Closed-loop Control of DC Drives with Chopper By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr

Closed-loop Control of DC Drives with ChopperByDr. Ungku Anisa Ungku AmirulddinDepartment of Electrical Power EngineeringCollege of Engineering

Dr. Ungku Anisa, July 2008 1EEEB443 - Control & Drives

OutlineClosed Loop Control of DC Drives with ChoppersCurrent Control for DC Drives with Choppers

Pulse-Width-Modulation (PWM) ControllerHysteresis-Current ControllerComparison between PWM and Hysteresis Controller

Transfer Function of PWM-Controlled ChopperTwo-quadrantFour-quadrant

Design of ControllersReferences

Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 2

Closed Loop Control of DC DrivesClosed loop control is when the duty cycle is varied

automatically by a controller to achieve a reference speed or torque

This requires the use of sensors to feed back the actual motor speed and torque to be compared with the reference values


Controller Plant

Sensor

+

Referencesignal

Outputsignal

Closed Loop Control of DC DrivesFeedback loops may be provided to satisfy one or more

of the following:ProtectionEnhancement of speed responseImprove steady-state accuracy

Variables to be controlled in drives:Torque – achieved by controlling currentSpeedPosition


Closed Loop Control of DC DrivesCascade control structure

Flexible – outer loops can be added/removed depending on control requirements.

Control variable of inner loop (eg: speed, torque) can be limited by limiting its reference value


For DC Drive, this can be:•Controlled rectifier or•DC-DC converter

Closed Loop Control for DC Drives with ChoppersOuter speed loop very similar to that in the controlled

rectifier dc driveInner current control loop – different


Current Control LoopSpeed Control

Loop

Current Control for DC Drives with ChoppersCurrent control loop is used to control torque via

armature current (ia)Output of current controller determines duty cycle (i.e.

switching) of DC-DC converterCurrent controller can be either:

Pulse-Width-Modulation (PWM) Controller contain PI controllers, i.e. linear fixed switching frequency

Hysteresis (bang-bang) controller on-off controllers, i.e. non-linear varying switching frequency

Selection of controller affects current control loop transient responseHence, affects speed loop bandwidth.


Current Control for Chopper Drives – PWM ControllerIn two quadrant chopper, upper and

lower switches are complementaryOnly ONE control signal requiredCurrent error is passed to PI controller

to produce control voltage vc vc is then passed to a PWM circuit to

produce the switching signal q.q = 1 T1 ‘on’, T2 ‘off’ Va = Vdc

q = 0 T1 ‘off’, T2 ‘on’ Va = 0


ierr

Vdc

Pulse WidthModulator

(PWM)

vcia

*

PI+

q

T1

T2

D1

+

Va

-

D2

ia

+

Vdc

ia

vtri

01

qvc > Vtri

vc < Vtri

T1 ‘on’, Va = Vdc

T2 ‘on’, Va = 0

Current Control for Chopper Drives – PWM Controller

In the PWM circuit:vc is compared with a triangular

waveformif vc > Vtri ‘on’ signal is produced (q

= 1)if vc < Vtri ‘off’ signal is produced (q

= 0)

(1)

Chopper switching frequency is fixed by triangular waveform frequency regardless of operating conditions

Bandwith of current loop controller is limited by frequency of VtriDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 9

01

qvc > Vtri

vc < Vtri

Ttri

ton

0

1

vc

0

Vdc

q

va

q = 1 T1 ‘on’, va = Vdc

q = 0 T2 ‘on’, va = 0

vc > Vtri vc < Vtri

In the PWM circuit:Average value of q over a cycle

determines duty cycle of chopper:

Average armature voltage:

Current Control for Chopper Drives – PWM Controller


Ttri

ton

0

1

vc

0

Vdc

Va

tri

onTt

ttri T

tdtq

T

tri

T1 , 1

dc

T

aa VdtvT

V 1

0

q

va

va switches between Vdc and 0

average armature voltage Va depends on duty cycle (i.e. how long T1 is on)

Current Control for Chopper Drives – PWM ControllerPWM controls chopper duty cycle once in every

cycleFrequency of Va fixed by frequency of Vtri

Hence, chopper is a variable voltage source with average current control

Instantaneous current control is not exercisedCurrent can exceed maximum armature current

between two consecutive switching


Current Control for Chopper Drives – Hysteresis ControllerInstantaneous current controlCurrent controlled within a narrow

band of excursion from the desired value ia

*

Hysteresis window determines allowable deviation of ia


Vdc

ia* q

T1

T2

D1

+

Va

-

D2

ia

+

Vdc

ierr

ia

ia*

q

ia

ia

ia

01

qia ia

* - ia

ia ia* + ia

HysteresisController

Current Control for Chopper Drives – Hysteresis ControllerActual current ia compared with reference

current ia* to obtain error signal ierr

If ia ia* + ia q = 0, T2 ‘on’ and Va = 0

If ia ia* - ia q = 1, T1 ‘on’ and Va = Vdc

Value of ia can be externally set or made to be a fraction of ia

Chopper switching frequency is not fixed


ia*

q

ia

ia

ia

q = 1 T1 ‘on’, va = Vdc

ia ia* - ia

q = 0 T2 ‘on’, va = 0

ia ia* + ia

01

qia ia

* - ia

ia ia* + ia

Current Control for Chopper Drives – Qualitative Comparison


Characteristics Hysteresis Controller PWM Controller

Switching frequency

Varying Fixed (follows sawtooth waveform

frequency i.e. carrier frequency)

Switching losses High (due to varying

switching frequency)

Low

Speed of response

Fastest(due to instantanous

change in current)

Fast

Ripple current Adjustable(depends on hysteresis

window ia )

Fixed

Filter size Depends on ia SmallPreferred method !

Closed Loop Control for DC Drives with ChoppersController design procedure:

1. Obtain the transfer function of all drive subsystemsa) DC Motor & Loadb) Current feedback loop sensorc) Speed feedback loop sensor

2. Design torque (current) control loop first Two options to choose from:

A. Hysteresis Controller – to design just choose value of ia

B. PWM Controller (contains PI controller)i. determine transfer function of PWM-controlled chopperii. design PI controller using the same procedure as in closed

loop control using controlled rectifier Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 15

Exactly the same as before (i.e. transfer functions obtained in closed loop control using controlled rectifier)

Closed Loop Control for DC Drives with ChoppersController design procedure (continued):

3. Then design the speed control loopi. Obtain 1st order model of the designed current controllerii. Design the speed PI controller using the same procedure as

in closed loop control using controlled rectifier


Transfer Function of PWM-Controlled ChopperPWM current controller is preferred over Hysteresis

ControllerBefore we can design the PI controller, need to obtain linear

relationship between control input vc and average armature voltage Va for PWM method


Pulse WidthModulator

(PWM)

vcia

*

PI+

q

ia

vtri

Chopper DC motor

Va ia

Need transfer function for PWM-controlled chopper

Transfer Function of PWM-Controlled Two-quadrant ChopperNeed to obtain linear relationship between control input vc

and average armature voltage Va for PWM method


Vtri

-Vtri vc

0q

01

qvc > Vtri

vc < Vtri

vc

-Vtri

Case 1:tric Vv

T1 off all the timei.e. ton, T1 = 0

0 1 T1 ,

tri

onTt

ttri T

tdtq

T

tri

Transfer Function of PWM-Controlled Two-quadrant Chopper


Vtri

-Vtri vc

cycle a 1/2for ,0

cycle a 1/2for ,1 q

01

qvc > Vtri

vc < Vtri

vc

-Vtri

0.5

Case 2:0 cv

T1 on ½ cyclei.e. ton, T1 = 0.5Ttri

5.0 1 T1 ,

tri

onTt

ttri T

tdtq

T

tri



Vtri

-Vtri vc

1 q

01

qvc > Vtri

vc < Vtri

vc

-Vtri

0.5

1

Vtri

Case 3:

tric Vv

T1 on all the timei.e. ton, T1 = Ttri

1 1 T1 ,

tri

onTt

ttri T

tdtq

T

tri

Relationship between and vc :

(2)

For the two-quadrant chopper: (3)

Hence, considering only the term due to vc, the two–quadrant chopper gain is:

(4)



ctri

vV2

15.0

0.5

vc

-Vtri+Vtri

ctri

dcdcdca v

V

VVVV

25.0

tri

dc

c

a

V

V

v

VK

2r

1

Transfer Function of PWM-Controlled Four-quadrant Chopper

Recap Chopper operation:Positive current:

Va = Vdc when T1 and T2 onVa = 0 when current

freewheels through T2 and D4

+ Va -T1

D1

T2D2

D3

D4

T3

T4

+

Vdc

-


Transfer Function of PWM-Controlled Four-quadrant Chopper

Recap Chopper operation:Positive current:

Va = Vdc when T1 and T2 onVa = 0 when current

freewheels through T2 and D4Negative current:

Va = -Vdc when T3 and T4 onVa = 0 when current

freewheels through T4 and D2Output voltage can swing

between:Vdc and -Vdc Vdc and 0

+ Va -T1

D1

T2D2

D3

D4

T3

T4

+

Vdc

-


Transfer Function of PWM-Controlled Four-quadrant ChopperNeed to obtain linear relationship between control input vc

and average armature voltage Va for PWM methodFour quadrant chopper has two legs, so it requires two

switching signals (one for each leg)Depending on relationship between the two switching signals,

4-quadrant chopper has two switching schemes:Bipolar switchingUnipolar switching

Switching schemedetermines output voltage swing betweenVdc and -Vdc or Vdc and 0.

+ Va -T1 D1

T2D2

D3

D4

T3

T4

Leg A Leg B

+

Vdc

−


EEEB443 - Control & Drives

Transfer Function of PWM-Controlled Four-quadrant Chopper (Bipolar Switching)Bipolar Switching PWMLeg A and Leg B obtain switching signals from the same control signal vc

Switching of Leg A and Leg B are always complementary

+ Va -T1 D1

T2D2

D3

D4

T3

T4

+

Vdc

−vc

vtri

q

q

Leg A

Leg B

Dr. Ungku Anisa, July 2008 25

01

q vc > Vtri

vc < Vtri

q = 1,q =0 T1 on, T2 on Va= Vdc

q = 0, q =1 T4 on, T3 on Va= -Vdc

Transfer Function of PWM-Controlled Four-quadrant Chopper (Bipolar Switching)Bipolar Switching PWM

+ Va -T1 D1

T2D2

D3

D4

T3

T4

+

Vdc

−vc

vtri

q

q

Leg A

Leg BVa+ Va

-

Va-

Vdc

0

Va+

Vdc

0

2vtri vc

Va

Vdc

-Vdc

Va jumps between +Vdc and –Vdc Bipolar Switching PWMDr. Ungku Anisa, July 2008 26EEEB443 - Control & Drives

Va = Va+- Va

-

Transfer Function of PWM-Controlled Four-quadrant Chopper (Bipolar Switching)Bipolar Switching PWM

Va-

Vdc

0

qVdc

0

2vtri vc

Va

Vdc

-Vdc

Va jumps between +Vdc and –Vdc

Bipolar Switching PWMDr. Ungku Anisa, July 2008 27EEEB443 - Control & Drives

Va = Va+- Va

-

qVdc

0

2vtri vc

Va+

Vdc

0dca VV A

T

t T1 on,A

0

1q

vc > Vtri

vc < Vtri

dcdca VVV AB 1 T

t T3 on,B

dca VV B

)1( qq

Transfer Function PWM-Controlled Four-quadrant Chopper (Bipolar Switching)Each leg is a two-quadrant chopper. Output of Leg A (average):

(5)where

(6)Output of Leg B (average):

(7)where

(8)Hence, average voltage across the motor:

(9)Subt. (6) into (9)


Vdc

Va-

Vdc

0

Va

Vdc

-Vdc

2vtrivc

dca VV A

dcdca VVV AB 1

dcaaa VVVV 12 A

ctri

dca vV

VV

Bipolar Switching PWM

Va+

0

Vdc

AtriofftrionB TtTt 1T1 ,T3 ,

ctritri

on vVT

t

2

15.0T1 ,

A

Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching)

Unipolar Switching PWMLeg B switching signals obtained from the inverse of control signal for

Leg A

Leg A

Leg B

+ Va -T1 D1

T2D2

D3

D4

T3

T4

+

Vdc

−

vc

vtri

qa

-vc

vtri

qb


0

1qa

vc > Vtri

vc < Vtri

0

1qb

-vc > Vtri

-vc < Vtri


Unipolar Switching PWMLeg A

Leg B

+

Vdc

−

vc

vtri

qa

-vc

vtri

qb

+ Va -T1 D1

T2D2

D3

D4

T3

T4

2Vtri

vc

-vc

Va+ Va

-

Va jumps between +Vdc and 0 Unipolar Switching PWM

Va+

Vdc

0

Va-

Vdc

0

Va

Vdc

0


Va = Va+- Va

-

Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching)Unipolar Switching PWM

2Vtri

vc

-vc

Va jumps between +Vdc and 0 Unipolar Switching PWM

Va

Vdc

0


2Vtri

vc

-vc

qa

Vdc

0

Va+

Vdc

0

qb

Vdc

0

Va-

Vdc

0dca VV A

dca VV B

Va = Va+- Va

-

T

t T1 on,A

T

t T3 on,B

0

1qa

vc > Vtri

vc < Vtri

0

1qb

-vc > Vtri

-vc < Vtri


2Vtri

vc

-vc

Va+

Vdc

0

Va-

Vdc

0

Va

Vdc

0

Each leg is a two-quadrant chopper. Output of Leg A (average):

(10)where

(11)Output of Leg B (average):

(12) where

(13)Hence, average voltage across motor armature:

(14)

dca VV A

dca VV B

dcdcaaa VVVVV 12 ABA

Same as Bipolar Switching Scheme!

Unipolar Switching PWM


ctritri

on vVT

t

2

15.0T1 ,

A

AT3 ,

B 12

15.0

c

tritri

on vVT

t

PWM-Controlled Four-quadrant ChopperComparison between Bipolar & Unipolar SwitchingBipolar Switching PWM Unipolar Switching PWM

2Vtri

vc

-vc

Va+

Vdc

0

Va-

Vdc

0

Va

Vdc

0


Va-

Vdc

0

2vtri vc

Va+

Vdc

0

Va

Vdc

-Vdc

ctri

dca vV

VV

• Output voltage swings from Vdc and –Vdc

• Output voltage frequency equal to frequency of triangle voltage (ftri)

• Output voltage swings from Vdc and 0• Output voltage frequency equal to 2 times frequency of triangle voltage (ftri)

PWM-Controlled Four-quadrant ChopperComparison between Bipolar & Unipolar Switching

Current ripple =

For same ftri and Vdc, unipolar scheme gives:better output voltage waveform (less ripple)lower current ripplebetter frequency response


Characteristics Bipolar Switching Unipolar Switching

Output voltage swing Vdc and -Vdc Vdc and 0

Output voltage frequency

ftri = frequency of Vtri 2ftri

tageoutput volripple f

Vi dc

Gain of the PWM-controlled chopper:

Two -quadrant: (15)

Four–quadrant: (16)

where Vdc = dc link voltage Vtri = maximum control voltage

(i.e. peak of the triangular waveform)Chopper also has a delay:

(17) where fc = carrier (triangular) waveform frequency

Transfer Function PWM-Controlled Chopper: Two and Four Quadrant


tri

dc

c

a

V

V

v

VK r

tri

dc

c

a

V

V

v

VK

2r

cr fT

2

1

PWM-controlled Chopper: (18)

Note: Kr and Tr as given in equations (15) – (17) above.Other subsystem transfer functions are as observed in ‘Closed-loop

Control of DC Drives with Controlled Rectifier’.DC Motor and Load:

Current Feedback: Speed feedback:

Transfer Function of Subsystems


rr

sT

K

1sG r

sV

sI

sI

sω

sV

sω

a

a

a

m

a

m

mt

b

sTB

K

1sI

sω

a

m

21

1a

a

11

1

sV

sI

sTsT

sTK m

cH

sT

K

1sGω

Design of Controllers – Block Diagram of Motor Drive

Assume that we are using PWM controlled chopperControl loop design starts from inner (fastest) loop to

outer(slowest) loop Only have to solve for one controller at a time Not all drive applications require speed control (outer loop) Performance of outer loop depends on inner loop


Speed Control Loop

Current Control Loop

PI type current controller: (19)Loop gain function:

(20)

Design procedure - same as for current controller in closed-loop control using controlled rectifiers

Design of Controllers– Current Controller


c

cc

sT

sTK

1sGc

r

mc

c

crc

sTsTsTs

sTsT

T

HKKK

111

11sHG

21

1i

DC Motor & Load

PWM-controlled Chopper

Approximated by adding Tr to T1

(21)

Design of Controllers– Current loop 1st order approximation


i

c

m

c

m

sT

K

sTT

THKKKsTT

TKKK

i

crc

rc

11

11

11

sI

sI

3

1

3

1

*a

a

rTTT 13

Design of Controllers– Current loop 1st order approximation

where (22)

(23)

(24)

1st order approximation of current loop used in speed loop design.

If more accurate speed controller design is required, values of Ki and Ti should be obtained experimentally.


c

mcrcfi T

THKKKK 1

fii K

TT

13

fic

fii KH

KK

1

1

PI type current controller: (25)

Assume there is unity speed feedback: (26)

Design of Controllers– Speed Controller


s

sss sT

sTK

1sG

11

sGω

sT

H

DC Motor & Load

1st order approximation of current

loop

1

Loop gain function: (27)

Design procedure - same as for speed controller in closed-loop control using controlled rectifiers

Design of Controllers– Speed Controller


mi

s

st

isB

sTsTs

sT

TB

KKK

11

1sGH

ReferencesKrishnan, R., Electric Motor Drives: Modeling, Analysis and

Control, Prentice-Hall, New Jersey, 2001.Mohan, Underland, Robbins, Power Electronics: Converters,

Applications and Design, 2nd ed., John Wiley & Sons, USA, 1995.

Nik Idris, N. R., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008.


Documents

Closed-loop Control of DC Drives with Chopper By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr