVti 1

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Back-EMF Observer Performance

0ms 5ms 10ms 15ms 20ms 25ms-120V

-100V

-80V

-60V

-40V

-20V

0V

20V

40V

60V

80V

100V

120VV(bemf) V(voltage_input)

0 25ms

sR sL i

emf

0416Ω

Observer simulationObserver sampling frequency = 10 KHz

-120 V

120 V

120 VAC60 Hz

1365 mH

One of three phases of Baldor PMSM motor

Back-EMFEstimated Back-EMF

+

-

Vin

LowPassFilter

+

-

i

i1

Rs^

PI -1

Back EMF Observer EMF estimate

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

-1Σ

PMSM Motor(2-phase representation)

αv

βv

ss RsL +1

+-

+

-

Σss RsL +

1+

-+

-

P I

Back EMF α

Back EMF β

( )θsinKminus

( )θcosK

Σs1

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

Σ

Σ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

minus=ss sLR

emfvi 1)( βαβαβα

αi βi

0

0

Stationary Frame State Observer for a Non-Salient Machine

-1P I

Texas Instruments

DaversquosMotor Control

Center

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Dual Motor Control with One Piccolo

AC Input

ACDC conversion (with PFC)

3 PhaseMotor Driver

3 PhaseMotor Driver

System Communication

F2802x

Dual Sensorless FOC with Sliding Mode ObserversDual Sensorless FOC with Sliding Mode Observers

Digital PFC implemented in the CLADigital PFC implemented in the CLA

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Axis of rotor flux is fixed with respect to the rotor ie it is ldquosynchronousrdquo

Source Electric Machinery by A E Fitzgerald Charles Kingsley Jr and Stephen D Umans McGraw-Hill 1990

( )[ ]qsdsqsdsqsdr IILLIPTorque minus+= λ22

3

Reaction TorqueReluctance Torque

Permanent Magnet Rotor

N

S

hellipbut what about SALIENT Machines

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Effect of Saliency on Optimum Torque Angle

New angle for optimum torque

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

( )( ) ( )( ) ( )

( ) ⎥⎦⎤

⎢⎣

⎡minussdot+primeminusminus+⎥

⎦

⎤⎢⎣

⎡sdot⎥⎦

⎤⎢⎣

⎡sdotminusminus

sdotminus+⎥

⎦

⎤⎢⎣

⎡sdot=⎥

⎦

⎤⎢⎣

⎡

e

esyneqdsynqd

dsynqd

synqdds kiiLL

ii

pLLLLLpL

ii

Rvv

θθ

ωωω

ω

β

α

β

α

β

α

cossin

sR dL

)sin( eK θminus ExtendedEMF α

voltagedtdcauses

dtdwithcombinedwhenwhich

ddcauses

ddL

=λθ

θλ

θ

Rotor with buried interior magnets(salient design)

+-

αvαi ( ) βω iLL synqd sdotminus

sR dL

)cos( eK θ ExtendedEMF α

+-

βvβi ( ) αω iLL synqd sdotminus

Salient PMAC Machine

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

-1

-1

Σs1

P I Σ

2-phase PMAC Motor

αv

βv

+-

+

( ) ωβiLL qd minus

P I Σ+

-

+

-

+

Back EMF α

Back EMF β

X

-

+

s1K 1Σ

X

K 2

L P F

( )nand

θ

( )nand

ω

cos

sin

ss RsL +1

ss RsL +1

Σ

αi βi

Σ-

( ) ωαiLL qd minus

-

Stationary Frame State Observer for a Salient Machine

( )θsinKminus

( )θcosK

Texas Instruments

DaversquosMotor Control

Center

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Perf

orm

ance

Broad C2000 32-bit MCU Portfolio for All Application Needs

Next Gen

F281xbull 150 MIPSbull 128-256 KB Flashbull 16 PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 128-QFP 176-QFP

179-BGA F280xbull 60-100 MIPSbull 32-256 KB Flashbull 16 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 100-QFP 100-BGA

F2823xbull 150 MIPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179- BGA

F2833xbull 150 MIPS300MFLOPSbull 196-512 KB Flashbull 18 PWMs 6 HR PWMsbull 16-ch 12-bit ADCbull CAP QEPbull 176-QFP 176-179-BGA

Delfino (Floating Point) Series

F2803xbull 60 MIPS + CLAbull 64-128 KB Flashbull 14 PWMs 7 HR PWMsbull 16-ch 12-bit ADCbull CAP QEP COMP OSCbull Single 33V Supplybull 64-QFP 80-QFP

F2802xbull 40-60 MIPSbull 16-64 KB Flash bull 8 PWMs 4 HR PWMsbull 13-ch 12-bit ADCbull CAP COMP OSCbull Single 33V Supplybull 38-TSSOP 48-QFP

PiccoloTM Series

Next Gen

Code compatible solutions scaling from 40MHz to 300MHz

C2834xbull 300 MIPS600 MFLOPSbull 196-516 KB SRAMbull 18 PWMs 6 HR PWMsbull CAP QEPbull 256-BGA 179-BGA

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

F2802x (Piccolo) Series

Key New Featuresbull 4060 MHz bull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 2 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 38-pin TSSOP or 48-pin TQFP

F2802x (Piccolo) Series

12 bit5 MSPS

Dual SHAuto Seq

ADC

A0VREFHIA1A2A3A4

A6A7

B1B2B3B4

B6B7

AnalogComparators

CMP1-Out

DAC10 bit

CMP2-Out

VSSAFlash

16-64 KB

C28 Core32 bit ndash 4060MHz PWM1 AB

CommsSCI

SPI

I2C

PWM2 AB

PWM3 AB

PWM4 AB

TripZonelogic

PWM-1APWM-1B

Int-Osc-1

VregPWR

GND

POR BOR

2

Int-Osc-2

6

DAC10 bit

Ext-Osc-2

3

CAP

Timer-0

Timers - 32bit

Timer-1Timer-2

GPIO Control

2

4

2

X1X2

PLL

WD

PWM-2APWM-2BPWM-3APWM-3BPWM-4APWM-4B

TZ1TZ2TZ3CMP1-outCMP2-out

ECAP

Vref

RAM 4-12 KB

TempSensor

System

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

F2803x (Piccolo with CLA) Series

Key New Featuresbull 60 MHz CPUbull New acceleration unit (CLA)bull CLA has 32bit floating Pt precisionbull Single 33V supplybull 12-bit ratio-metric ADCbull Low latency ADC trigger amp seqbull 3 Analog comparators lt 30nSbull 10 bit DAC reference lt 2uS settlingbull 150ps PWM resolution Duty amp Freqbull Dual ldquozero-pinrdquo on-chip oscillatorsbull 64-pin or 80-pin TQFP

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

32-bit CLA 60MHz

Data0RAM

2KByte

ProgRAM

8KByte

Data1RAM

2KByteSecure

MsgRAM

256Byte

InterruptSleep

32-bit C28-CPU60MHz

DAC3 x

Comp3 xComp

DAC

3 x Comp

F2803x PiccoloTM Device With CLA

GPIO

Mux

SCIFLASH64128KByte

48 sectors

Per

Bus

3xDAC10-bit

M0M1RAM

4KByte

EPWM1 HRPWM

Per

Bus

SPI

I2CCAN

EPWM2 HRPWM

ECAP

EQEP

OTP 2KByte

Secure

BootROM

32b32b 32b

OSC110MHz

LIN (SCI)

OSC210MHz

PLLWDLPM

mux

EXTXTAL

GPIOMUXXCLKIN

EPWM3 HRPWM

EPWM4 HRPWM

GPIO0

GPIOx

Ax

X1X2

+

-

Interrupt

2 SPI

EPWM5 HRPWM

EPWM6

EPWM7

PORBOR XRSnVSS

VREGENZVDD (core voltage)VDDIO

Digital Power VREG

33V +-10

VDDAVSSA

Analog Power33V +-10

ADC12-bit2 SH

46MSPS

AIO

Mux

Per BusBx

L0RAM

4KByte

3 External InterruptsJTAG

HRPWM

HRPWM

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Piccolo controlSTICK

Power LED

Application LEDTMS320F28027

USB JTAGInterface and Power

On-board USBJTAG Emulation

PeripheralHeader Pins

(GPIO 34)

(48-Pin Package)

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Sensorless BLDCPMAC Field Oriented Control

Dual-axis Motor Control Kit

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

High Voltage Motor Control Kit

Sensorless BLDCPMAC Field Oriented ControlAC Induction

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

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Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Stellaris LM3S818

Scalar Control Only

AC Induction Motor Control

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

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C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

Project ManagerSource amp object filesFile dependenciesCompiler Assembler ampLinker build options

Full CC++ amp Assembly Debugging

C amp ASM SourceMixed modeDisassembly (patch)Set Break PointsSet Probe Points

EditorStructure Expansion

Help CPU Window

Memory WindowGraph Window

Status Window

Watch Window

Menus or Icons

Code Composer Studio

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

C2000 Signal Processing LibrariesSignal Processing Libraries amp Applications Software Literature ACI3-1 Control with Constant VHz SPRC194ACI3-3 Sensored Indirect Flux Vector Control SPRC207ACI3-3 Sensored Indirect Flux Vector Control (simulation) SPRC208ACI3-4 Sensorless Direct Flux Vector Control SPRC195ACI3-4 Sensorless Direct Flux Vector Control (simulation) SPRC209PMSM3-1 Sensored Field Oriented Control using QEP SPRC210PMSM3-2 Sensorless Field Oriented Control SPRC197PMSM3-3 Sensored Field Oriented Control using Resolver SPRC211PMSM3-4 Sensored Position Control using QEP SPRC212BLDC3-1 Sensored Trapezoidal Control using Hall Sensors SPRC213BLDC3-2 Sensorless Trapezoidal Drive SPRC196DCMOTOR Speed amp Position Control using QEP without Index SPRC214Digital Motor Control Library (FC280x) SPRC215Communications Driver Library SPRC183DSP Fast Fourier Transform (FFT) Library SPRC081DSP Filter Library SPRC082DSP Fixed-Point Math Library SPRC085DSP IQ Math Library SPRC087DSP Signal Generator Library SPRC083DSP Software Test Bench (STB) Library SPRC084C28x FPU Fast RTS Library SPRC664DSP2803x CC++ Header Files and Peripheral Examples SPRC892

Available from TI Website rArr httpwwwticomc2000

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom

C2000 Modeling amp Code Generation

bull Link for Code Composer Studiobull Real Time Workshop Embedded Coderbull Target for TI C2000

Compileamp Link

CASMCodeTexas Instruments

Code Composer Studiotrade

Environment

Download

Debug

TI C2000DSC

MathWorks Modeling Environment

MATLABreg Simulinkreg Stateflowreg

The Mathworks Support for C2000

VisSimEmbedded Controls Developer Model Based Development for TI C2000

wwwvissimcom