Sensorless Field Oriented Control (FOC) of an AC …...solution for sensorless Field Oriented Control (FOC) of induction motors using a dsPIC® Digital Signal Controller (DSC). OVERVIEW

AN1162Sensorless Field Oriented Control (FOC) of an

AC Induction Motor (ACIM)

INTRODUCTIONThe requirement of low-cost, low-maintenance, robustelectrical motors has resulted in the emergence of theAC Induction Motor (ACIM) as the industry leader.Typical applications requiring the use of an inductionmotor drive range from consumer to automotiveapplications, with a variety of power and sizes.

Where efficiency, low cost, and control of the inductionmotor drive is a concern, the sensorless Field OrientedControl (FOC), also known as vector control, providesthe best solution. The term “sensorless” does notrepresent the lack of sensors entirely, but the fact thatin comparison with other drives from the same categoryof field oriented control, it denotes that the speedand/or position sensor is missing. This featuredecreases the cost of the drive system, which is alwaysdesired, but this is not the only reason for thisapproach, as some applications have requirementsconcerning the size, and the lack of additional wiring forsensors or devices mounted on the shaft (due to hostileenvironments such as high temperature, corrosivecontacts, etc.).

The intent of this application note is to present onesolution for sensorless Field Oriented Control (FOC) ofinduction motors using a dsPIC® Digital SignalController (DSC).

OVERVIEW

AC Induction MotorThe AC Induction Motor (ACIM) is the workhorse ofindustrial and residential motor applications due to itssimple construction and durability. These motors haveno brushes to wear out or magnets to add to the cost.The rotor assembly is a simple steel cage.

ACIMs are designed to operate at a constant inputvoltage and frequency, but you can effectively controlan ACIM in an open loop variable speed application ifthe frequency of the motor input voltage is varied. If themotor is not mechanically overloaded, the motor will

operate at a speed that is roughly proportional to theinput frequency. As you decrease the frequency of thedrive voltage, you also need to decrease the amplitudeby a proportional amount. Otherwise, the motor willconsume excessive current at low input frequencies.This control method is called Volts-Hertz control.

The benefits of field oriented control can be directlyrealized as lower energy consumption. This provideshigher efficiency, lower operating costs and reducesthe cost of drive components.

In sensorless field oriented control, the speed and/orposition are not directly measurable; their values areestimated using other parameters such as phasevoltages and current, that are directly measured.

For additional information on the ACIM modelingequation and other induction motor topologies, see“References” for a complete list of relateddocumentation available from Microchip.

Control StrategyTraditional control methods, such as the Volts-Hertzcontrol method described above, control the frequencyand amplitude of the motor drive voltage. In contrast,field oriented control methods control the frequency,amplitude and phase of the motor drive voltage. Thekey to field oriented control is to generate a 3-phasevoltage as a phasor to control the 3-phase statorcurrent as a phasor that controls the rotor flux vectorand finally the rotor current phasor.

The key to understanding how field oriented controlworks is to form a mental picture of the coordinatereference transformation process. If you picture how anAC motor works, you might imagine the operation fromthe perspective of the stator. From this perspective, asinusoidal input current is applied to the stator. Thistime variant signal causes a rotating magnetic flux to begenerated. The speed of the rotor is going to be afunction of the rotating flux vector. From a stationaryperspective, the stator currents and the rotating fluxvector look like AC quantities.

Now, instead of the previous perspective, imagine thatyou could climb inside the motor. Once you are insidethe motor, picture yourself running alongside thespinning rotor at the same speed as the rotating fluxvector that is generated by the stator currents. Lookingat the motor from this perspective during steady stateconditions, the stator currents look like constant values,

Author: Mihai ChelesMicrochip Technology Inc.

Co-Author: Dr.-Ing. Hafedh SammoudAPPCON Technologies SUARL

© 2008 Microchip Technology Inc. DS01162A-page 1

AN1162
and the rotating flux vector is stationary! Ultimately, youwant to control the stator currents to get the desiredrotor currents (which cannot be measured directly).With the coordinate transformation, the stator currentscan be controlled like DC values using standard controlloops.
The transition of coordinates is usually calleddecoupling. This strategy is based on the inductionmotor’s equations written in the rotating coordinate axisof the rotor. To transition from the stator fixed-frame tothe rotor rotating frame, the position of the rotor needsto be determined. This can be done throughmeasurement or can be estimated using other methodsavailable such as sensorless control.

A method of sensored field oriented control forinduction motor can be found in application note AN908“Using the dsPIC30F for Vector Control of an ACIM”(see “References”). The sensorless control blockdiagram differs from the one used in sensored controlby the absence of the speed measurement and by theaddition of the estimator block. The sensorless controlestimator block needs as input the voltages andcurrents, as indicated in the following sections.

CONTROL LOOP

Control Block SchematicThis application note is grouped around a speedcontrol loop for ACIM using field oriented control.Figure 1 provides a schematic of the control block.

FIGURE 1: SENSORLESS FOC FOR ACIM BLOCK DIAGRAM

d,q

α,β

3-PhaseBridge ACIM

A,B

α,βd,q

α,β

Estimator

ωref Iqref

Idref

PI PI

PIFieldWeakening

Vq

Vd

Vα

Vβ

SVM

AngleEstimation

SpeedEstimation

Iα

Iβ

IA

IB

Software Hardware

-

-

-

ρestimωmech

Iα

Iβ

Vβ

Vα

+

IA

IB

IC

Iq

Id

1

2

3

4

5

6

7

8

+ +

Hardware blocks

1. ACIM induction motor2. 3-Phase Bridge – rectifier, inverter, and acquisition and protection circuitrySoftware blocks (run by dsPIC® DSC device)3. Clarke forward transform block4. Park forward and inverse transform block5. Angle and speed estimator block6. PI controller block7. Field weakening block8. SVM block

DS01162A-page 2 © 2008 Microchip Technology Inc.

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CURRENT DECOUPLINGThe decoupling block (shaded area in Figure 2)comprises a set of blocks: Clarke and Park transform.The Clarke forward transform block is responsible fortranslating three axes, two-dimensional coordinatessystem attached to the stator to two axes systemreference to the stator. The Park forward block isresponsible for translating two axes from the statorfixed frame to the rotating rotor frame. Refer to AN908“Using the dsPIC30F for Vector Control of an ACIM”(see “References”) for more details.

FIGURE 2: COORDINATE TRANSITION (DECOUPLING) BLOCK DIAGRAM

d,q

α,β

3-PhaseBridge ACIM

A,B

α,βd,q

α,β

Estimator

ωref Iqref

Idref

PI PI

PIFieldWeakening

Vq

Vd

Vα

Vβ

AngleEstimation

SpeedEstimation

Iα

Iβ

IA

IB

Software Hardware

-

-

-

ρestimωmech

Iα

Iβ

Vβ

Vα

+

IA

IB

IC

Iq

Id

+ +

SVM


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SPEED AND ANGLE ESTIMATORThe speed and angle estimator (shaded area inFigure 3) have as inputs, the fixed reference statorframe, two axes voltages and currents. Back ElectroMotive Force (BEMF) is used to estimate speed andposition. When magnetizing current is constant, theBEMF equations (see Equation 4 and Equation 5) aresimplified.

FIGURE 3: SPEED AND ANGLE ESTIMATOR BLOCK DIAGRAM

First the induced BEMF is calculated, using theestimator block inputs shown in Equation 1.

EQUATION 1:

Equation 2 shows the calculations that can be used totransform α and β to d-q coordinates.

EQUATION 2:

Figure 4 presents the d-q estimated BEMF; however,when the magnetizing current is constant, thed component of BEMF is ‘0’.

d,q

α,β

3-PhaseBridge ACIM

A,B

α,βd,q

α,β

Estimator

ωref Iqref

Idref

PI PI

PIFieldWeakening

Vq

Vd

Vα

VβSVM

AngleEstimation

SpeedEstimation

Iα

Iβ

IA

IB

Software Hardware

-

-

-

ρestimωmech

Iα

Iβ

Vβ

Vα

+

IA

IB

IC

Iq

Id

+ +

Eα Vα RSIβ δLSdIαdt

--------––=

Eβ Vβ RSIβ δLSdIβdt

--------––=

Eq E– α ρestim( )sin Eβ ρestim( )cos+=

Ed Eα ρestim( )cos Eβ ρestim( )sin+=


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FIGURE 4: BEMF VECTOR COMPONENTS: α-β AND d-q
α

β

Eq

Es

Ed

Eβ

Eα

qestim destim

ρestim

Positive Speed


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If the estimated BEMF is not equal to the actual BEMF,the angle between the estimated and the actual BEMFis Δρ = ρ - ρestim, as shown in Figure 5.
In Figure 5, the estimated d component of BEMF isgreater than ‘0’, which results in Δρ < 0.

If BEMF is less than ‘0’, Δρ > 0, as shown in Figure 6.

FIGURE 5: ANGLE ESTIMATION WHEN Ed > 0 AND POSITIVE SPEED

α

β

Esqf

Es

Esdf

Eβ

Eα

d

q

destimqestim

ρestim

Δρ<0

Positive Speed

ρ


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FIGURE 6: ANGLE ESTIMATION WHEN Ed < 0 AND POSITIVE SPEED
A simple way to correct the error between estimatedBEMF and actual BEMF would be to subtract from theestimated angle ρestim, the error, Δρ. However, thiscould lead to numeric instabilities.

A solution to the angle estimation correction is to usethe speed instead of angle. Since the angle is theintegral of speed, the numeric instabilities are avoided.

BEMF is proportional with magnetizing flux variation.Equation 3 shows the results of splitting the d-q axes.

EQUATION 3:

Equation 4 and Equation 5 (the rotor flux is consideredconstant) shows the decomposition on the d-q axes.

EQUATION 4:

EQUATION 5:

Therefore, the rotor speed can now be written asEquation 6.

EQUATION 6:

α

β

qestim

Esqf

Es

Esdf

Eβ

Eα

dq

ρestimρ

Positive Speed

Δρ>0

destim

E 11 δR+---------------

dΨmRdt

--------------=

Ed1

1 δR+---------------

dΨmRdt

-------------- 0→=

Eq1

1 δR+---------------ωmRΨmR=

ωmR1 δR+ΨmR

---------------Eq=


http://www.microchip.com/stellent/idcplg?IdcService=SS_GET_PAGE&nodeId=1824&appnote=en019806

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An error in estimation generates a non-zero Ed. Also,the larger Ed is, the larger the error, which leads to thecorrection term for the rotor estimated speed, as shownin Equation 7.
EQUATION 7:

Depending on the direction of rotation, the followingcorrective action can be taken, as shown in Table 1.

TABLE 1:

As shown in Equation 8, the angle is the speed integral.

EQUATION 8:

The scheme of the estimator’s “PLL” correction block isshown in Figure 7.

FIGURE 7: ESTIMATED SPEED AND ANGLE AS A FUNCTION OF BEMF AND CONSTANT MAGNETIZING FLUX

Condition Action on ωmR

Correction Term

Positive speed, Ed > 0 Decrease - EdPositive speed, Ed < 0 Increase - EdNegative speed, Ed > 0 Increase + EdNegative speed, Ed < 0 Decrease + Ed

ωmR1 δR+ΨmR

--------------- Eq Eq( ) Ed⋅sgn–=

correction

ρ ωmR∫ dt=

d,q

α,β

1s

Eα

Eβ

Ed

Eq

Edf

Eqf

ω

ΨmR

LPF

LPF Sign

+

+

ρestimmR


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Figure 8 shows the inclusion of the correction block intothe global scheme of the estimator to obtain theinputs/outputs presented in the sensorless FOC blockdiagram (Figure 1).
The estimated BEMF is determined by low-passfiltering the value obtained from the Parktransformation. The first order filter is used to reducethe noise due to the currents derivation. The filter’sconstants should be chosen so that the noise on thesignal is significantly reduced and at the same time sothat the filter not to introduce a dynamic changes for theestimated BEMF.


d,q

α,β

1s

1s1s

d,q

α,β

σLs

Rs

Rs

σLs

Vα

Vβ

Iβ

IαEd

EqEqf

Edf

ωmR

Iq

Id

ω2ωmech

ImR

-

Magnetizing curve

LPF

LPF

LPF

Sign

SWITCH ΨmRref

+

+

-

-

+

--

+

+

ρestim

Eα

Eβ

RR/1 σR

+


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PI CONTROLLERThe PI controller is the control loop feedbackmechanism that corrects the error between themeasured process variable and its reference value, itoutput adjusting the process. In the case of inductionmotor control process three PI controllers are used,one for each current component corresponding tomagnetizing flux and to torque generation and one forthe speed control loop.

More information concerning the PI controller can befound in application note AN908 “Using the dsPIC30Ffor Vector Control of an ACIM” (see “References”).

FIELD WEAKENINGWhen exceeding the nominal motor speed, the rotorflux must be weakened. A mechanical speed increasewill require an increase of the stator currents frequency,but this must be done with respect to the simpleequation, V/Hz = ct. Since the voltage cannot beincreased over the nominal value, the increase ofspeed must be done in detriment of torque produced,keeping the constant power curve.

In closed loop field oriented control, when exceedingthe nominal motor speed, the Id and Iq control loopssaturate, limiting the motor flux. The field weakeningalgorithm will decrease the Id current as the motorspeed is increase thus removing saturation of thecontrol loops.

Space Vector ModulationThe voltages produced by Clarke transformation blockfeed the SVM module, which creates command signalsfor the inverter’s gates. The principles of functioning ofthe SVM are explained in application note AN908“Using the dsPIC30F for Vector Control of an ACIM”(see “References”).

The main advantages of SVM with respect to sinePWM are:

• Increased line to line voltage (15% more) in the linear operating range - this leads to smaller current ratings for the same power rating; a lower current implies lower costs for the power inverter on one hand, smaller power loss in commutation on the other hand;

• Since the input of the module is a vector defined in the fixed stator frame, this enables the controls of the 3-phase sine waves generation using only one quantity, thus reducing computation power needs.

HIGH LEVEL SYSTEM DECOMPOSITIONThe application’s design has the advantage of usingsome already existing hardware block components pro-vided by Microchip for supporting the demos for motorcontrol. Also, the use of Microchip’s development boardsand their special adapted enhancement boards ease thedevelopment process, shortening the time to output forany system.

HARDWARE

Component BlocksThe system components are:

3-PHASE ACIMThe recommended 3-Phase ACIM is Lesson ACIM thatcan be obtained from Microchip or from an electricmotor distributor. If another motor is used than themotor parameters and the PI controller coefficientsmust be modified inside the software.

The motor parameters as they are indicated by themanufacturer need to be normalized in order to fit theactual software implementation. To support theparameters normalization, inside the applicationsoftware archive it is available a conversion table(EstimParameters.xls file) which produces thenormalized parameters needed by the applicationsoftware.

MICROCHIP dsPICDEM™ MC1H 3-PHASE HIGH VOLTAGE MODULEThe 3-Phase High Voltage Module contains: the powerelectronics gate drive stages, fault detection andlatching circuitry, isolated Hall Effect currenttransducers. A detailed description of the module canbe found in the DS70096 “dsPICDEM™ MC1H3-Phase High Voltage Power Module User’s Guide”(see “References”).

MICROCHIP DEVELOPMENT BOARDThere are several options for the control developmentboard, depending on the dsPIC chose. As an example,for dsPIC30F the Development Board is dsPICDEM™

MC1 as for dsPIC33F the Development Board isExplorer 16. These boards provide connectors to thedsPICDEM™ MC1H, directly or using an adaptor boardsuch as PICtail™ Plus Motor Control Daughter Card forExplorer 16. Refer to “References” for information onrelated documentation for the development boardspreviously mentioned. The software archives providedwith the application note cover several dsPIC solutionsfor implementation. Within the software archive thehardware components are enumerated for eachrecommended setup (Readme.doc file).


AN1162
Application dsPICThe dsPIC devices contain extensive DSP functionalitywith high-performance 16-bit digital signal controllerarchitecture (modified RISC CPU).
• High-Performance CPU Features:- Modified Harvard architecture- C compiler optimized instruction set architecture

with flexible addressing modes- 24-bit wide instructions, 16-bit wide data path- 83 base instructions- Up to 40 MIPS operation- 44 interrupt sources- 16 x 16-bit working register array

• DSP Engine Features:- Single-cycle multiply and accumulate- Modulo and Bit-Reversed Addressing modes- Two, 40-bit wide accumulators with optional

saturation logic- ± 16-bit single-cycle shift

• Motor Control PWM Module Features:- 8 PWM output channels- Complementary or Independent Output

modes- Edge and Center-Aligned modes- 4 duty cycle generators- Dedicated time base- Programmable output polarity- Dead-time control for Complementary mode- Manual output control- Trigger for A/D conversions

• Quadrature Encoder Interface Module Features:- Phase A, Phase B and Index Pulse input- 16-bit up/down position counter- Count direction status- Position Measurement (x2 and x4) mode- Programmable digital noise filters on inputs- Alternate 16-bit Timer/Counter mode- Interrupt on position counter rollover/underflow

SOFTWAREComponent ModulesThe software project components have a modulardesign, each function being contained by its own file.The control algorithm consists of an interrupt serviceroutine triggered by control measures sampling and atask on which the user interference and control ishandled together with the control state machine.

The control algorithm was developed by adapting thesensored vector control for ACIM application note,AN908 “Using the dsPIC30F for Vector Control of anACIM” (see “References”) to the sensorless control

requirements, the modifications referring only to theestimator part module and to the adaptation ofpreviously existing modules to the estimator. Thus,details about the existing software components canalso be found in this same application note.

Table 2 lists the most important software modules:

TABLE 2:

Associated to the source files enumerated abovestands the header files, an important header being theuser parameters configuration header(UserParams.h file). The user parameters comprisethe motor and the inverter parameters. The motorparameters are to be normalized to fit the software con-trol algorithm - in order to support the ease of actualcontrol solution porting for other system componentswithin the software archive it may be found a conver-sion utility from physical measures to their normalizedvalues (EstimParameters.xls file).

Debug Capabilities and DMCIMicrochip’s MPLAB® IDE provides all in onedevelopment environment for its dsPIC products.Besides the enhanced code editor, the IDE provides anefficient C code compiler and a debugger that supportsingle-stepping with enhanced breakpoints and tracingcapabilities. All these features are available under oneeasy-to-use unified GUI.

DMCI is a tool which provides a graphical interface thatenables a quick and dynamic yet easy to useinteraction with the system’s key variables. Theintuitive representation of the system variables throughsliders and on/off buttons, the dynamically assignablegraph windows for program generated data analysisshortens the development and calibration/tuning time.Moreover, DMCI provides project-aware navigation ofprogram variables for their easy selection andassignation to the interface’s dedicated controls andvisualization features.

Module Description

acim.c ISR and user interference and control task. Contains the control algorithm, the user interface, and control states handling.

estim.c Estimator for speed and angle of the rotor.pi.s Proportional-integral controller.trig.s Sinus computation.svgen.s SVM generation.clkpark.s Clarke-Park direct transformation.invclark.s Inverse Clark transformation.invpark.s Inverse Park transformation.curmodel.s Magnetizing current and angle computation.fdweak.s Field weakening algorithm.


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Execution and Data FlowThe software program execution consists of two maintasks: the sensorless control of the ACIM and theuser’s commands and information handling.
The sensorless control cannot be achieved startingfrom zero speed; therefore the application must bestarted in open loop, using a simple Volt per Hertzcontrol. Once the motor is spinning the BEMF can beused for sensorless control - the user’s touch of a but-ton switching between open loop to closed loop fieldoriented vector control. For PI controller parameter tun-ing purpose there is the option of doubling the refer-ence speed, getting the system response to stepexcitation.

The major control loop is controlling the motor’s speed;therefore the reference speed is one of the algorithminputs - it is read from a potentiometer. Table 3 showsthe states included in the control state machine.

TABLE 3:

The stepping through these states is done by pressingcertain buttons available on the development board.The hardware setup description available in eachsoftware archive (Readme.doc file) will indicate pre-cisely which potentiometer and which buttons are used.

As input for the sensorless field oriented vector controlthe measured current is needed. The control outputsare the three PWM module signals for controlling theinverters’ gates.

The reference rotor flux can be calculated using themotor’s parameters or if the flux weakening is used it isdetermined as a function of the speed of the rotor.

FIGURE 9: SOFTWARE STATE MACHINE

State Description

Stop The motor is stopped.Open Loop To start the motor, it must be passed

through this state, which determines the rotor position.

Closed Loop The actual sensorless field oriented control SVM is executed.

Closed Loop Double Speed

Closed loop algorithm doubling the reference speed. Necessary for PI Controller parameters tuning and for data acquisition.

STOP

OPEN LOOP

CLOSED LOOP

CLOSED LOOPDOUBLE SPEED

BUTTON COMMAND

SENSORLESS FOC SVMALGORITHM

DATA ACQUISITION ISR

USER COMMAND AND INTERFACE TASK

LCD DISPLAY AND LED STATUS

INFINITE LOOP

INTERRUPT


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FIGURE 10: SOFTWARE DATA FLOW
Code PerformanceFor MC1 board, using a dsPIC30F, the followingperformance is achieved:

• Execution time: 212-250 cycles• Clock speed: 7.2-8.5 µs @ 29.491 MHz• Code size: 226 words• RAM: less than 76 words

Forward Park

Reference VαVoltage

Forward Clarke

Measured Id Current

Measured Iq Current

Estimated Angle

Reference VβVoltage

Angle and Speed Estimator

Estimated Angle

Estimated Speed

Reference Flux Reference Id

CurrentReference

Speed

PI ControllerPI Controller

Reference Iq Current

PI Controller

Reference Vq Voltage

Reference Vd Voltage

Inverse Clarke

Reference VαVoltage

Reference VβVoltage

SVM

Reference Va Voltage

Reference Vb VoltageReference Vc Voltage

Estimated Angle

+

-

-

+

-

+

~ Measured Iα Current

Measured

Iβ Current

Iα CurrentMeasuredIβ Current

Measured


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IMPLEMENTATION AND RESULTS

Speed and Angle EstimatorThe estimator block has as inputs the currents andvoltages obtained after Park transform (see Figure 3).The estimator equations implemented in theapplication software are described below.

The BEMF voltages are calculated as shown inEquation 9.

EQUATION 9:

As shown in Figure 11, the shaded area representsEquation 9.


Figure 12 shows the resulting waveform of theinductive BEMF.

EstimParm.qVIndalpha = ((long)MotorEstimParm.qLsDt * (long)(EstimParm.qDIalpha))>>10;

where MotorEstimParm.qLsDt is 210 δ LsIo

Uo 8 Tsample⋅ ⋅( )------------------------------------------⋅ ⋅

d,q

α,β

1s

1s1s

d,q

α,β

σLs

Rs

Rs

σLs

Vα

Vβ

Iβ

IαEd

EqEqf

Edf

ωmR

Iq

Id

ω2ωmech

ImR

-

Magnetizing curve

LPF

LPF

LPF

Sign

SWITCH ΨmRref

+

+

-

-

+

--

+

+

ρestim

Eα

Eβ

RR/1 σR

+


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FIGURE 12: INDUCTIVE BEMF RESULTS

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To reduce noise, the derivation of the current is madeevery eight interrupt cycles. SinceMotorEstimParm.qLsDt is scaled with 210 it isnecessary to limit EstimParm.qDIalpha andEstimParm.qDIbeta between -1023 and 1023.Equation 10 shows how the α component of the BEMFis calculated.
EQUATION 10:



Figure 14 shows the resulting waveform of the α BEMF.

EstimParm.qEsa = ParkParm.qValpha-(((long)MotorEstimParm.qRs * (long)ParkParm.qIalpha) >>15)- EstimParm.qVIndalpha;

where MotorEstimParm.qRs is Rs 215 IoUo------⋅ ⋅

d,q

α,β

1s

1s1s

d,q

α,β

σLs

Rs

Rs

σLs

Vα

Vβ

Iβ

IαEd

EqEqf

Edf

ωmR

Iq

Id

ω2ωmech

ImR

-

Magnetizing curve

LPF

LPF

LPF

Sign

SWITCH ΨmRref

+

+

-

-

+

--

+

+

ρestim

Eα

Eβ

RR/1 σR

+


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FIGURE 14: α BEMF RESULTS

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Continuing, the calculated α-β components of theBEMF are transformed to the d-q coordinates, asshown in Equation 11. The transformation angle is theestimated flux angle ρestim calculated in the last controlstep, as shown in Figure 15.
EQUATION 11:



Figure 16 shows the resulting waveform of the α-β andd-q BEMF.

EstimParm.qEsd = (((long)EstimParm.qEsa * (long)SincosParm.qCos) >> 15) + (((long)EstimParm.qEsb * (long)SincosParm.qSin) >> 15);

d,q

α,β

1s

1s1s

d,q

α,β

σLs

Rs

Rs

σLs

Vα

Vβ

Iβ

IαEd

EqEqf

Edf

ωmR

Iq

Id

ω2ωmech

ImR

-

Magnetizing curve

LPF

LPF

LPF

Sign

SWITCH ΨmRref

+

+

-

-

+

--

+

+

ρestim

Eα

Eβ

RR/1 σR

+


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FIGURE 16: α-β, AND d-q BEMF RESULTS

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The d-q components of the BEMF should be filtered(see Equation 12) to reduce the noise from the currentmeasurements. The time constant of the first orderlow-pass filter should be chosen so that the noise onthe signal is significantly reduced; however, dynamicchanges of EstimParm.qEsdf andEstimParm.qEsqf are possible.
EQUATION 12:



Figure 18 shows the resulting waveform of the d-qBEMF filter.

EstimParm.qEsdStateVar = EstimParm.qEsdStateVar + ((long)(EstimParm.qEsd - EstimParm.qEsdf) * (long)EstimParm.qKfilterd);EstimParm.qEsdf = (int)(EstimParm.qEsdStateVar >> 15);

where EstimParm.qKfilterd is 215 TsampleTd

------------------⋅

d,q

α,β

1s

1s1s

d,q

α,β

σLs

Rs

Rs

σLs

Vα

Vβ

Iβ

IαEd

EqEqf

Edf

ωmR

Iq

Id

ω2ωmech

ImR

-

Magnetizing curve

LPF

LPF

LPF

Sign

SWITCH ΨmRref

+

+

-

-

+

--

+

+

ρestim

Eα

Eβ

RR/1 σR

+


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FIGURE 18: d-q BEMF FILTER RESULTS

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The correction of the estimated angular speed iscorrected with the BEMF on the d-axis added orsubtracted depending on the sign of BEMF on theq-axis.
EQUATION 13:



if(EstimParm.qEsqf>0){EstimParm.qOmegaMr = (((long)MotorEstimParm.qInvPsi*(long)EstimParm.qEsqf) >> 15) - EstimParm.qEsdf;} else{EstimParm.qOmegaMr = (((long)MotorEstimParm.qInvPsi * (long)EstimParm.qEsqf) >> 15) + EstimParm.qEsdf}

where MotorEstimParm.qInvPsi is equal to 1 δR+( ) U0 215⋅ ⋅

Ψref ω 0⋅--------------------------------------------

d,q

α,β

1s

1s1s

d,q

α,β

σLs

Rs

Rs

σLs

Vα

Vβ

Iβ

IαEd

EqEqf

Edf

ωmR

Iq

Id

ω2ωmech

ImR

-

Magnetizing curve

LPF

LPF

LPF

Sign

SWITCH ΨmRref

+

+

-

-

+

--

+

+

ρestim

Eα

Eβ

RR/1 σR

+


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As shown in Equation 14, the flux frequency is thenlimited to augment the stability and convergence of theestimator.
EQUATION 14:

Figure 20 shows the resulting waveform of theestimated angular speed.

FIGURE 20: ESTIMATED ANGULAR SPEED RESULTS

if(EstimParm.qOmegaMr>EstimParm.qOmegaMrMax){EstimParm.qOmegaMr=EstimParm.qOmegaMrMax;}if(EstimParm.qOmegaMr<EstimParm.qOmegaMrMin){EstimParm.qOmegaMr=EstimParm.qOmegaMrMin;}


AN1162
The angle of the magnetizing current is calculated byintegrating the flux frequency.
EQUATION 15:



Figure 22 shows the results of the estimated rotorangle.

EstimParm.qRhoStateVar = EstimParm.qRhoStateVar + (long)(EstimParm.qOmegaMr) * (long)(EstimParm.qDeltaT);EstimParm.qRho = (int) (EstimParm.qRhoStateVar>>15);

where EstimParm.qDeltaT is 215 Tsampleω 0ε0------⋅ ⋅

d,q

α,β

1s

1s1s

d,q

α,β

σLs

Rs

Rs

σLs

Vα

Vβ

Iβ

IαEd

EqEqf

Edf

ωmR

Iq

Id

ω2ωmech

ImR

-

Magnetizing curve

LPF

LPF

LPF

Sign

SWITCH ΨmRref

+

+

-

-

+

--

+

+

ρestim

Eα

Eβ

RR/1 σR

+


AN1162
FIGURE 22: ESTIMATED ANGLE RESULTS

AN1162
The current model software module (curmodel.s),calculates the magnetizing current value, which is notrequired for the estimator. It is possible to avoid thisrequirement by ensuring that the magnetizing current isset to a constant reference value at all times.
EQUATION 16:



EstimParm.qImrStateVar=EstimParm.qImrStateVar+( (long)(ParkParm.qId - EstimParm.qImr) * (long)MotorEstimParm.qInvTr) ;EstimParm.qImr = (int)(EstimParm.qImrStateVar>>15);

where MotorEstimParm.qInvTr is 215 TsampleTr

------------------⋅

d,q

α,β

1s

1s1s

d,q

α,β

σLs

Rs

Rs

σLs

Vα

Vβ

Iβ

IαEd

EqEqf

Edf

ωmR

Iq

Id

ω2ωmech

ImR

-

Magnetizing curve

LPF

LPF

LPF

Sign

SWITCH ΨmRref

+

+

-

-

+

--

+

+

ρestim

Eα

Eβ

RR/1 σR

+


AN1162
The mechanical speed is calculated in two steps. Thefirst step is calculate the slip velocity assuming that thecurrent model is not executed, as shown inEquation 17.
EQUATION 17:

The second step is to subtract the slip velocity from therotor flux velocity and filter, as shown in Equation 18.

EQUATION 18:

As shown in Figure 24, the shaded area representsEquation 17 and Equation 18.

EstimParm.qOmeg2Estim = ((long)ParkParm.qIq*(long)MotorEstimParm.qRrInvTr)>>15;

where MotorEstimParm.qRInvTr is 215 I0ω 0 Tr Idref⋅ ⋅-------------------------------⋅

EstimParm.qVelEstimStateVar=EstimParm.qVelEstimStateVar+( (long)(EstimParm.qOmegaMr-EstimParm.qOmeg2Estim-EstimParm.qVelEstim)*(long)EstimParm.qVelEstimFilterK );EstimParm.qVelEstim = (int)(EstimParm.qVelEstimStateVar>>15);EstimParm.qVelEstim= (int) ((long)EstimParm.qVelEstim*(long)Polpair)>>15);

where EstimParm.qVelEstimFilterK is and Polpair is 215 TsampleTω

------------------⋅215

Ppol---------- 1–


AN1162
Figure 25 shows the results of the estimatedmechanical speed.

FIGURE 25: MECHANICAL SPEED ESTIMATION RESULTS

d,q

α,β

1s

1s1s

d,q

α,β

σLs

Rs

Rs

σLs

Vα

Vβ

Iβ

IαEd

EqEqf

Edf

ωmR

Iq

Id

ω2ωmech

ImR

-

Magnetizing curve

LPF

LPF

LPF

Sign

SWITCH ΨmRref

+

+

-

-

+

--

+

+

ρestim

Eα

Eβ

RR/1 σR

+


AN1162
Sensorless versus SensoredThe experimental results prove that there is nosignificant difference between the step response of thesensorless control and the sensored control (seeFigure 26). The estimator can replace the sensorwithout reduction of the dynamic of the control.
As shown in Figure 27, the results prove that theestimated speed at steady state condition has a goodaccuracy, which can be compared with the speedinformation from the sensor.

FIGURE 26: EXPERIMENTAL RESULTS: SENSORED (LEFT) VS. SENSORLESS (RIGHT)

FIGURE 27: SPEED ESTIMATION ACCURACY


AN1162

STARTUP AND TUNINGTo increase the stability of the sensorless control ofACIM, the following startup strategy is employed, whichlimits the lowest allowed reference speed and allowssafe startup from a standstill.

• When the motor is running and the analog reference value (CtrlParm.qVelRef) is below the minimum limit set by software (qVelMinContrOff/2), the control speed reference value (PIParmQref.qInRef) is set to ‘0’. Speed control is deactivated.

• When the motor is running and the analog reference value (CtrlParm.qVelRef) is greater than the minimum limit set by software (qVelMinContrOff/2), the speed controller reference value (PIParmQref.qInRef) is set to the analog reference value (CtrlParm.qVelRef).

• When the motor is at a standstill and the analog reference value (CtrlParm.qVelRef) is greater than the minimum limit set by software (qVelMinContrOff), the control speed reference value(PIParmQref.qInRef) is set to the analog reference value (CtrlParm.qVelRef).

To make tuning the PI Controller parameters easier, theTorque mode can be used. In Torque mode, the speedcontroller remains inactive and the torque referencevalue is set directly, bypassing the PI speed controller.Torque mode is also possible at low speeds and at astandstill. No startup or limitation algorithm is usedwhen this control mode is selected.

To select the Torque mode, simply define it within theacim.c file, as follows:#define TORQUE_MODE

Figure 28 shows the high-dynamic torque responseduring the change in reference value. The magnetizingcurrent remains unchanged while the motor continuesto accelerate until the voltage source limit is reachedand the torque falls to zero.

FIGURE 28: SPEED RESPONSE


AN1162

CONCLUSIONThis application note presents a solution forimplementing a sensorless field oriented control of anACIM using Microchip’s dsPIC30F and dsPIC33Fdigital signal controllers. The obtained results do notdiffer significantly from the sensored version of the fieldoriented control from the dynamics perspective, but itsignificantly reduces the cost of the system.

REFERENCES• AN887 “AC Induction Motor Fundamentals”

(DS00887), Microchip Technology Inc., 2003• AN908 “Using the dsPIC30F for Vector Control of

an ACIM” (DS00908), Microchip Technology Inc., 2007

• dsPICDEM™ MC1 Motor Control Development Board User’s Guide (DS70098), Microchip Technology Inc., 2003

• dsPICDEM™ MC1H 3-Phase High Voltage Power Module User’s Guide (DS70096), Microchip Technology Inc., 2004

• Explorer 16 Development Board User’s Guide (DS51589), Microchip Technology Inc., 2005

• Motor Control Interface PICtail™ Plus Daughter Board User’s Guide (DS51674), Microchip Technology Inc., 2007


AN1162
NOTES:

Note the following details of the code protection feature on Microchip devices:• Microchip products meet the specification contained in their particular Microchip Data Sheet.

• Microchip believes that its family of products is one of the most secure families of its kind on the market today, when used in the intended manner and under normal conditions.

• There are dishonest and possibly illegal methods used to breach the code protection feature. All of these methods, to our knowledge, require using the Microchip products in a manner outside the operating specifications contained in Microchip’s Data Sheets. Most likely, the person doing so is engaged in theft of intellectual property.

• Microchip is willing to work with the customer who is concerned about the integrity of their code.

• Neither Microchip nor any other semiconductor manufacturer can guarantee the security of their code. Code protection does not mean that we are guaranteeing the product as “unbreakable.”

Code protection is constantly evolving. We at Microchip are committed to continuously improving the code protection features of ourproducts. Attempts to break Microchip’s code protection feature may be a violation of the Digital Millennium Copyright Act. If such actsallow unauthorized access to your software or other copyrighted work, you may have a right to sue for relief under that Act.

Information contained in this publication regarding deviceapplications and the like is provided only for your convenienceand may be superseded by updates. It is your responsibility toensure that your application meets with your specifications.MICROCHIP MAKES NO REPRESENTATIONS ORWARRANTIES OF ANY KIND WHETHER EXPRESS ORIMPLIED, WRITTEN OR ORAL, STATUTORY OROTHERWISE, RELATED TO THE INFORMATION,INCLUDING BUT NOT LIMITED TO ITS CONDITION,QUALITY, PERFORMANCE, MERCHANTABILITY ORFITNESS FOR PURPOSE. Microchip disclaims all liabilityarising from this information and its use. Use of Microchipdevices in life support and/or safety applications is entirely atthe buyer’s risk, and the buyer agrees to defend, indemnify andhold harmless Microchip from any and all damages, claims,suits, or expenses resulting from such use. No licenses areconveyed, implicitly or otherwise, under any Microchipintellectual property rights.

© 2008 Microchip Technology Inc.

Trademarks

The Microchip name and logo, the Microchip logo, Accuron, dsPIC, KEELOQ, KEELOQ logo, MPLAB, PIC, PICmicro, PICSTART, PRO MATE, rfPIC and SmartShunt are registered trademarks of Microchip Technology Incorporated in the U.S.A. and other countries.

AmpLab, FilterLab, Linear Active Thermistor, MXDEV, MXLAB, SEEVAL, SmartSensor and The Embedded Control Solutions Company are registered trademarks of Microchip Technology Incorporated in the U.S.A.

Analog-for-the-Digital Age, Application Maestro, CodeGuard, dsPICDEM, dsPICDEM.net, dsPICworks, dsSPEAK, ECAN, ECONOMONITOR, FanSense, In-Circuit Serial Programming, ICSP, ICEPIC, Mindi, MiWi, MPASM, MPLAB Certified logo, MPLIB, MPLINK, mTouch, PICkit, PICDEM, PICDEM.net, PICtail, PowerCal, PowerInfo, PowerMate, PowerTool, REAL ICE, rfLAB, Select Mode, Total Endurance, UNI/O, WiperLock and ZENA are trademarks of Microchip Technology Incorporated in the U.S.A. and other countries.

SQTP is a service mark of Microchip Technology Incorporated in the U.S.A.

All other trademarks mentioned herein are property of their respective companies.

© 2008, Microchip Technology Incorporated, Printed in the U.S.A., All Rights Reserved.

Printed on recycled paper.

DS01162A-page 33

Microchip received ISO/TS-16949:2002 certification for its worldwide headquarters, design and wafer fabrication facilities in Chandler and Tempe, Arizona; Gresham, Oregon and design centers in California and India. The Company’s quality system processes and procedures are for its PIC® MCUs and dsPIC® DSCs, KEELOQ® code hopping devices, Serial EEPROMs, microperipherals, nonvolatile memory and analog products. In addition, Microchip’s quality system for the design and manufacture of development systems is ISO 9001:2000 certified.


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