外文翻译原文-高性能异步电机控制通过反馈线性化

633HighPerformanceInductionMotorControlViaFeedbackLinearizationM.P.KazmierkowskiandD.L.SobczukInstituteofControlandIndustrialElectronics,WarsawUniversityofTechnology,ul.Koszykowa75,00-662WarszawaPolandPhone:+48/2/6280665;Fax:+48/2/6256633E-mail:.pl;.plAbstract-Thispaperpresentsafeedbacklinearizationapproachforhighperformanceinductionmotorcontrol.TheprincipleofthemethodisdiscussedandcomparedwithmostpopularinACmotordrivetechnologyfieldorientedcontroltechnique.SomeoscillogramsillustratingthepropertiesofthePWMinverter-fedinductionmotorwithcontrolviafeedbacklinearizationarepresented.INTRODUCTIONTheinductionmotorthankstoitswellknownadvantagesassimplyconstruction,reliability,raggednessandlowcosthasfoundverywideindustrialapplications.Furthermore,incontrasttothecommutatordcmotor,itcanalsobeusedinaggressiveorvolatileenvironmentssincethereisnoprob-lemswithsparkandcorrosion.Theseadvantages,however,areoccupiedbycontrolproblemswhenusinginductionmotorinspeedregulatedindustrialdrives.Thsisdueprimarilythreereasons:(a)-theinductionmotorishighordernonlineardynamicsystemwithinternalcoupling,(b)-somestatevariables,rotorcurrentsandfluxes,aredirectlynotmeasurable,(c)-rotorresistance(duetoheating)andmagnetisinginductance(duetosaturation)variesconsider-ablywithasigluficantimpactonthesystemdynamics.ThemostpopularhighperformanceinductionmotorcontrolmethodknownasFieldOrientedControl(FOC)orVectorControlhasbeenproposedbyHasse4andBlaschke11.Inthismethodthemotorequationare(rewritten)transformedinacoordmatesystemthatrotateswiththerotorfluxvector.Thesenewcoordinatesarecalledfieldcoordinates.Infieldcoordinates-fortheconstantrotorfluxamplitude-thereisalinearrelationshpbetweencontrolvariablesandspeed.Moreover,asinseparatelyexcitedDCmotor,thereferenceforthefluxamplitudecanbereducedinfieldweakeningregioninordertolimitthestatorvoltageathighspeed.TransformationoftheinductionmotorequationsinthefieldcoordinateshasagoodphysicalbasisbecauseitcorrespondstothedecoupledtorqueproductioninseparatelyexcitedDCmotor.However,fromthetheoreticalpointofviewothertypeofcoordinatescanbeselectedtoachievedecouplingandlinearizationoftheinductionmotorequations.Krzeniinski7hasproposedanonlinearcontrollerbasedonmultiscalarmotormodel.Inthisapproach,similarlyasinfieldorientedcontroller,itisassumedthattherotorfluxIEEECatalogNumber:95TH8081amplitudeisregulatedtoaconstantvalue.Thus,themotorspeedisonlyasymptoticallydecoupledfromtherotorfluxBodsonetal.2,3havedevelopedanonlinearcontrolsys-tembasedoniiiput-outputlinearization.Inthissystem,themotorspeedandrotorfluxaredecoupledexactly.Thesystem,however,usethetransformationinfieldcoordinates.Marinoetal.8,9haveproposedanonlineartransformationofthemotorstatevariables,sothatinthenewcoordinates,thespeedandrotorfluxamplitudearedecoupledbyfeedback.SimilartransformationhavebeenusedbySabanovicetal.EfordecoupledrotorfluxandspeedsliQngmodecontroller.Inthepaperthefeedbacklinearizationcontrolofinductionmotorispresented.Incontrasttotheworks2,3theblockdiagramsandrelationshipstofieldorientedcontrolaredis-cussed.Also,figuresillustratedthepropertiesofthecontrolsystemwhenthemotorisfedbyPWMinverterareshown.MATHEMATICALMODELOFTHEINDUCTIONMOTORMathematicaldescriptionoftheinductionmotorisbasedoncomplexspacevectors,whicharedefinedinacoordinatesystemrotatingwithangularspeedoK.Inperunitandreal-timerepresentationthefollowingvectorialequationsdescribebehaviourofthemotor6:TheelectromagnetictorquemcanbeexpressedasInthecaseofthesquirrel-cageinductionmotor,therotorvoltage-vectorvanishesfromEq.2,havingzerovalue.Ifa633currentcontrolledPWMinverterisused,thestatorvoltageEq.1canbeneglectedbecauseitdoesnotaffectthecontroldynamicsofthedrive.FIELDORIENTEDCONTROL(FOC)Inthecaseoffieldorientedcontrol,itisveryconvenienttoselecttheangularspeedofthecoordmatesystemoKequala,.Undertheseassumptions,substitutingtherotorcurrentvectorfromtherotorvoltageEq.2byEq.4veobtainadifferentialequationfortherotorfluxvector:EquationsEq.10,Eq.12andEq.5formtheblockdiagramoftheinductionmotorinthefieldorientedcoordmatesxy(Fig.1).Diagramofcontrolsystemappliedtoinductionmotor(directfieldorientation)is.presentedinFig2.Inmanycasesasflux,speed,i,i,controllers,simplePIregulatorsareused.FEEDBACKLTNEARTZATIONCONTROL(FLC)Usingp.u.timewecanwritetheinductionmotorequationsinthefollowingform6,11:(7)-whereT,istherotortimeconstantexpressedasx=f(x+%.ga+uspgp(13)XTr=ITNrrForthefieldorientedcoordinatesx-ywehaveWm=Yry=orywhereandm.INotethatam,yra,yqarenotdependentoncontrolsignalsU,U$.Inthiscaseitiseasilytochoosetwovariablesdependentonxonly.Forexamplewecandefine5,10.Fig1Blockdiagramofinductionmotorinx-yfieldcoordinatesEq.10describestheinfluenceofthefluxstatorcurrentaccordingtoEq5,canbeexpressedasfollows:componentsi,ontherotorflux.Themotortorque,XI=Vra2+vr3=V:(18)&(x)=0,(19)635dP-P1sa1SG-1rpVector1Sigoals.+rffiatioc&aEstimaiion-Transfor-vr*vrB*%Fig.2.ControlofinductionmotorviafieldorientationLet+,(x),I$(X)aretheoutputvariables.Theaimofcontrolistoobtain:0constantfluxamplitude,0referenceangularspeed.PartofthenewstatevariableswecanchooseaccordingtoEq.IS,Eq.19.Sothefulldefinitionofnewcoordinatesaregivenby8,9:Inthefurtherpartofthissectionwewillconsiderthesystemconsistsofthefirstfourthequations.Note,thatthefifthequationisasfollows:WecanrewitetheremainsystemEq.22inthefollowingform:Disgivenby:Aftersimplecalculationsonecanobtain:6whereD-IwecancalculateusingthefollowingformulaItiseasilytoshowthatif+lf0thendet(D)#0.Inthiscasewecandefinelinearizingfeedbackas:Theresultingsystemisdescribedbytheequations:2,=z2z,=,z3=z42,=v2BlockdiagramofinductionmotorwithnewcontrolsignalsispresentedinFig3.Controlsignalsv1,v2onecancalculateusinglinearfeedback:wherecoefficientsk,k,k,k,arechosentodeterminateclosedloopsystemdynamic.Controlalgorithmconsistsoftwosteps:0calculationsv1,v2accordingtoEq.32,Eq33,0calculationsU,uSpaccordingtoEq.29.Diagramofcontrolsystemappliedtoinductioniiiotor(feedbacklinearization)ispresentedinFig.4.Fig.4.Controlofinductionmotorviafeedbacklinearization637-04611-09ElRESULTS-04FI,-09.!ThesimulatedoscillogranisobtainedforFLCandFOCsys-temswithlinearspeedandrotorfluxcontrollers(motor,in-verterandcontrollersdataaregiveninAppendix)areshowninFig.5.Theseoscilllograms,showthespeedreversalovertheconstantfluxamplitudeandfieldweakeningrangeswhenmotorisfedfromVSIinverterwithsinusoidalPWM.AscanbeseenfromFig.5Bthefieldorientedcontroldoesnotguaranteefulldecouplingbetwenspeedandfluxofthemotor.WithlinearspeedcontrollertheFOCsysteinimple-mentstorquecurrentlimitation,whereastheFLCsystemlimitsthemotortorque(seeFig.5A).Therefore,intheFOCsystemthetorqueisreducedinfieldweakeningregionandthespeedtransientisslowerinFLCsystem.A-FLCB-FOClineatrOC61C20.36405,-0.00120.240.3604808Cl;01005050000-05-05-1c-!0d)oC0102030405d)OO01202403601806j-0961Ic9f1t)C7L1(703045e)O0Ci024036048OtO01D:03040500Oli02403604B06Flg5Conk01ofmduclonmotorviafeedbacklinearizationandfieldorientedcontrol(Speedreversalmcludmgfieldweakeningrange).a)actualandreferencespeed(comercon,)b)torquem.c)fluxcomponentandamplrtude(y,.yr),d)fluxcurrentisX.e)torquecurrentis,.f)currentcomponentlsoToguaranteefulldecouplinginFOCsystemworkingwithfieldweakeningregionaPIspeedcontrollerwithnonlinearpart(controlleroutputsignalshouldbedividedovertherotorfluxamplitudemrdyr)hastobeapplied.Thisdivisioncompensatesfortheinternalmultiplication(m=vri)svneededformotortorqueproductioninfieldorientedcoordi-nates(Fig.1.).WithsuchanonlinearspeedcontrolleraverysimilarbehaviourtoFLCcanbeachieved(seeFig.6.).InFig.7.theresponsetospeedreferencechangeforconstantfluxamplitudeispresented.Note,thatincontrasttotheFOCsystem(wherethecontrolvariablesareU,u),thecontrolvariablesinFLCsystem(vl,VJareexactlydecoupledFig.6.Controlofmdudionmotoriafeedbacklinearizationandfieldorientedcontrolwithnonlniearterm(Speedreversalincludingfieldweak&yrange):a)adualandreferencespeed(omrepom)b)torquem,c)fluxcomponentandamplitude(iy,.ty,).d)fluxcurrentisx.e)torquecurrentis,.,9cunentcomponentiSPA-FOC0);y04t,CO003ODE00912GI5-,1206d)G0003006005GI?015)GO003GO600s0120150600-06-0E-1i-12e)00003GO&009ClIOl5e)GC003GO6005G12000iI00003006003012D!:CC06303100501;0:Fig7.Controlofmdudionmotorviafeedbacklmeariiattonandfieldonitcdconk01(theresponsetospeedrcfercncedmigc-mstmtflusraigc)a)adualandrefaencespeed(oum).b)refercncecontrolagialA-us,.B-vl.c)referencemtrof%&lA-us).B-v2.d)fluxcurrailishe)torquecurratI6)638CONCLUSIONSKurzchlusslauferniotoren,Reglungstechnik,20:pp.60-66.1972.InthisworkahighperformanceFeedbackLinearizationControl(FLC)systemforPWMinverter-fedinductionmotordrivesispresented.TheblockdiagramsandrelationshpstoconventionalFieldOrientedControlCFOC)arediscussed.SIAIsidori:NonlinearControlSystems,Comniunica-tionsandControlEngineering.SpringerVerlag,Berlin,secondehtion,1989.IThemainfeaturesandadvantagesofthepresentedcontrol6M.P.KaimierkomkiandH.Tunia:AutomaticControlsystemscanbesummarisedasfollows:ofConverter-FedDrives,ELSEVIERAmsterdam-withcontrolvariablesv,17,theFLCguaranteetheexactlyLondon-NewYork-Tokyo,1994.decouplingofthemotorspeedandrotorfluxcontrolinbothdynamicandsteadystates.Therefore,lughperformancedrivesystemworkinginbothconstantandfieldweakeningrangecanbeimplementedusingalinearspeedandflux7Z.Krzeminski:Multi-scalarmodelsofaninductionmotorforcontrolsystemsynthesis,ScieiiiaElectrica,33(3):pp.9-22,1987.controllers.Adaptivepartialwithcontrolvariablesis,is,theFOCcannotguaranteefeedbacklinearizationofinductionmotors,InPro-theexactlydecouplingofthemotorspeedandrotorfluxceedingsofthe29thConferenceonDecisionaidcontrolindynamicstates.Therefore,highperformancedriveControl,Honolulu,Hawaii,pp.3313-3318,Dec.1990.8R.Marino,S.Peresada,andP.Valigi:9R.MarinoandP.Valigi:Nonlinearcontrolofinductionmotors:asimulationstudy,InEuropeanCoiitrolCorifereme.Greiioble,France,pp.1057-1062,1991,systemworkinginbothconstantandfieldwakeningrangerequiresaspeedcontrollerwithnonlinear(divisionovertherotorfluxamplitude)part.FLCisimplementedinastatefeedbackfashionandneedsmorecomplexsignalprocessing(fullinformationaboutmotorstatevariablesandloadtorqueisrequired).Also,theloH.NijmeijerandAvanderSchaft:Nonlineardy-namicalcontrolsystems,SpringerVerlag,1990.llD.L.Sobczuk:IfNonlinearcontrolforinductionnietransformationandnewcontrolvariablesvl,v2usedinFLChavenosodlrectphysicalmeaningasin,is,(fluxandtorquecurrent,respectively)inthecaseofFOCsystem.tor,InProceedingsPEIIK94,pp.684-689,1994.FOCcanbeimplementedinclassicalcascadecontrol(121ASabanovicandD.B.Izosiniov:Applicationsofstructureand,therefore,anoverloadprotectioncaneasybeslidingmodestoinductionmotorcontrol,IEEEachievedusingreferencecurrentslimitersontheoutputsofTransactiononIndustryApplicatio