Sensorless Field Oriented Control (FOC) of a Permanent ......oriented control for PMSM using Microchip digital signal controllers. The control software offers these features: • Implements

AN1078Sensorless Field Oriented Control of a PMSM

INTRODUCTIONDesigners can expect environmental demands tocontinue to drive the need for advanced motor controltechniques that produce energy efficient airconditioners, washing machines and other homeappliances. Until now, sophisticated motor controlsolutions have only been available from proprietarysources. However, the implementation of advanced,cost-effective motor control algorithms is now a reality,thanks to the new generation of Digital SignalControllers (DSCs).

An air conditioner, for example, requires fast responsefor speed changes in the motor. Advanced motorcontrol algorithms are needed to produce quieter unitsthat are more energy efficient. Field Oriented Control(FOC) has emerged as the leading method to achievethese environmental demands.

This application note discusses the implementation ofa sensorless FOC algorithm for a Permanent MagnetSynchronous Motor (PMSM) using the MicrochipdsPIC® DSC family.

Why Use the FOC Algorithm?The traditional control method for BLDC motors drivesthe stator in a six-step process, which generatesoscillations on the produced torque. In six-step control,a pair of windings is energized until the rotor reachesthe next position, and then the motor is commutated tothe next step. Hall sensors determine the rotor positionto electronically commutate the motor. Advancedsensorless algorithms use the back-EMF generated inthe stator winding to determine the rotor position.

The dynamic response of six-step control (also calledtrapezoidal control) is not suitable for washingmachines because the load is changing dynamicallywithin a wash cycle, and varies with different loads andthe selected wash cycle. Further, in a front loadwashing machine, the gravitational power worksagainst the motor load when the load is on the top sideof the drum. Only advanced algorithms such as FOCcan handle these dynamic load changes.

This application note focuses on the PMSM-basedsensorless FOC control of appliances because thiscontrol technique offers the greatest cost benefit inappliance motor control. The sensorless FOCtechnique also overcomes restrictions placed on someapplications that cannot deploy position or speedsensors because the motor is flooded, or because ofwire harness placement constraints. With a constantrotor magnetic field produced by a permanent magneton the rotor, the PMSM is very efficient when used in anappliance. In addition, its stator magnetic field isgenerated by sinusoidal distribution of windings. Whencompared to induction motors, a PMSM is powerful forits size. It is also electrically less noisy than a DC motor,since brushes are not used.

Why Use Digital Signal Controllers for Motor Control?dsPIC DSCs are suitable for appliances like washingmachines and air conditioner compressors becausethey incorporate peripherals that are ideally suited formotor control, such as:

• Pulse-Width Modulation (PWM)• Analog-to-Digital Converter (ADC) • Quadrature Encoder Interface (QEI)

When performing controller routines and implementingdigital filters, dsPIC DSCs enable designers to optimizecode because MAC instructions and fractionaloperations can be executed in a single cycle. Also, foroperations that require saturation capabilities, thedsPIC DSCs help avoid overflows by offering hardwaresaturation protection.

The dsPIC DSCs need fast and flexibleAnalog-to-Digital (A/D) conversion for currentsensing—a crucial function in motor control. The dsPICDSCs feature ADCs that can convert input samples at1 Msps rates, and handle up to four inputssimultaneously. Multiple trigger options on the ADCsenable use of inexpensive current sense resistors tomeasure winding currents. For example, the ability totrigger A/D conversions with the PWM module allowsinexpensive current sensing circuitry to sense inputs atspecific times (switching transistors allow current toflow through sense resistors).

Authors: Jorge Zambada and Debraj DebMicrochip Technology Inc.

© 2010 Microchip Technology Inc. DS01078B-page 1

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MOTOR CONTROL WITH DIGITAL SIGNAL CONTROLLERSThe dsPIC DSC Motor Control family is specificallydesigned to control the most popular types of motors,including:

• AC Induction Motor (ACIM)• Brushed DC Motor (BDC)• Brushless DC Motor (BLDC)• Permanent Magnet Synchronous Motor (PMSM)

Several application notes have been published basedon the dsPIC DSC motor control family (see the“References” section). These application notes areavailable on the Microchip web site(www.microchip.com).

This application note demonstrates how the dsPICDSC takes advantage of peripherals specifically suitedfor motor control (motor control PWM and high-speedADC) to execute sensorless field oriented control of aPMSM. The DSP engine of the dsPIC DSC supportsthe necessary fast mathematical operations.

Data Monitoring and Control Interface The Data Monitor and Control Interface (DMCI) pro-vides quick dynamic integration with MPLAB® IDE forprojects in which operational constraints of the applica-tion depend on variable control of range values, on/offstates or discrete values. If needed, application feed-back can be represented graphically. Examples includemotor control and audio processing applications.

The DMCI provides:

• Nine slider controls and nine boolean (on/off) controls (see Figure 1)

• 35 input controls (see Figure 2)• Four graphs (see Figure 3)

The interface provides project-aware navigation ofprogram symbols (variables) that can be dynamicallyassigned to any combination of slider, direct input orboolean controls. The controls can then be usedinteractively to change values of program variableswithin MPLAB IDE. The graphs can be dynamicallyconfigured for viewing program generated data.

Application HighlightsThe purpose of this application note is to illustrate asoftware-based implementation of sensorless, fieldoriented control for PMSM using Microchip digitalsignal controllers.

The control software offers these features:

• Implements vector control of a PMSM.• Position and speed estimation algorithm.

eliminates the need for position sensors.• Speed range tested from 500 to 17000 RPM.• With a 50 µs control loop period, the software

requires approximately 21 MIPS of CPU overhead (about 2/3 of the total available CPU).

• The application requires 450 bytes of data memory storage. With the user interface, approximately 6 Kbytes of program memory are required. The memory requirements of the application allow it to run on the dsPIC33FJ12MC202, which is the smallest and most cost-effective dsPIC33F device at the time of this writing.

• An optional diagnostics mode can be enabled to allow real-time observation of internal program variables on an oscilloscope. This feature facilitates control loop adjustment.

Note: The characteristics of the DMCI tool aresubject to change. This description of theDMCI tool is accurate at the date ofpublication.

DS01078B-page 2 © 2010 Microchip Technology Inc.

http://www.microchip.com

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FIGURE 1: DYNAMIC DATA CONTROL INTERFACE
FIGURE 2: USER-DEFINED DATA INPUT CONTROLS


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FIGURE 3: GRAPHICAL DATA VIEW

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SYSTEM OVERVIEWAs shown in Figure 4, there are no position sensorsattached to the motor shaft. Instead, low-inductanceshunt resistors, which are part of the inverter are usedfor current measurements on the motor. A 3-phaseinverter is used as the power stage to drive motorwindings. Current sensing and fault generation circuitrybuilt into the power inverter protects the overall systemagainst over currents.

Figure 5 illustrates how the 3-phase topology, as wellas the current detection and fault generation circuitry,are implemented.

The first transistor shown on the left side of the inverteris used for Power Factor Correction (PFC), which is notpart of this application note.

The hardware that is referred to in this application noteare the dsPICDEM™ MCLV Development Board(DM330021) (up to 50 VDC) and the dsPICDEM™MCHV Development Board (DM330023) (up to400 VDC), which are available from the Microchip website (www.microchip.com).

FIGURE 4: SYSTEM OVERVIEW

FIGURE 5: 3-PHASE TOPOLOGY

PWM1H

PWM1L

PWM2H

PWM2L

PWM3H

PWM3L

3-PhaseInverter

AN0

AN1

RB8

Ia

Ib

Over Current

3-PhasePMSM

VR1Speed DemandAN8

S2Start/StopRA8

dSPI

C33

FJ32

MC

204

User Interface

PWM1H

PWM1L

PWM2H

PWM2L

PWM3H

PWM3L

115/230 VAC

PMSM

Ia Ib< CurrentLimit

Fault

Optional Power Factor Correction


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FIELD ORIENTED CONTROL

A Matter of PerspectiveOne way to understand how FOC (sometimes referredto as vector control) works is to form a mental image ofthe coordinate reference transformation process. If youpicture an AC motor operation from the perspective ofthe stator, you see a sinusoidal input current applied tothe stator. This time variant signal generates a rotatingmagnetic flux. The speed of the rotor is a function of therotating flux vector. From a stationary perspective, thestator currents and the rotating flux vector look like ACquantities.

Now, imagine being inside the motor and runningalongside the spinning rotor at the same speed as therotating flux vector generated by the stator currents. Ifyou were to look at the motor from this perspectiveduring steady state conditions, the stator currents looklike constant values, and the rotating flux vector isstationary.

Ultimately, you want to control the stator currents toobtain the desired rotor currents (which cannot bemeasured directly). With coordinate referencetransformation, the stator currents can be controlledlike DC values using standard control loops.

Vector Control SummaryThe indirect vector control process can be summarizedas follows:

1. The 3-phase stator currents are measured.These measurements provide values ia and ib. Icis calculated by the following equation:

ia + ib + ic = 0.

2. The 3-phase currents are converted to atwo-axis system. This conversion provides thevariables iα and iβ from the measured ia and iband the calculated ic values. iα and iβ aretime-varying quadrature current values asviewed from the perspective of the stator.

3. The two-axis coordinate system is rotated toalign with the rotor flux using a transformationangle calculated at the last iteration of thecontrol loop. This conversion provides the Id andIq variables from iα and iβ. Id and Iq are thequadrature currents transformed to the rotatingcoordinate system. For steady state conditions,Id and Iq are constant.

4. Error signals are formed using Id, Iq andreference values for each. • The Id reference, controls rotor magnetizing

flux• The Iq reference, controls the torque output

of the motor• The error signals are input to PI controllers• The output of the controllers provide Vd and

Vq, which are voltage vector that will be sent to the motor

5. A new transformation angle is estimated wherevα, vβ, iα and iβ are the inputs. The new angleguides the FOC algorithm as to where to placethe next voltage vector.

6. The Vd and Vq output values from the PIcontrollers are rotated back to the stationaryreference frame using the new angle. Thiscalculation provides the next quadrature voltagevalues vα and vβ.

7. The vα and vβ values are transformed back to3-phase values va, vb and vc. The 3-phasevoltage values are used to calculate new PWMduty cycle values that generate the desiredvoltage vector. The entire process oftransforming, PI iteration, transforming back andgenerating PWM is illustrated in Figure 6.

The next sections of this application note describethese steps in greater detail.


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FIGURE 6: VECTOR CONTROL BLOCK DIAGRAM
α,β

α, β

α, β

d,q

d,q

a,b,c

PI PI

SVM3-Phase Bridge

ω REF IQREF

PI

Vq

Vd

Vα

Vβ

ia

ib

Motor

Speed (ω )

∑ ∑

∑

- -

-

Position and Speed

Estimator

Position Vα

Vβ

Iq

Id

θ InverseParkTransform

InverseClarkeTransform

ParkTransform

ClarkeTransform

iα

iβ

IDREF


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COORDINATE TRANSFORMSThrough a series of coordinate transforms, you canindirectly determine and control the time invariantvalues of torque and flux with classic PI control loops.The process begins by measuring the 3-phase motorcurrents. In practice, the instantaneous sum of thethree current values is zero. Therefore, by measuringonly two of the three currents, you can determine thethird. Because of this fact, hardware cost can bereduced by the expense of the third current sensor.

A single shunt implementation for 3-phase currentmeasurement is also possible with the dsPIC DSC.Refer to the AN1299, “Single-Shunt Three-PhaseCurrent Reconstruction Algorithm for Sensorless FOCof a PMSM” (DS01299) for detailed description ofsingle shunt algorithm.

Clarke TransformThe first coordinate transform, called the ClarkeTransform, moves a three-axis, two-dimensionalcoordinate system, referenced to the stator, onto atwo-axis system, keeping the same reference (seeFigure 7, where ia, ib and ic are the individual phasecurrents).

FIGURE 7: CLARKE TRANSFORM

Park TransformAt this point, you have the stator current representedon a two-axis orthogonal system with the axis calledα-β. The next step is to transform into another two-axissystem that is rotating with the rotor flux. Thistransformation uses the Park Transform, as illustratedin Figure 8. This two-axis rotating coordinate system iscalled the d-q axis. θ represents the rotor angle.

FIGURE 8: PARK TRANSFORM

PI ControlThree PI loops are used to control three interactivevariables independently. The rotor speed, rotor flux androtor torque are each controlled by a separate PImodule. The implementation is conventional andincludes term (Kc.Excess) to limit integral windup, asillustrated in Figure . Excess is calculated bysubtracting the unlimited output (U) and limited output(Out). The term Kc multiplies the Excess and limitsthe accumulated integral portion (Sum).

FIGURE 9: PI CONTROL

α

βClarke

ab

(c)

ia + ib + ic = 0iα = iaiβ = (ia +2ib)/√ 3

βb

a,α

c

iα

iβ is

IqIdPark

iαiβθ

Id = iα cosθ + iβ sinθIq = -iα sinθ + iβ cosθ

βq

αiα

iβ

is θIqId

d

KP Err Ki E∫ RRdt••+•

InRef

-

∑ Out

Err = InRef - FB U = Sum + Kp.Err If (U > Outmax) Out = Outmax else if (U < Outmin) Out = Outmin else Out = U Excess = U - Out

Sum = Sum + (Ki.Err)-(Kc.Excess)

FB(Feedback)


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PID CONTROLLER BACKGROUNDA complete discussion of Proportional IntegralDerivative (PID) controllers is beyond the scope of thisapplication note; however, this section provides youwith some basics of PID operation.
A PID controller responds to an error signal in a closedcontrol loop and attempts to adjust the controlledquantity to achieve the desired system response. Thecontrolled parameter can be any measurable systemquantity such as speed, torque or flux. The benefit ofthe PID controller is that, it can be adjusted empiricallyby varying one or more gain values and observing thechange in the system response.

A digital PID controller is executed at a periodicsampling interval. It is assumed that the controller isexecuted frequently enough so that the system can beproperly controlled. The error signal is formed bysubtracting the desired setting of the parameter to becontrolled from the actual measured value of thatparameter. The sign of the error indicates the directionof change required by the control input.

The Proportional (P) term of the controller is formed bymultiplying the error signal by a P gain, causing the PIDcontroller to produce a control response that is afunction of the error magnitude. As the error signalbecomes larger, the P term of the controller becomeslarger to provide more correction.

The effect of the P term tends to reduce the overallerror as time elapses. However, the effect of the P termdiminishes as the error approaches zero. In mostsystems, the error of the controlled parameter gets veryclose to zero but does not converge. The result is asmall remaining steady state error.

The Integral (I) term of the controller is used toeliminate small steady state errors. The I termcalculates a continuous running total of the error signal.Therefore, a small steady state error accumulates intoa large error value over time. This accumulated errorsignal is multiplied by an I gain factor and becomes theI output term of the PID controller.

The Differential (D) term of the PID controller is used toenhance the speed of the controller and responds tothe rate of change of the error signal. The D term inputis calculated by subtracting the present error valuefrom a prior value. This delta error value is multiplied bya D gain factor that becomes the D output term of thePID controller.

The D term of the controller produces more controloutput as the system error changes more rapidly. Notall PID controllers will implement the D or, lesscommonly, the I terms. For example, this applicationdoes not use the D terms due to the relatively slowresponse time of motor speed changes. In this case,the D term could cause excessive changes in PWMduty cycle that could affect the operation of thealgorithms and produce over current trips.

Adjusting the PID GainsThe P gain of a PID controller sets the overall systemresponse. When you first tune a controller, set the I andD gains to zero. You can then increase the P gain untilthe system responds well to set point changes withoutexcessive overshoot or oscillations. Using lower valuesof P gain will ‘loosely’ control the system, while highervalues will give ‘tighter’ control. At this point, the systemwill probably not converge to the set point.After you select a reasonable P gain, you can slowlyincrease the I gain to force the system error to zero.Only a small amount of I gain is required in mostsystems. The effect of the I gain, if large enough, canovercome the action of the P term, slow the overallcontrol response and cause the system to oscillatearound the set point. If oscillation occurs, reducing theI gain and increasing the P gain will usually solve theproblem.This application includes a term to limit integral windup,which occurs if the integrated error saturates the outputparameter. Any further increase in the integrated errordoes not affect the output. The accumulated error,when it does decrease, will have to fall (or unwind) tobelow the value that caused the output to saturate. TheKc coefficient limits this unwanted accumulation. Formost situations, this coefficient can be set equal to Ki.All three controllers have a maximum value for theoutput parameter. These values can be found in theUserParms.h file and are set by default to avoidsaturation in the SVGen() routine.

Control Loop DependenciesThere are three interdependent PI control loops in thisapplication. The outer loop controls the motor velocity.The two inner loops control the transformed motorcurrents, Id and Iq. As mentioned previously, the Id loopis responsible for controlling flux, and the Iq value isresponsible for controlling the motor torque.

Inverse ParkAfter the PI iteration, you have two voltage componentvectors in the rotating d-q axis. You will need to gothrough complementary inverse transforms to get backto the 3-phase motor voltage. First, you transform fromthe two-axis rotating d-q frame to the two-axisstationary frame α-β. This transformation uses theInverse Park Transform, as illustrated in Figure 10.

FIGURE 10: INVERSE PARK

VαVβ

InverseVdVq

θ

Vα = Vd.cosθ - Vq.sinθVβ = Vd.sinθ + Vq.cosθ

βq

αVα

Vβ

Vs θVq Vd

dPark


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Inverse ClarkeThe next step is to transform from the stationarytwo-axis α-β frame to the stationary three-axis, 3-phasereference frame of the stator. Mathematically, thistransformation is accomplished with the Inverse ClarkTransform, as illustrated in Figure 11.
FIGURE 11: INVERSE CLARKE

Space Vector Modulation (SVM)The final step in the vector control process is togenerate pulse-width modulation signals for the3-phase motor voltage signals. If you use Space VectorModulation (SVM) techniques, the process ofgenerating the pulse width for each of the three phasesis reduced to a few simple equations. In thisimplementation, the Inverse Clarke Transform hasbeen folded into the SVM routine, which furthersimplifies the calculations.

Each of the three inverter outputs can be in one of twostates. The inverter output can be connected to eitherthe plus (+) bus rail or the minus (-) bus rail, whichallows for 23 = 8 possible states of the output as shownin Table 1.

The two states in which all three outputs are connectedto either the plus (+) bus or the minus (-) bus areconsidered null states because there is no line-to-linevoltage across any of the phases. These are plotted atthe origin of the SVM star. The remaining six states arerepresented as vectors with 60 degree rotationbetween each state, as shown in Figure 12.

FIGURE 12: SVM

The process of SVM allows the representation of anyresultant vector by the sum of the components of thetwo adjacent vectors. In Figure 13, UOUT is the desiredresultant. It lies in the sector between U60 and U0. Ifduring a given PWM period T, U0 is output for T1/T andU60 is output for T2/T, the average for the period will beUOUT.

FIGURE 13: AVERAGE SVM

T0 represents a time where no effective voltage isapplied into the windings; that is, where a null vector isapplied. The values for T1 and T2 can be extracted withno extra calculations by using a modified Inverse Clarktransformation. If you reverse Vα and Vβ, a referenceaxis is generated that is shifted by 30 degrees from theSVM star. As a result, for each of the six segments, oneaxis is exactly opposite that segment and the other twoaxes symmetrically bound the segment. The values ofthe vector components along those two bounding axisare equal to T1 and T2. See the CalcRef.s andSVGen.s files in the source code for details of thecalculations.

You can see from Figure 14 that for the PWM period T,the vector T1 is output for T1/T and the vector T2 isoutput for T2/T. During the remaining time the nullvectors are output. The dsPIC DSC is configured forcenter-aligned PWM, which forces symmetry about thecenter of the period. This configuration produces twopulses line-to-line during each period. The effectiveswitching frequency is doubled, reducing the ripplecurrent while not increasing the switching losses in thepower devices.

Vα

Vβ

Vr1Vr2Vr3

Vr1 = VβVr2 = (-Vβ + √ 3.Vα)/2Vr3 = (-Vβ - √ 3.Vα)/2

βVr2

Vr1,α

Vr3

Vα

Vβ Vs

Inverse Clarke

U60(011)U120(010)

U180(110) U(111) U(000) U0(001)

U240(100) U300(101)

U60(011)

UOUT

T2/T. U60

T1/T .U0 U0(001)

T0 = Null VectorT = T1 + T2 + T0 = PWM PeriodUOUT = (T1/T.U0) + (T2/T.U60)


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TABLE 1: SPACE VECTOR MODULATION INVERTER STATES
FIGURE 14: PWM FOR PERIOD T

Phase C Phase B Phase A Vab Vbc Vca Vds Vqs Vector

0 0 0 0 0 0 0 0 U(000)0 0 1 VDC 0 -VDC 2/3VDC 0 U00 1 1 0 VDC -VDC VDC/3 VDC/3 U600 1 0 -VDC VDC 0 -VDC/3 VDC/3 U1201 1 0 -VDC 0 VDC -2VDC/3 0 U1801 0 0 0 -VDC VDC -VDC/3 - VDC/3 U2401 0 1 VDC -VDC 0 VDC/3 - VDC/3 U3001 1 1 0 0 0 0 0 U(111)

PWM1

PWM2

PWM3

T0/4 T1/2 T2/2 T0/4 T2/2 T1/2 T0/4T0/4

T


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SENSORLESS FOC FOR PMSMAn important part of the algorithm is how to calculatethe commutation angle needed for FOC. This section ofthe application note explains the process of estimatingcommutation angle (θ) and motor speed (ω ).

The sensorless control technique implements the FOCalgorithm by estimating the position of the motorwithout using position sensors. Figure 16 illustrates asimplified block diagram of the position estimatorfunction.

Motor position and speed are estimated based onmeasured currents and calculated voltages.

Motor ModelYou can estimate the PMSM position by using a modelof a DC Motor, which can be represented by windingresistance, winding inductance and back-EMF, asshown in Figure 15.

FIGURE 15: MOTOR MODEL

From the motor model, the input voltage can beobtained by Equation 1.

FIGURE 16: POSITION ESTIMATOR FUNCTION BLOCK DIAGRAM

es

Motor

R L

vs

is

InverterPWM1H

Fault

Ia

Ib

PMSM

Position and Speed Estimation

I

FOC Control

V

Vcc

θω

ω REF

dsPIC® DSC

PWM1LPWM2HPWM2LPWM3HPWM3LP

WM

A/D

A/D


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EQUATION 1: DIGITIZED MOTOR MODEL Calculating F and G Parameters
The motor model has two parameters that need to bemodified for a particular motor. These two parametersare F and G gains, where:

EQUATION 2:

Constants R and L are measured using a simplemultimeter. For example, if a line to line resistance ismeasured, the R used for F and G gains is themeasurement divided by two, since the phaseresistance is needed. The same procedure applies toinductance calculation L. For example, the Hurst motoris run with algorithm at 20 kHz, where the line-to-lineresistance measured is 5.34Ω, and line-to-lineinductance measured is 3.84 mH, then the motormodel parameters are:

EQUATION 3:

Current ObserverThe position and speed estimator is based on a currentobserver. This observer is a digitized model of themotor, as represented by Equation 1. Variables andconstants include:

• Motor Phase Current (is) • Input voltage (vs) • Back-EMF (es) • Winding resistance (R) • Winding inductance (L) • Control period (Ts)• Output Correction Factor Voltage (z)

vs Ris L ddt-----is es+ +=

Where:

Motor current is obtained by solving for is:

In the digital domain, this equation becomes:

Solving for is:

or

i ( 1) F i ( ) G ( ( ) ( ))

is = Motor Current Vectorvs = Input Voltage Vectores = Back-EMF VectorR = Winding ResistanceL = Winding InductanceTs = Control Period

ddt-----is

RL---–⎝ ⎠

⎛ ⎞ is1L--- vs es–( )+=

is n 1+( ) is n( )–

Ts--------------------------------------- R

L---–⎝ ⎠

⎛ ⎞ is n( ) 1L--- vs n( ) es n( )–( )+=

is n 1+( ) 1 Ts RL---•–⎝ ⎠

⎛ ⎞ is n( )TsL----- vs n( ) es n( )–( )+=

G = TLs

F 1 Ts RL---•–=

G = TLs

F 1 Ts RL---•–=

F 1 Ts RL---• 1 1

20 KHz-----------------–⎝ ⎠

⎛ ⎞ 5.34Ω( ) 2⁄3.84mH( ) 2⁄

-----------------------------------• 0.9304==–=

G TsL------ 1 20⁄( )kHz

3.84mh( ) 2⁄--------------------------------- 0.026===


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The digitized model provides a software representationof the hardware. However, in order to match the mea-sured current and estimated current, the digitizedmotor model needs to be corrected using the closedloop, as shown in Figure 17.
Considering two motor representations, one inhardware (shaded area) and one in software, with thesame input (vs) fed into both systems, and matching

the measured current (is) with estimated current(is*)from the model, we can presume that back-EMF(es*) from our digitized model is the same as the back-EMF (es) from the motor.

FIGURE 17: CURRENT OBSERVER BLOCK DIAGRAM

The sliding-mode controller has a limit valueMaxSMCError defined in UserParms.h. When theerror value is lesser than the MaxSMCError, the outputof sliding-mode controller works in the linear range asgiven by the equation beneath the PMSM block inFigure 17.

For an error value outside of the linear range, the out-put of the sliding mode controller is (+Kslide)/(-Kslide)depending on the sign of the error.

A slide-mode controller, or SMC, is used to compen-sate the digitized motor model. A SMC consists of asummation point that calculates the sign of the errorbetween measured current from the motor and esti-mated current from the digitized motor model. Thecomputed sign of the error (+1 or -1) is multiplied by aSMC gain (K). The output of the SMC controller is thecorrection factor (Z). This gain is added to the voltageterm from the digitized model, and the process repeatsevery control cycle until the error between measuredcurrent (is) and estimated current (is*) is zero (i.e., untilthe measured current and estimated current match).

Back-EMF EstimationAfter compensating the digitized model, you have amotor model with the same variable values for the inputvoltage (Vs) and for current (is*). Once the digitizedmodel is compensated, the next step is to estimateback-EMF (es*) by filtering the correction factor (Z), asshown in Figure 18. The back-EMF estimation (es*) isfed back to the model to update the variable es* afterevery control cycle. Values eα and eβ (vectorcomponents of es) are used for the estimated Thetacalculation.

Note: * implies the estimated variable.

PMSMis

is*

z

-

+ Sign(is* - is)

Vs

*Estimated variable

ddt

i*s =RL

i*s + 1L

(v - e* - z)s s

Hardware

-

Is Error < MaxSMCError?

Is Error > 0? Z = -Kslide

Error Yes

No

No

Yes

Z = +Kslide

SMC in Linear Region

Kslide Error•( )MaxSMCError----------------------------------------


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FIGURE 18: BACK-EMF ESTIMATION MODEL
Back-EMF FilteringTo provide the filtering, a first-order, digital low-passfilter is used with Equation 4.

EQUATION 4: FIRST-ORDER DIGITAL LOW-PASS FILTER:

The cut-off frequency value is set to be equal to thefrequency of the drive current and the motor voltage,which is the electrical revolutions per second. Due tothe implementation of the adaptive filter, there is a fixedphase delay of -45° (per filter) for Theta compensationin all speed ranges, because the cut-off frequencychanges as the motor gains speed.

The output of the first filter is used in two blocks. Thefirst block is the model itself, used to calculate the nextestimated current (is*), and also to calculate theestimated Theta (θ∗). A second, first-order filter is usedto calculate a smoother signal coming out of the motormodel.

Relationship Between Back-EMF and Rotor PositionOnce the back-EMF has been filtered for the secondtime, Theta is calculated. The relationship between esand θ can be explained based on the graph shown inFigure 19.

FIGURE 19: BACK-EMF AND THETA RELATIONSHIP

The plot shows a trigonometric function relating thevector components of the back-EMF (eα and eβ) androtor angle (θ). The arctangent is computed on theback-EMF vector components to calculate Theta.Equation 5 illustrates how the function is implementedin software:

EQUATION 5: THETA CALCULATION

The actual implementation uses a numeric and iterativealgorithm called Coordinate Rotation by DigitalComputer (CORDIC), which is fast, yet takes lessmemory than a floating point implementation.Discussion of the CORDIC algorithm is beyond thescope of this application note.

arctaneαeβ

efiltered*s θ*LPF

e*s

LPFz

ddt i*s = R

Li*s + 1

L(v - e* - z)s s-

From Slide-ModeController

To filter z to obtain e*, 8kHz is substituted in theequation, which results in:

Where:

e(n) = Next estimated back-EMF valuee(n-1) = Last estimated back-EMF valuefpwm = PWM frequency at which the digital

filter is being calculatedfc = Cut-off frequency of the filterz(n) = Unfiltered back-EMF, which is output

from the slide-mode controller

y n( ) y n 1–( ) T2πfc x n( ) y n( )–( )•+=

e n( ) e n 1–( ) 1fpwm-----------⎝ ⎠

⎛ ⎞ 2πfc• z n( ) e n( )–( )+=eα eβ θ

1

0.5

0

-1.5

-1

-1.5

11 21 31 41 51 61 71 81 91 101|||||||||||||||||||| |||||||||||||||||||| |||||||||||||||||||| |||||||||||||||||||||||||||||||||||||||||||||||||

1.5

θ = arctan (eα , eβ)


AN1078
Speed CalculationDue to the filtering function applied during the Thetacalculation, some phase compensation is neededbefore the calculated angle is used to energize themotor windings. The amount of Theta compensationdepends on the rate of change of Theta, or speed of themotor. The Theta compensation is performed in twosteps:
1. The speed of the motor is calculated based onthe uncompensated Theta calculation.

2. The calculated speed is filtered and used tocalculate the amount of compensation, asshown in Figure 20.

Speed is calculated by accumulating Theta values overm samples and then multiplying the accumulated Thetaby a constant. The formula used in this application notefor speed calculation is shown in Equation 6.

EQUATION 6: SPEED CALCULATION

To secure a smoother signal on the speed calculation,a first-order filter is applied to Omega (ω*) to obtainFilteredOmega (ω*filtered). The first-order filter topologyis the same as the one used for back-EMF filtering.

Adaptive FilterThe adaptive filter performs the following two functions:

• Calculation of gain for low-pass filter for the sliding-mode controller

• Dynamically compensate for Theta for the complete speed range

Two low-pass filters are implemented for the estimationof the position. The first filter, filters the output of slidingmode controller (correction factor (Z)) in to estimatedback-EMF (es*) and the second filter, filters theestimated back-EMF (es*) into the filtered estimatedback-EMF (efiltered*s). The derivation for calculatinggain for low-pass filter is shown in Equation 7.

FIGURE 20: SPEED CALCULATION BLOCK DIAGRAM

Where,

Omega (ω ) = Angular velocity of the motor

Theta (θn) = Current Theta valuePrevTheta (θn-1) = Previous Theta valueKspeed = Amplification factor for

desired speed rangem = Number of accumulated

Theta deltas

ω θn θn 1––( ) Kspeed•

i 0=

m

∑=

arctaneαeβ

LPF

θ* +

+

θ*comp

ω*

ω*filteredω θ n( ) θ n 1–( )–( )

i 0=

m 1–

∑ Kspeed•=


AN1078
EQUATION 7:
The design of the adaptive filter keeps a fixed-phasedelay for Theta compensation in all speed ranges asthe cut-off frequency keeps changing with theincreasing motor speed. Due to the implementation oftwo adaptive filters, the fixed phase delay of 90° is onlya constant offset that is added to the calculated Theta.

The following derivation explains the calculation of gain for low-pass filter, where:

Kslf = Tpwm.2 .PI .eRPS --- (3)

eRPS = (RPM .Pole_Pair)/60 --- (4)

Also,

RPM = (Q15(Omega) .60)/(SpeedLoopTime .Motor Poles) --- (5)

Substituting (5) in (4),

eRPS = (Q15(Omega) .60 .Pole Pairs)/(SpeedLoopTime . Pole Pairs.2 .60)

eRPS = Q15(Omega)/(SpeedLoopTime .2) --- (6)


Kslf = Tpwm . 2 . PI .Q15(Omega)/(SpeedLoopTime .2) --- (7)

Now,

IRP_PERCALC = SpeedLoopTime/Tpwm --- (8)


Kslf = Tpwm. 2 .Q15(Omega) .PI/(IRP_PERCALC .Tpwm .2)

Simplifying,

Kslf = Q15(Omega) .PI/IRP_PERCALC

We use a second filter to get a cleaner signal with the same coefficient:

Kslf = KslfFinal = Q15(Omega) .PI/IRP_PERCALC

Kslf = Gain of low-pass filter for sliding mode controllerTpwm = Time period of PWM in secondseRPS = Electrical rotation of motor in RPSOmega = Angular velocity of motor in rad/sSpeedLoopTime = Time for speed loop execution in secondsIRP_PERCALC = Number of PWM loops per speed loop


AN1078

FIELD WEAKENINGThe field weakening for PMSM implies imposing anegative value for the stator current on the d-axis of therotating frame, which has the role of weakening the airgap flux linkage.

In the case of an inverter, the voltage output drops onthe stator’s resistance and inductive reactance, and theremaining voltage is used to counteract BEMF. BEMFis proportional to the motor’s speed and the voltageconstant, ΚΦ, of the motor. Considering the inverter’slimitation of maximum output voltage, an increase inspeed (above nominal speed) can be achieved bydecreasing the voltage constant (ΚΦ), which isproportional with the air gap flux linkage. However, adecrease in air gap flux linkage is synonymous to thedecrease in torque. However, for certain applications,the motor needs to run higher than the rated speedsand therefore, the field weakening feature is useful,which increases the speed range of motor beyond itsnominal speed rating.

In a PMSM, the field weakening is achieved byreducing the value of Id from ‘0’ to a negative value.

The field weakening table consists of values for Iddefined in UserParms.h (from dqKFw0 to dqKFw15),which can be changed based on the user requirement.

If the user does not want to use the field weakeningfeature, allow NOMINALSPEEDINRPM to be equal toFIELDWEAKSPEEDRPM in UserParms.h.

The FieldWeakening function takes the inputparameter, velocity reference CtrlParm.qVelRef,and checks if the value is smaller or larger thanNOMINALSPEEDINRPM defined in UserParms.h.

• If the velocity reference is smaller, field weakening is not performed

• If the velocity reference is larger, the suitable value is returned from FdWeakParm.qFwCurve through linear interpolation

Figure 21 illustrates the block diagram of fieldweakening.

Figure 22 illustrates a field weakening curve, usedduring testing.

FIGURE 21: FieldWeakening FUNCTION BLOCK DIAGRAM

Q15 FieldWeakening

Where:• CtrlParm.qVelRef = Velocity command from user • CtrlParm.qVdRef = Reference for D-component PI loop

Q15abs(CtrlParm.qVelRef) CtrlParm.qVdRef

CtrlParm.qVelRef

-2.5

-2

-1.5

-1

-0.5

0

0.5

0 1000 2000 3000 4000 5000 6000


AN1078
FIGURE 22: Id vs. SHAFT RPM OF MOTOR
PERFORMANCE MODE

Speed ModeIn Speed mode, the measured motor velocity iscompared with the reference from the potentiometerusing a PI loop. The output of PI is applied as input toPI of Q-component of the current.

During the motor operation, the shaft RPM is heldconstant regardless of the variation in load. Thismode can be selected by commenting the definition //#define TORQUEMODE in UserParms.h.

Figure 23 illustrates the block diagram of the Speedmode.

FIGURE 23: SPEED MODE BLOCK DIAGRAM

-2.5

-2

-1.5

-1

-0.5

0

0.5

0 1000 2000 3000 4000 5000 6000

Series

Speed (RPM)

I d (A

mps

)

PI

smc1.Omega

CtrlParm.qVqRef

CtrlParm.qVelRef RAMP POT

Where, RAMP = Software module that provides a smooth acceleration and deceleration of motor based on input from potentiometer.To change the rate of RAMP, change SPEEDDELAY in UserParms.h.smc1.Omega = Measured velocity of motorCtrlParm.qVelRef = Velocity command from userCtrlParm.qVqRef = Output of velocity PI loop and input for PI loop of Q-component


AN1078
Torque ModeIn Torque mode, the velocity PI loop is bypassed andthe reference from the potentiometer is directly fed asinput to the PI loop of Q-component of current.
During the motor operation, the torque generated bythe motor and the current consumption are heldconstant (as set by the potentiometer). Therefore,under a heavier load, the shaft RPM may drop. Thismode can be selected by uncommenting the definition//#define TORQUEMODE in UserParms.h.

Figure 24 illustrates the block diagram of Torque mode.

Voltage Ripple CompensationThe ripple compensation is used to compensate the Vdand Vq (inputs to inverse park transform block) basedon the DC bus ripple. The user can enable the ripplecompensation section of the code through #defineENVOLTRIPPLE in UserParms.h. If this feature isenabled in the code, the software compensates for thevoltage ripple on the DC bus. This in turn makes thehardware design economical by reducing the size ofthe buffer capacitor on the DC bus.

Equation 8 describes the implementation of ripplecompensation for D-component. Figure 25 andFigure 26 illustrates the block diagram of bus voltageripple compensation for D-axis and Q-axis,respectively.

FIGURE 24: TORQUE MODE BLOCK DIAGRAM

EQUATION 8:

RAMP POT

Where,RAMP = Software module that provides a smooth acceleration and deceleration of motor based on input frompotentiometer. To change the rate of ramp, change SPEEDDELAY in UserParms.h.CtrlParm.qVelRef = Velocity command from userCtrlParm.qVqRef = Output of velocity PI loop and input for PI loop of Q-component

CtrlParm.qVelRef CtrlParm.qVqRef

ParkParm qVd• PIParmD qOut• T etDCbusarg DCbus–DCbus

----------------------------------------------------------- PIParmD qOut••+=

If(TargetDCbus > DCbus)

DCbus = Measured voltage of DC bus

TargetDCbus = Required voltage of DC bus

ParkParm qVd• T etDCbusargDCbus

----------------------------------- PIParmD qOut••=

If(DCbus > TargetDCbus)


AN1078
FIGURE 25: BUS VOLTAGE RIPPLE COMPENSATION FOR D-AXIS CURRENT(1,2)
FIGURE 26: BUS VOLTAGE RIPPLE COMPENSATION FOR Q-AXIS CURRENT(1,2)

PI Loop for D-component Ripple Compensation

Enabled

PIParmD.qOut ParkParm.qVd

Disabled

Note 1: When voltage ripple compensation is disabled, the PIParmD.qOut (output of PI loop forD-component) is passed directly to ParkParm.qVd.

2: When voltage ripple compensation is enabled, the PIParmD.qOut is passed to the functionVoltRippleComp. This function returns the compensated value which is passed to ParkParm.qVd.

Enabled

Disabled

PI Loop for Q-component Ripple Compensation

ParkParm.qVqPIParmQ.qOut

Note 1: When voltage ripple compensation is disabled, the PIParmQ.qOut (output of PI loop forQ-component) is passed directly to ParkParm.qVq.

2: When voltage ripple compensation is enabled, the PIParmQ.qOut is passed to VoltRippleComp.This function returns the compensated value which is passed to ParkParm.qVq.


AN1078

FLOW CHARTSThe FOC algorithm is executed at the same rate as thePWM. It is configured so that the PWM triggers A/Dconversions for two windings using two shunt resistorsand a potentiometer that sets the reference speed ofthe motor. Interrupts of the A/D are enabled to performthe algorithm. Figure 27 illustrates the generalexecution of the A/D interrupt subroutine.

FIGURE 27: A/D INTERRUPT SUBROUTINE

Figure 28 illustrates the process of using the Slide-Mode Controller to estimate the position and speed ofthe motor.

FIGURE 28: MOTOR POSITION AND SPEED ESTIMATION

A/D Interrupt

Use Clarke Transform to Convert

Phase CurrentsFrom 3-Axis to 2-Axis

Use Park Transformto Convert

2-Axis Currents to Rotating Coordinate System

Use Slide Mode Controllerto Estimate

Motor Position and Speed

Run PI Controllersfor

Currents and Speed

Use Inverse Park Transformto Convert

Rotating Coordinate Systemto Axis Stationary System

Use Inverse Clarke Transformto Convert

2-Axis to 3-Axis

Use Space Vector Modulationto Update

PWM Duty Cycle

End of A/D Interrupt

Filter Output FromSlide-Mode Controller

to EstimateBack-EMF

Use Slide-Mode Controllerand Motor Model

to EstimateMotor Currents

Slide-Mode Controller

Accumulated Theta count = m?

Yes

No

Filter EstimatedBack-EMFto Create

Smoother Signal

UseEstimated Rotor Position

to CalculateRotor Speed

Calculate Filter Coefficient for Adaptive Filters

End ofSlide-Mode Controller

Subroutine

Filter Estimated Speed

Use Arctangent to ComputeEstimated Motor Position

Based onEstimated Back-EMF

Compensate Theta for Fixed Phase Delay


AN1078

MOTOR START-UPSince the sensorless FOC algorithm is based on theback-EMF estimation, a minimum speed is needed toget the estimated back-EMF value. Therefore, themotor windings must be energized with the appropriateestimated angle. To handle this, a motor start-upsubroutine (see Figure 29) was developed.

When the motor is at a standstill and the Start/Stopbutton has been pressed, the dsPIC DSC generates aseries of sinusoidal voltages to start the motorspinning. The motor spins at a fixed acceleration rate,and the FOC algorithm controls the currents Id and Iq.The Theta angle (commutation angle) is incrementedbased on the acceleration rate.

As shown in the diagram, phase angle is incrementedat a squared rate to get a constant acceleration on themotor. Even if Theta is being generated by theopen-loop state machine, FOC blocks are still beingexecuted and are controlling torque component currentand flux component current. An external potentiometeris used to set the desired torque required to start themotor. This potentiometer is set experimentallydepending on mechanical load characteristics. Thisstart-up subroutine provides a constant torque to startup the motor. At the end of the start-up ramp, thesoftware switches over to closed loop, sensorlesscontrol, taking Theta from the position and speedestimator, as shown in Figure 6.

FIGURE 29: MOTOR START-UP

∑

Motor Start Up

PI

PI

-

-

θ

d,q

α, β

Motor

α, β

a,b,c

Position

∑

Iq ref 3-PhaseBridgeSVM

Iq

Id

iα

iβ

ia

Id ref

Vq

Vd

d, q

α, β

vα

vβ

ib

t

θ

(VR1)


AN1078

MAIN SOFTWARE STATE MACHINEIt is helpful to visualize the FOC algorithm as a softwarestate machine (see Figure 30). First, the motorwindings are de-energized and the system waits for theuser to press the Start/Stop button (S2 on thedsPICDEM MCLV Development Board). Once the userpresses Start/Stop button, the system enters theinitialization state, where all variables are set to theirinitial value and interrupts are enabled. Then, the start-up subroutine is executed, where current componentsfor torque (Iq) and flux production (Id) are beingcontrolled, and commutation angle (Theta) is beinggenerated in a ramp fashion to get the motor spinning.

After going through the start-up subroutine, the systemswitches over to sensorless FOC control, where thespeed controller is added to the execution thread, andthe Slide-Mode Controller (SMC) starts estimatingTheta as previously explained. When the motor enterssensorless FOC control state, the reference speed iscontinuously read from an external potentiometer andthe start/stop button is monitored to stop the motor.

Any fault in the system causes the motor to stop andreturn to the Motor Stopped state until S2 is pressedagain. The state diagram shows all the different statesof the software and the conditions that make thesystem transition to a different state.

FIGURE 30: MAIN SOFTWARE STATE MACHINE

Reset

Initialize Variables and

Peripherals

Motor Stopped

InitializeVariables forRunning the

Initialize PI ControllerParameters

EnableInterrupts

Motor Running Start Up

ReadReference

Torque fromVR1

MeasureWindingCurrents

ConvertCurrents

Iq and IdExecute

PI Controllers

Iq and Id

IncrementTheta

Ramp

Set NewDuty Cycles

SVM

Motor Running

Sensorless FOC

ReadReference

Speed

MeasureWindingCurrents

ConvertCurrents

Iq and IdEstimate

usingCalculate

Speed

CompensateTheta

Speed

ExecutePI Controllers

for Speed,

Set NewDuty Cycles

SVM

Stop Motor

A/D Interrupt

A/D InterruptEnd of Start Up Ramp

S2 Pressed

S2 Pressed or FAULT

S2 Pressed or FAULT

Motor

to

for

Based onusing

Iq and Id

using

Based onTheta

SMC

from VR2

to

Initialization State

Start-Up State

Sensorless FOC State


AN1078

BENEFITS OF DSC-BASED FOC CONTROLA major advantage of deploying DSCs in motor controlis the practicality of a common design platform, whichmakes the production of appliances more efficient. Thismeans appliance makers now have an economical wayto offer a range of appliance models that use PMSM orother type of motors with sensorless FOC algorithmcontrol.

These software-based motor control designs enablerapid customization to address multiple markets bychanging only the control parameters.

Protection of firmware Intellectual Property (IP) isanother major issue for manufacturers who frequentlydeploy appliance design teams that collaborate acrossmany geographies. It is easy to imagine a scenario inwhich the implementation of FOC for an appliance mayhave come from place A, the user-interface board fromplace B and the final system integration being done inplace C.

CONCLUSIONThis application note illustrates how designers can takeadvantage of DSCs to implement advanced motorcontrol techniques such as the Sensorless FOCalgorithm in appliance applications. Sinceprogramming a dsPIC DSC is similar to programming aMCU, appliance designers can quickly design theirmotor control algorithm and test their prototypes.

Fine tuning motor control is made easy, thanks to thepowerful IDE-based tools such as the DMCI, whichallow the designer to easily port their algorithms acrossa variety of motor platforms including PMSM, BLDC,BDC and ACIM.

REFERENCES Several application notes have been published byMicrochip Technology describing the use of DSCs formotor control.

For ACIM control see:

• AN984, “An Introduction to AC Induction Motor Control Using the dsPIC30F MCU” (DS00984)

• AN908, “Using the dsPIC30F for Vector Control of an ACIM” (DS00908)

• GS004, “Driving an ACIM with the dsPIC® DSC MCPWM Module” (DS93004)

• AN1206, “Sensorless Field Oriented Control (FOC) of an AC Induction Motor (ACIM) Using Field Weakening” (DS01206)

• AN1162, “Sensorless Field Oriented Control (FOC) of an AC Induction Motor (ACIM)” (DS01162)

For BLDC motor control see:

• AN957, “Sensored BLDC Motor Control Using dsPIC30F2010” (DS00957)

• AN1160, “Sensorless BLDC Control with Back-EMF Filtering Using a Majority Function” (DS01160)

For PMSM control see:

• AN1017, “Sinusoidal Control of PMSM Motors with dsPIC30F DSC” (DS01017)

• AN1292, “Sensorless Field Oriented Control (FOC) for a Permanent Magnet Synchronous Motor (PMSM) Using a PLL Estimator and Field Weakening (FW)” (DS01292)

• AN1299, “Single-Shunt Three-Phase Current Reconstruction Algorithm for Sensorless FOC of a PMSM” (DS01299)

For Stepper motor control see:

• AN1307, “Stepper Motor Control with dsPIC® DSCs” (DS01307)

For information on the dsPICDEM MC1 Motor ControlDevelopment Board see:

• “dsPICDEM™ MCLV Development Board User’s Guide” (DS70331)

• “dsPICDEM™ MCHV Development System User’s Guide” (DS70605)

• “dsPICDEM™ MCSM Development Board User’s Guide” (DS70610)

• “dsPICDEM™ MC1 Motor Control Development Board User’s Guide” (DS70098)

• “dsPICDEM™ MC1H 3-Phase High Voltage Power Module User’s Guide” (DS70096)

• “dsPICDEM™ MC1L 3-Phase Low Voltage Power Module User’s Guide” (DS70097)

These documents are available on the Microchip website (www.microchip.com).


www.microchip.com

AN1078

APPENDIX A: HARDWARE RESOURCES

The sensorless FOC code for a PMSM has been testedon the following development boards:

• dsPICDEM™ MCLV Development Board (DM330021)

• dsPICDEM™ MCHV Development Board (DM330023)

REVISION HISTORYRevision A (March 2007)This is the initial release of this document.

Revision B (March 2010)This revision incorporates the following updates:

• Updated third paragraph in “System Over-view”:

• Added the following sections: - “Field Weakening”- “Performance Mode”

• Note:- Added a note with information regarding the

use of asterik (*) as an estimated variable (see note above Figure 17).

• Sections:- Updated the speed range from 500RPM-

7300 RPM to 500RPM-17000 RPM in “Application Highlights”.

- Removed the following point in “Application Highlights”: An air conditioner compresser rated at 1.5 kw is targeted as the main motor.

- Removed Phase Compensation, Changing Phase Compensation Formulas section.

- Added a sub section “Adaptive Filter”.- Added a sub section “Voltage Ripple

Compensation”.• Appendix :

- Removed Hardware Modifications section in Appendix A: “Hardware Resources”.

• Figures:- Removed Figure 25 through Figure 30 from

Appendix A: “Hardware Resources”.• Additional minor corrections such as language

and formatting updates are incorporated throughout the document.


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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.

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ISBN: 978-1-60932-099-7

DS01078B-page 27

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EUROPEAustria - WelsTel: 43-7242-2244-39Fax: 43-7242-2244-393Denmark - CopenhagenTel: 45-4450-2828 Fax: 45-4485-2829France - ParisTel: 33-1-69-53-63-20 Fax: 33-1-69-30-90-79Germany - MunichTel: 49-89-627-144-0 Fax: 49-89-627-144-44Italy - Milan Tel: 39-0331-742611 Fax: 39-0331-466781Netherlands - DrunenTel: 31-416-690399 Fax: 31-416-690340Spain - MadridTel: 34-91-708-08-90Fax: 34-91-708-08-91UK - WokinghamTel: 44-118-921-5869Fax: 44-118-921-5820

01/05/10

chnology Inc.

Documents

Sensorless Field Oriented Control (FOC) of a Permanent ......oriented control for PMSM using Microchip digital signal controllers. The control software offers these features: • Implements