Sensor Less Flux Vector White Paper

7/28/2019 Sensor Less Flux Vector White Paper

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Sensorless Flux Vector Control of AC and

Brushless DC Motors

Authored by, Karl Konecny

NW Motion Products

Modern pwm drives for AC induction motors without a shaft sensor employ one of three controlmethodologies: constant volts per hertz, open loop flux vector, and sensorless flux vector. Afourth technique, direct torque control, shares many similarities with sensorless flux vector controland attempts to simplify the numerical complexity through the application of fuzzy logic. Thispaper will focus on the capabilities and issues of sensorless flux vector control as well as itsextension to the control of BLDC machines.

Volts per hertz control of an AC induction motor is based on the principle that to maintainconstant magnetic flux in the motor, the terminal voltage magnitude must increase roughlyproportional to the applied frequency. This is only an approximate relationship and volts per hertz

drives typically add a low frequency voltage boost, referred to as IR compensation, to increasestarting torque capability. Volts per hertz drives may also add a steady state slip compensationthat increases frequency based on a current measurement to give better steady state speedregulation. Volts per hertz drives may also add stability compensation to overcome midfrequency instabilities evident in high efficiency motors.

Volts per hertz drives work well on applications that the load is predictable and does not changequickly such as fan loads. For better torque control, flux vector techniques were developed.These techniques control not only the magnitude of the ac excitation but also the orientation, thusthe vector name. They are based on the principle of field orientation, which states that if thecurrent vector is controlled relative to the rotor flux vector then the magnitude of the flux vectorand the motor torque can be independently controlled. In the rotor flux oriented reference frame,the equations for rotor flux magnitude and torque are shown in equation 1. The rotor flux is a low

pass filtered mirror of the stator current component oriented with it and the torque is the productthe rotor flux and the stator current orthogonal to it.

r

Lm

Ids

Lr

Rr

s 1

T3

2

n

2

Lm

Lr

r Iqs

Equation 1

Open loop flux vector drives use indirect field orientation, which is based on the principle thatspecifying stator currents and slip frequency completely specifies motor flux and torque.Therefore, if equation 1 is held as well as the aligned slip frequency equation (Equation 2) thenthe currents must be oriented to the rotor flux.

s

Rr

Lr

Iqs

Ids

Equation 2

Preliminary Release Page 1 7/18/2013


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Open loop flux vector drives demonstrate a much greater dynamic performance than volts perhertz drives but suffer from several shortcomings. First, the rotor flux (equation 1) and the slipare very dependent upon motor electrical parameters. Lm and Lr are typically not constant asinduction motors are designed to operate near the magnetic saturation point to minimize weight.The rotor resistance, Rr, can vary by over 40% from internal heating. Thus, these parameters aredifficult to know accurately over all operating conditions. Finally, the actual slip can only beknown by measuring the rotor speed with a shaft sensor. Thus an open loop flux vector drivecannot directly control the current vector and slip. Therefore, one of the above equations areassumed to be true, typically the flux equation. This assumption is validated by imposing a voltsper hertz relationship as done in a volts per hertz drive. Overall, the performance of open loopflux vector drives can be quite good as long as all torque disturbances are small.

Sensorless flux vector drives use direct field orientation to provide yet higher performance.Instead of implying the orientation of the flux vector by satisfying equations 1 and 2, the fluxvector is directly measured from the terminal electrical quantities of voltage and current.Equations 3 are continuously integrated and solved to give an instantaneous measurement of therotor flux vector.

qs

0

t

tVqs Rs Iqs d qs0

ds

0

t

tVds

Rs

Ids

d ds0

qr

Lr

Lm

qs

Lr

Ls

Lm

2

Lm

Iqs

dr

Lr

Lm

ds

Lr

Ls

Lm

2

Lm

Ids

Equation 3

The inputs to these equations are the stator voltage and current vector. The current vector isbest directly measured but the voltage vector can be deduced from a DC link voltagemeasurement and the PWM switching pattern.

Equation 4 shows that the Lr/Lm term nearly equals one and the current multiplier term nearlyequals the sum of rotor and stator leakage inductance as the ratio L lr/Lm is typically between 0.02and 0.06. Thus, the key motor parameters are stator resistance and leakage inductance, themagnetizing inductance term virtually drops out of the equations.

Lr

Lm

1L

lr

Lm

Lr

Ls

Lm

2

Lm

Llr

Lls

Llr

Lls

Lm


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Equation 4

An error in the leakage inductance term primarily causes an error in the estimate of the angle ofthe rotor flux at high torque conditions. The error is linear with torque and a 50% error in leakageinductance can cause a five-degree error in the flux angle estimate at rated torque.

The stator resistance affects the accuracy of the flux estimator at low frequencies. On a typical 5hp, 4 pole motor, operating at full torque, the magnitude of the voltage drop across the statorresistance equals the magnitude of the BEMF generated by the rotor flux when the motor isoperating at 24 RPM. As long as the stator resistance estimate is within 10% of the actual value,flux estimators based on equation 3 can operate well under these conditions. Stator resistancecan be automatically measured during start up to a precision much greater than this. Typically,current or voltage measurement offset errors and voltage errors due to switching dead time causethe greatest errors at low frequencies and must be carefully compensated for. Eventually, theaccuracy of the flux estimator will become unreliable at some low frequency due to thediminishing magnitude of the BEMF compared to other terms.

The topology of the inner loops of a sensorless flux vector drive is shown in figure 1. The variousblocks are as follows: The flux estimator updates the integrals from equation 3. It also calculatesmotor torque based on equation 5. Note that this equation for torque is independent oforientation and all inductance parameters. The only motor parameter that can affect the accuracyof equation 5 is stator resistance, which is only significant at low speeds. This is in contrast tothe aligned torque equation used in the open loop flux vector drives (equation 1).

T3

2

n

2I

qs dsI

ds qs

Equation 5

The primary output of the flux estimator is the rotor flux vector given as the q and d axis Cartesiancomponents. This is the input to the flux vector orientation block, which generates theinstantaneous orientation and rate of rotation of the flux vector. Conceptually this can be

achieved with an arc-tangent function and a differentiation. Differentiation is a noise amplifyingfunction, therefore the flux vector orientation block uses a phase locked loop to track the flux witha smoothly rotating vector. This produces a reference frame aligned with the rotor flux vector.

Another advantage of a phase locked loop is that the flux vector can be smoothly tracked throughzero speed, where the flux estimate is unreliable, due to the inherent memory of the PI trackingregulator and the fact neither rotor flux nor rotor speed can change instantaneously.


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Voltage Vector

Current Vector Torque

flux vectorfrequency

Flux vector angle

Motor ModelCurrentRegulators

Motor parameters

Rotorspeed

estimate

VoltageVector

Command

Rotor FluxVector

FluxCommandD axis CurrentCommand

Torque Conversion

Flux RegulatorPI Regulator

TorqueCommand

QaxisCurrent Command

Pwm SystemCurrent Vector Sampling Flux Estimator

Flux Vector OrientationPI regulator

Figure 1

Once the orientation, magnitude, and frequency of the rotor flux vector is known, the motor modelblock can calculate a steady state voltage vector command based on d and q axis currentcommands (equation 6). This block also includes d and q axis current regulators and a rotormechanical speed estimator based on the aligned slip equation (equation 7). Note that this slipequation does not include the dependency on rotor inductance shown in equation 2 due to theratio or magnetizing to rotor inductance. Also note that errors in the slip calculation do not impactflux orientation but only impact the accuracy of the mechanical speed estimate.

Vqs ss Rs Iqs

Lr

Ls

Lm

2

Lr

Ids

Lm

Lr

dr

Vds

ss Rs

Ids

Lr

Ls

Lm

2

Lr

Iqs

Equation 6

s

Lm

Lr

Rr

Iqs

dr

Equation 7


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Induction Motor Torque Mode

-2

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Speed (RPM)

Torque(nt-m)

Torque Command = 0

Torque Command = 6

Torque Command = 12

Torque Command = 18

Figure 2

The PWM block converts a voltage vector command into gate command signals for the inverter.To accomplish this it samples the DC link voltage real time to determine instantaneous dutycycles for each phase. It also controls the sampling of the phase currents and passes the actual

voltage and current vector measurements to the flux estimator.

The flux regulator generates the d axis current command through a PI regulator by comparingcommanded to measured rotor flux. This eliminates the need to have an accurate estimate ofmagnetizing inductance. The torque command is converted to a q axis current command usingthe aligned torque equation (equation 1). If higher accuracy is required, comparing the calculatedtorque from the flux estimator with the commanded torque can generate a correction.

A sensorless flux vector drive operated per figure 1 is a torque mode drive. If a regenerativerectifier or a braking chopper circuit is added, the drive will behave as a 4-quadrant torque

controller. A torque speed plot of a 3 hp, 230 volt MTS DriveBlok driving a 3 hp, 230 volt, 4 pole

Dayton premium efficiency motor is shown in figure 2. Note that the discrepancy betweencommanded and measured torque is primarily due to friction, windage, and hysteresis.


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Torque Controller

Flux Command

Torque

CurrentVector

Voltage Vector

Rotor SpeedEstimate

PISpeed RegulatorLoadLimit

Slip Limit

BrakingLimit

Regeneration OverrideLineDropout Ride-thru

TorqueCommand

Motor Rated Flux

DC BusVoltageBreakingResistor Controller

PIRegulator

Accel /DecelRamp

"S" CurveJump Speeds

Min/Max speed Limits

Forward /Reverse

Speed Command

Figure 3

A sensorless flux vector drive can operate as a speed mode drive by adding a speed regulatoraround the torque control loop, as shown in figure 3. In this figure, the entire control system offigure 1 has been condensed into a single block labeled "Torque Controller". The speedcommand comes from a speed preprocessor that includes acceleration and deceleration ramps,

jerk limits, critical speed avoidance, and speed limits. The speed feedback comes from thespeed estimate of the motor model. A conventional PI regulator generates a torque command.Figure 4 illustrates the dynamic speed response of the system to a step change in load from 10%to 90% of motor rated load. Note that the speed droops 25 RPM and recovers in 75 msec.


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Figure 4

AC Induction Motor, Speed Mode

0

2

4

6

8

10

12

14

16

18

20

800 850 900 950 1000 1050 1100

Speed (RPM)

Torque(nt

Figure 5


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The torque command can be limited in both motoring and braking to provide a precise speed foldback during overloads. This is demonstrated in torque speed curve of figure 5. The drive iscommanded to run at 1000 rpm with a torque limit of 18 nt-m, 150% of motor rated torque. Theload on the motor was slowly raised from 0 to 18.5 nt-m. The speed remains within 1 RPM of thecommanded speed until the load reaches 17 nt-m at which point the speed begins to fold back onthe torque limit, eventually collapsing to zero unless the load is removed. When the load isremoved, the speed recovers with no integrator wind up.

Additional blocks have been added that can modify the torque command generated by the speedregulator. The line drop out ride through voltage regulator block monitors the DC bus and, whenit drops to a point where a loss of input power is evident, the speed regulator output is overriddenwith a regenerative command that will hold the bus at a specified level until all mechanical energyis consumed or the line is restored. This is demonstrated in figure 6. The drive is commanded torun at rated speed, 1765 rpm, with a 4 nt-m load and the input power is dropped. Themechanical speed is maintained until the DC bus drops to the predetermined line dropoutregulation voltage. At this point, the mechanical speed begins to droop as the line drop out ridethrough voltage regulator commands sufficient negative torque to sustain the bus. When theinput power is restored, the speed regulator takes over and restores the speed to 1765 rpm,again with not integrator wind up.

Figure 6

Both volts per hertz drives and open loop flux vector drives rely on the inherent open loop speedstability of an AC induction motor. This is the same stability that allows across the line operation.These types of drives cannot drive a brushless DC motors without shaft position sensors becausethese motors lack open loop speed stability. A sensorless flux vector drive can be modified todrive a brushless DC motor without a shaft sensor because direct field orientation measures theorientation of the rotor flux and responds appropriately.


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To operate a brushless DC motor, figure 1 must be modified by removing the flux regulator as theflux is maintained by the permanent magnets on the rotor. The d axis current command is set tozero. The motor model must also be modified to remove the slip equation in the speed estimate.The speed estimate on a brushless DC motor is simply the frequency of rotation of the magneticfield as the magnets are fixed to the rotor, thus the absolute speed accuracy of a sensorless fluxvector drive can be extremely high, limited by the bit resolution and crystal accuracy of thecontroller card.

Figure 7

Figures 7 and 8 demonstrate the performance of the MTS DriveBlok in brushless DC mode.

Again, this is a 3 hp 230 volt drive. It is operating a Reliance Electric F-4050 brushless servomotor. The load inertia is 10 times rotor inertia. The disturbance response is similar to that of the

AC induction motor as the bandwidth of the speed regulator is dominated by the dynamometerinertia, which was the same in the two motor cases.

The torque mode torque-speed curves shown in figure 8 demonstrate a fairly constant torqueover a wide speed range. Again the discrepancy between commanded and actual torque is dueto friction, windage, and hysteresis losses in the motor. Note that these losses are, to the firstorder, independent of the torque command. This is demonstrated by the nearly constant two nt-m change in measured torque with a two nt-m change in commanded torque.


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BLDC Torque Mode

-1

0

1

2

3

4

5

6

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Speed (RPM)

Torque(nt-

Torque Command = 0

Torque Command = 2

Torque Command = 4

Torque Command = 6

Figure 8

Conclusion

Sensorless flux vector drives can provide excellent control of AC motors giving superior speedregulation and dynamic response. The control algorithms can be arranged to minimize thedependence on motor parameters. Sensorless flux vector drives do not depend on the inherentspeed stability of AC induction motors, as do volts per hertz and open loop flux vector drives, andcan be operated in a true torque mode. For the same reason, sensorless flux vector drives canalso control brushless PM motors in both torque and speed modes.

References

F. Blaschke, The Principle of Field Orientation the Basis for the Transvector Control of

Three-Phase Machines, Siemens Zeitschrift, Vol. 45, No. 10, 1971.

D. W. Novotney and T. A. Lipo, Vector Control and Dynamics of AC Drives, Oxford

University Press, 1996.

Paul C. Krause, Analysis of Electric Machinery, McGraw-Hill, 1986

Gordon R. Slemon, Electric Machines and Drives, Addison-Wesley Publishing Company,

1992

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Sensor Less Flux Vector White Paper