Fast response Antiwindup PI speed controller of Brushless DC motor drive: Modeling, simulation and implementation on DSP

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Availableonlineatwww.sciencedirect.com

ScienceDirect

JournalofElectricalSystemsandInformationTechnology3(2016)1–13

Fast

response

Antiwindup

PI

speed

controller

of

Brushless

DC

motor

drive:

Modeling,

simulation

and

implementation

on

DSP

Mohd

Tariq

a,b,∗

,

T.K.

Bhattacharya

b

,

Nidhi

Varshney

a

,

Dhilsha

Rajapan

a

a_National_Institute_of_Ocean_Technology,_Ministry_of_Earth_Sciences,_Government_of_India,_Chennai_600100,_India b_Department_of_Electrical_Engineering,_Indian_Institute_of_Technology,_Kharagpur_721302,_India Received26September2014;receivedinrevisedform11November2015;accepted22November2015

Availableonline18March2016

Abstract

MostoftheBrushlessDC(BLDC)motorsdriveadoptsproportional,integralandderivative(PID)controllerandpulsewidth modulation(PWM)schemeforspeedcontrol.Hence,BLDCmotordrivehasstrongsaturationcharacteristics.Thesaturationresults inatypicalwindupphenomenon.ThepaperpresentsanAntiwindupdriveforBLDCmotor.AnAntiwindupcontroller(AWC)has beenusedinthepaper.AWChasbeenmodeledinMATLAB/SimulinkandcomparisonhasbeendonebetweenconventionalPI controllerandAWCatdifferentstartingloads.DynamiccharacteristicsoftheBLDCmotordrivehavebeenexaminedandresults arepresentedanddiscussedindetailinthispaper.DetailsofDSPbasedexperimentalvalidationofthesimulatedresultsarealso presentedhere.

Keywords: BLDCmotor;Pulsewidthmodulation;Antiwindup;MATLAB/Simulink;DSP

1. Introduction

BLDCmotorspeedcontrolplaysanimportantroleinmodernmotorcontrol(Venkatratnam,2009;Darbaetal., 2015).TheBLDCmotorhasatrapezoidalbackEMF,andrectangularstatorcurrentsareneededtoproduceaconstant electrictorque.However,idealrectangularcurrentshapescannotberealizedinpracticeduetothephaseinductanceand finiteinvertervoltage(Krishnan,2001;Tariqetal.,2013;TariqandVarshney,2014).Tomaintaintheactualcurrents flowingintothemotorascloseaspossibletotherectangularreferencevalueshysteresisorPWMcurrentcontrollers areused(Krishnan,2010;Miller,1989).Inliteraturedualclosed-loopspeedcontrolisfoundcommon.Theouterloop isforspeedwhereastheinnerloopisforcurrentortorquecontrol(Lajoie-Mazencetal.,1985;Bose,2006;Sonetal.,

∗_{Corresponding}_author._Present_address:_School_of_Electrical_and_Electronic_Engineering,_Nanyang_{Technological}_University,_Singapore._Tel.: +6581756406.

E-mailaddress:[email protected](M.Tariq).

PeerreviewundertheresponsibilityofElectronicsResearchInstitute(ERI).

http://dx.doi.org/10.1016/j.jesit.2015.11.008

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2015).PIDcontrolhasbeenoneofthemostdevelopedstrategiesinthelinearcontrolsystemsforover75yearsand isstillcommonlyusedinindustrial controlsystems.PIDcontrolissopopularbecauseofitssimplicity,robustness andeasytuningparameters(Gopal,2003;TariqandIqbal,2014;TariqandYuvarajan,2013).AsBLDCmotorisa multivariablenonlinearsystemmanyotherproblemsneedtobesolvedfurther.BLDCmotordriveusingPIDcontrol andPWMschemeshasstrongsaturationcharacteristicswhichresultsinwindupphenomenon.Itisasituation,wherein alargechangeinsetpointoccursandduringtherise,theintegraltermhastostore(accumulates)alargeerror.

Theaccumulationofsignificanterrorresultsinovershootinganditcontinuestoincreaseastheaccumulatederror isunwoundonlywithanoffsetbyerrorsintheoppositedirection.Henceovershootandsettlingtimearethusspecific problemsassociatedwithatypicalPIDcontroller.ForthisanAntiwindupPIcontrollerhasbeenusedinsteadofPI controller.

Inliteraturemany typesofAWChavebeendiscussed. Bohnetal.paper discussedthe followingfourtypesof AWC,conditionalintegration,limitedintegrator,trackingAntiwindupandmodifiedtrackingAntiwindup(Bohnand Atherton,1995).Hodeletal.’spaperproposedanewvariable-structure(switching)methodforthepreventionofPID controllerintegratorwindup.Theyimplementeditincontinuousaswellasindiscrete-time(HodelandHall,2001). Zhangetal.proposedandimplementedstochasticAntiwindupPIcontrollers(Zhangetal.,2006).Integralclamping AWCisfoundcommonandmostusedamongallmethodduetoitssimplicity(Xia,2012;Mingetal.,2015).

Antiwindupmethodhasbeenusedininductionmotorandpermanentmagnetsynchronousmotorcontrol(Mishra, 2014).Forinductionmotordrive,experimentalapplicationofthespeedcontrolofvectorcontrolledinductionmotor drivenbyapulsewidth-modulatedvoltagesourceinverterhasbeenpresentedindetail(Shin,1998).AnovelAWC hasbeenproposedtoregulatethecurrentinfluxweakeningcontrolofsurface-mountedpermanent-magnetmotor.The newAWCutilizesthedc-linkvoltagemoreefficiently,thusmakingthemotortogeneratehigheroutputtorquethan theconventionalAWCmethodsforthesamevoltageandcurrentlimits(KwonandSul,2005).

Previousresearches anddevelopmentof control schemeshavemade avery goodcontributiontoBLDCmotor drives,butacomprehensiveapproachisnotavailableformodelingandanalysisofAntiwindupPIcontrolledBLDC motordrivesusingTMS320F2808hardwareexperimentalsetup.AnAWCcanbeeasilyimplementedasthereisno extrahardwarerequired.Inthispapermodeling,simulationandexperimentalresultsarepresentedanddiscussedin detailtoensurethevalidityandperformanceoftheAWCBLDCmotordrive.

Thepaperisorganizedasfollows:Section2discussesthecompletemodelingofthesystemindetail.Simulation detailsof thesystemarecoveredinSection3.Section4 introducesthe windupphenomenonas wellasdiscusses theAWCtonullifythewindupphenomenon.ExperimentalsetupareshownanddiscussedinSection5.Resultsof simulationandexperimentalsetuparepresentedanddiscussedindetailinSection6.FinallySection7concludesthe paper.

2. Modelingofthesystem

ThemathematicalmodelofBLDCmotorisfundamentalforitsperformanceanalysisandcontrolsystemdesign. Thecommonmathematicalmodeli.e.differentialequationmodelispresentedinthissection.TheBLDCmotorhas threestatorwindingsandapermanentmagnetrotor.Rotorinducedcurrentscanbeneglectedduetothehighresistivity ofbothmagnetsandstainlesssteel.Nodamperwindingsaremodeled.Forasymmetricalwindingandbalancedsystem, thevoltageequationacrossthemotorwindingisasfollows:

⎡ ⎢ ⎢ ⎣ vas vbs vcs ⎤ ⎥ ⎥ ⎦= ⎡ ⎢ ⎢ ⎣ Rs 0 0 0 Rs 0 0 0 Rs ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ ia ib ic ⎤ ⎥ ⎥ ⎦+_dtd ⎡ ⎢ ⎢ ⎣ Laa Lab Lac Lba Lbb Lbc Lca Lcb Lcc ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ ia ib ic ⎤ ⎥ ⎥ ⎦+ ⎡ ⎢ ⎢ ⎣ ea eb ec ⎤ ⎥ ⎥ ⎦ (1) Laa=Lbb =Lcc=L Lab=Lba =Lac=Lca=Lbc=Lcb=M

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whereListheself-inductanceandMisthemutualinductance. ⎡ ⎢ ⎢ ⎣ vas vbs vcs ⎤ ⎥ ⎥ ⎦= ⎡ ⎢ ⎢ ⎣ Rs 0 0 0 Rs 0 0 0 Rs ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ ia ib ic ⎤ ⎥ ⎥ ⎦+_dtd ⎡ ⎢ ⎣ L M M M L M M M L ⎤ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ ia ib ic ⎤ ⎥ ⎥ ⎦+ ⎡ ⎢ ⎢ ⎣ ea eb ec ⎤ ⎥ ⎥ ⎦ (2)

Forathreephasestarwindingmotor,

ia+ib+ic=0 (3) ⎡ ⎢ ⎢ ⎣ vas vbs vcs ⎤ ⎥ ⎥ ⎦= ⎡ ⎢ ⎢ ⎣ Rs 0 0 0 Rs 0 0 0 Rs ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ ia ib ic ⎤ ⎥ ⎥ ⎦+_dtd ⎡ ⎢ ⎣ L−M 0 0 0 L−M 0 0 0 L−M ⎤ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ ia ib ic ⎤ ⎥ ⎥ ⎦+ ⎡ ⎢ ⎢ ⎣ ea eb ec ⎤ ⎥ ⎥ ⎦. (4)

Theelectromagnetictorqueisgivenas Ta=eaia+ebib+ecic

ωm(Nm)

(5) whereωm istheangularmechanicalspeedinradianspersecond;ea,eb,ecarethebackEMFofphasesa,b andc respectivelyandia,ib,icarethecurrentsinphasesa,bandcrespectively.

J=Jm+Jl (6)

Jdwm

dt +Bwm=(Te−Tl) (7)

whereJismomentofinertia,JmisinertiaofmotorandJl isinertiaofload;Bisdampingconstant,Teiselectrical torqueandTlisloadtorque.

dθr dt =

p

2wm (8)

wherePisno.ofpolesinthemotorandθrisangularrotation. ea= ke 2wmF(θ) (9) eb= ke 2wmF θ−2π 3 (10) ec=ke 2wmF θ−4π 3 (11)

ThefunctionF(θ)givesthetrapezoidalwaveformofbackEMF.Oneperiodofthisfunctioncanbewrittenasgivenin Eq.(12)andshowninFig.1.

F(θ)= 1 0<θ< 2π 3 1− 6 π θ−2π 3 2π 3 <θ<π −1 π<θ<5π 3 −1+ 6 π θ+5π 3 5π 3 <θ<2π (12)

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-1.5 -1 -0.5 0 0.5 1 1.5 0 50 100 150 200 250 300 350 400 450 F(Theta) Theta

Fig.1.ThefunctionforgeneratingtrapezoidalbackEMFwaveform.

3. SimulationsinMATLAB/Simulink

TheMATLAB/SimulinkimplementationoftheBLDCmotordrivesispresentedinthissection.Fig.2describesthe basicbuildingblocksoftheBLDCmotordrive.ThedriveconsistsofanAntiwindupspeedcontroller(afastresponse controller),hysteresiscurrentcontroller,Hallsensor,themotorandanIGBTbasedvoltagesourceinverter(VSI).The speedofthemotorwascomparedwithitsreferencevalue,andtheerrorwasgiventotheAWCforcorrectivemeasures. Theoutputofcontrollerwasconsideredasthereferencetorque.Thereferencecurrentwasgeneratedfromthereference torque,ascurrentwasdirectlyproportionaltothetorque.Thereferencecurrentwasthencomparedwithactualcurrent withahysteresisbandof10%.TheoutputofthehysteresiscontrollerwasgiventotheANDlogicwhereitwasAND withtheswitchingsignalforIGBT.Henceswitchingcommandsweregeneratedtodrivetheinverterswitches.

ThehysteresiscurrentcontrollercontributestothegenerationoftheswitchingsignalsfortheIGBTsofinverter. Hysteresis-bandPWMisbasicallyaninstantaneousfeedbackcurrentcontrolmethodofPWMwheretheactualcurrent continuallytracksthereferencecurrentwithinhysteresis-band.Whenthecurrentexceedsupperbandlimittheswitching signalwillbezero(low)sothatthecurrentcandecrease.Andasthecurrentexceedlowerbandlimittheswitching signalwillbeone(high)sothatthecurrentcanincrease.

TheHallsensorswitchesgivedigitalpulsesthatcanbedecodedintothedesiredthree-phaseswitchingsequence. ThelogicfordecodingisasgiveninTable1andshowninFig.6.

4. IntegralclampingAntiwindupPIcontroller

AsimpleintegratorclampingAntiwindupPIcontrollershowninFig.3wasusedforspeedcontroloftheBLDC motor. Reference Current Actual Current DC Source Hall Sensor Decoder Circuit for

Generang Switching Signals Hysteresis Current Controller Brushless DC Motor IGBT Inverter AND Logic

Speed Measurement Anwindup

Controller

Reference Speed

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Table1

GenerationofswitchingsequencefromHallsensorsignals.

Hallsensorsignals SwitchingsequenceforIGBTswitches

H1 H2 H3 S1(a+) S2(a−) S3(b+) S4(b−) S5(c+) S6(c−) 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1

Ithasaswitchforselecting(orclamping)integratorgain.Theoutputandinputofthecurrentlimiteriscompared. Ifinputandoutputareequalthenthatmeansthecontrollerhassaturatedandintegratoractionhastobeswitchedoff. Similarlytheerrorandcontrolledoutputisalsocomparedandiftheyareoppositeinvaluesthenintegratorhasto beswitchedoff.Withthehelpofthislogicwecanavoidovershootandcanreducesettlingtime.Thecorresponding variablestructurecontrollawofthecontrolleris

H=Ki.e if e.Cn>0,Cn=/ Cs (13)

H=0 if e.Cn<0,Cn=Cs (14)

where H=input to the integrator block; e=speed error; Cn=controlled output (before current limiter) and Cs=controlledoutput(aftercurrentlimiter).

Figs.2and3wereimplementedinSimulinkandacomparisonstudyhasbeendonebetweenaPIandanAntiwindup PIcontroller.ThecomparisonresultsareshowninFigs.7–12.TheresultsarefurthertabulatedinTable3.

5. Experimentalvalidation

ThehardwareimplementationofanAntiwindupPIcontrollerforBLDCmotordriveisdiscussedinthissection. Thesimulationresultsforspeedcontrolareverifiedbytheexperimentalresultshere.Theparametersofthemotorused forexperimentaswellassimulationaregiveninTable2.

CommutationpulsesweregeneratedbasedontheinformationfromHallsensorsandinformationwereacquired throughtheTexasInstrumentationDSPboard(TMS320F2008).AthreephaseIGBTbasedintelligentpowermodule wasusedtocommutatethephasecurrents.Halleffectcurrentsensorwasusedformeasuringthedclinkcurrentfor implementinghysteresiscurrentcontroller.Forcalculationofspeed,theHallsensorsignalwasgiventoFtoVconverter LM2907.TheoutputofLM2907wasrecordedanddiscussed.Simpleblockdiagramofexperimentalsetupisshown

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Table2

RatingofBLDCmotor.

Ratedpower 500W

No.ofpoles 16

No.ofphases 3

Typeofconnection Star

DCvoltage(Vs) 24V Ratedcurrent(I) 25A Ratedspeed 2500rpm Ratedtorque 1.9Nm Resistance/phase 0.3 Self-inductance 2.5mH Mutualinductance 1.2mH Momentofinertia 1271×10−7_kg_m/s2 IGBT Inverter Hall sensor BLDC Motor F to V converter Oscilloscope DSP Board PC DC Source Opto-coupler Current Sensor and

Signal Conditioner

PMDC Generator

Rheostat

Fig.4.Asimplestructurediagramofexperimentalsetup.

inFig.4andinFig.5snapshotoftheexperimentalsetupisshown.Experimentalresultsareshownanddiscussedin

Figs.14–19.

6. Resultsanddiscussion

ThespeedregulationperformanceofaBLDCmotorwithPIandAntiwindupPIcontrollerisshownanddiscussed inthissectionatdifferentstartingloads.Fullratedloadofthemotoris25A.Fig.6showssixIGBTpulsesgenerated bydecodingHallsensorsignals,astabulatedinTable1.

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Fig.6. IGBTswitchingsignalsfor3leginverter.

Fig.7.Speedresponseat0%loadstarting.

InFig.7,resultshavebeencomparedwithnoloadcondition.UsingPI controllertheovershootis275rpmand settlingtimeis0.2s,whilewithAntiwindupPIcontrollerovershootisonly75rpmandsettlingtimeisonly0.07s.

InFig.8,resultshavebeencomparedwith30%loadcondition.UsingPIcontrollertheovershootis225rpmand settlingtimeis0.1s,whilewithAntiwindupPIcontrollerthereis0%overshootandsettlingtimeisonly0.05s.

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 1000 1100 1200 1300 1400 1500 1600

1700 Speed response for PI and AWC at 50% loads

Time in Seconds

Speed in RPM

Conventional PI Controller,Overshoot 175 RPM (11.7%) Settling Time = 0.1 seconds Antiwindup PI Controller, Overshoot 0 RPM ( 0 %) Settling Time = 0.07 seconds

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1000 1100 1200 1300 1400 1500 1600 Time in Seconds Speed in RPM

Speed Responce for PI and AWC for 100 % Load (Full Load Starting)

Conventional PI Controller, Overshoot 25 RPM (1.7%),Settling Time = 0.6 seconds AntiWindup PI Controller, Overshoot 0 RPM (0%),Settling Time = 0.1 seconds

InFig.9,resultshavebeencomparedfor50%loadcondition.UsingPIcontrollertheovershootis175rpmand settlingtimeis0.1s,whilewithAntiwindupPIcontrolleragainthereisnoovershootandsettlingtimeisonly0.06s. InFig.10,resultshavebeencomparedfor100%loadcondition.UsingPIcontrollertheovershootis25rpmand settlingtimeis0.6s,whilewithAntiwindupPIcontrolleragainthereisnoovershootandsettlingtimeisonly0.1s.

Itcanbe observedfromthesefiguresthat the AntiwindupPI controller hasbetteranti disturbanceability, less overshootandlesssettlingtimeofthesystem,andcanimprovethespeedresponseability.MoreoverinFigs.11and12

thespeedresponseofPIandAWChasbeengiventoshowthevariationsatdifferentloads.

ThecomparisonbetweenPIandAntiwindupPIcontrolleratdifferentstartingloadsisalsoshowninTable3.Itcan beseenfromthetableaswellasfromFig.12,thattheovershootiszeroforAntiwindupPIcontrollerat30%,50% Table3

ComparisonbetweenPIandAntiwindupPIcontrolleratdifferentstartingloads. Loadatstarting

(%ofratedload)

PIcontroller AntiwindupPIcontroller

Overshoot (rpm) Overshoot (%ofrated) Settling time(s) Overshoot (rpm) Overshoot (%ofrated) Settling time(s) 0 275 18.3 0.2 75 5.0 0.07 30 210 14.0 0.1 0 0.0 0.05 50 175 11.7 0.1 0 0.0 0.06 100 25 1.7 0.6 0 0.0 0.1

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Fig.11.SpeedresponseatdifferentloadsusingPIcontroller.

Fig.12.SpeedresponseatdifferentloadsusingAntiwindupcontroller.

and100%ratedload.SettlingtimehasalsoreducedforAntiwindupcontrollerbyalmost40–65%for0%,30%and 50%ratedloadwhereasitreducedby83%for100%ratedload.

ExperimentswereperformedusingTargetSupportPackageofMATLABandTMS320F2008.Theresultsobtained areshowninFigs.14–19anddiscussedhere.Itcanbeobservedfromthefiguresthat,theexperimentalresultsvalidate thesimulationresults.Fig.13showsthecircuitofIGBTinverterused.

TheswitchingpulsestakenfromdigitaloutputofDSPboardisshowninFig.14fortopswitch(Q1)ofphaseA andbottomswitch(Q6)ofphaseB.

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Fig.14.SwitchingpulsetoIGBTinverter(toQ1(Vap)andQ6(Vbn)switches).

ItcanbeobservedfromFig.14thattheswitchingpulseshavevariableONperiodasitwasgeneratedbyhysteresis currentcontroller.Wheneverthecurrentwasexceeding10%oftheratedvalue,IGBTswitchesweregettingOFF.And wheneverthecurrentwaslessthantheratedvaluebymorethan10%,thenIGBTswitchesweregettingON.

Forrecordingspeedinoscilloscope,FtoVconverterwasused.HallsensorAsignalwasgiventoFtoVconverter. AsBLDCmotorhas16poles,sofrequencyofHallsensorAsignalwillbe8timesthefrequencyoftherotationof rotor.

SpeedofthemotorisgivenbytherelationN=120f/Pwherefisthemechanicalfrequency.

Thecomparisonbetweensimulationresult andexperimentalresultare showninFigs. 15and16.In Fig.15,1 divisioncorrespondsto4V;therefore6divisionscorrespond24V.FromFtoVconverter,for67Hzitwillgive1V, hence24Vcorresponds1608Hz.ThefrequencyofHallsensorAis1608Hz,hencemechanicalfrequencywillbe8 timeslessi.e.201Hz.Thespeedcorrespondingto201HzwillbeN=(120×201)/16=1507.5rpm.

Timetaken forsettlingtoreferencespeedfor experimentalsystemwas80msinFig.15,whereasforsimulated systemitwas50msinFig.16.

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0 0.02 1000 1100 1200 1300 1400 1500 1600 Speed in RPM 0.04 0.06 0.08

Simulation Result for AW Controller at 30 % Load

8 0.1 0.12

Time in Seconds

0.14 0.16 0.18 0.2

Fig.16.Simulationresult(AntiwindupPIcontrollerat30%startingload)[settlingtime50ms].

SimilarlywaveformforspeedchangewasrecordedandshownhereinFig.17.

AsobservedfromFig.17,initiallyvoltagewas25V;itimplies25×67=1675Hz;socorrespondingmechanical frequency=(1675×P/2);f=210Hz.

HenceinitialspeedN=120f/P;N=1600rpm.

Finalspeed:voltage=12V;itimplies12×67=804Hz;mechanicalfrequency=804/8=100.5Hz.

N=120f/P;N=750rpm.

Fig.18showsthedynamicresponseofthesystemduringincreaseofspeedfrom750rpmto1600rpm.Initially voltagewas12V;itmeans12×67=804Hz;socorrespondingmechanicalfrequency=(804×P/2);f=100.5Hz.

HenceinitialspeedN=120f/P;N=750rpm.

Finalspeed:voltage=25V;itimplies25×67=1675Hz;mechanicalfrequency=1675/8=210Hz.

N=120f/P;N=1600rpm.

Fig.19showstheresultfordecreaseinloadby30%.Asloadwasdecreased;speedincreasesbutagaingotsettled with200mstoitsreferencevalue.

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Fig.18.Speedincreasedfrom750rpmto1600rpm.

Fig.19.Loaddecreasedby30%,speedsettledtoitsreferencein200ms.

7. Conclusion

The paperpresented a performancecomparisonbetween an Antiwindup PI controllerand the conventional PI controllerhasbeencarriedout.SimulationresultsconfirmthevalidityandsuperiorityoftheAntiwindupPIcontroller forimplementingonhardware.TheresultsprovethattheAntiwindupPIcontrollerhasbetterantidisturbanceability, lessovershootandlesssettlingtimeofthesystem,andcanimprovethespeedresponseability.Theexperimentalsetup wasdonebyusingTMS320F2808DSPboardandexperimentalresultsverifiedthesimulationresultofspeedcontrol. InfutureanAntiwindupPIcontrollercanbeusedforspeeddriveofBrushlessDCmotorwithoutpositionsensor.

Acknowledgements

Thisworkisfunded completelybyNationalInstituteofOceanTechnology(NIOT),MinistryofEarthSciences, Govt.ofIndia.TheauthorsaregratefultotheDirector,NIOTforprovidingfacilitiesforthecompletionoftheproject. TheauthorsarealsothankfultoK.ArumugamandothermembersofMarineSensorSystemsgroupofNIOTfortheir intensesupport.

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