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1598IEEETRANSACTIONSONINDUSTRYAPPLICATIONS,VOL.45,NO.5,SEPTEMBER/OCTOBER2009Anti-WindupCompensatorDesignsforNonsalientPermanent-MagnetSynchronousMotorSpeedRegulatorsPhilMarch,Member,IEEE,Abstract—Thispaperpresentsandcomparesanumberofanti-windupcompensatordesignswhichaddresstheproblemofcurrentsaturationwitpensatorvariantsin-cludeanintegratorresetscheme,backcalculationandtracking,manceiscomparedﬁrstthroughsimulationtestsusinganonli,simulationandexperiment,thebackcalculationandtrackingandlow-orderdesignserms—Anti-windup(AW),constraints,currentlimita-tion,nonsalient,optimal,permanent-magnetsynchronousmotor(PMSM),saturation,UCTIONWNOMENCLATUREia,ib,icidiqVa,Vb,VcVdVqθeθmωmψfloadTPφpeed(mechanical).gcoefﬁ2008-IDC-078.R1,presentedatthe2007IEEEInternationalElectricMachinesandDrivesConference,Antalya,Turkey,May3–5,andapprovedforpublicationintheIEEETRANSACTIONSONINDUSTRYAPPLICATIONSbytriptsubmittedforreviewSeptember18,2008andreleasedforpublica-tionMarch8,tversionpublishedSeptember18,horsarewiththeDepartmentofEngineering,UniversityofLeicester,Leicester,LE17RH,U.K.(e-mail:@;mct6@).ColorversionsofoneormoreoftheﬁguresinthispaperareavailableonlineatlObjectIdentiﬁer10.1109/TIA.2009.2027157ITHINpermanent-magnetsynchronousmotor(PMSM)controlsystems,certainconstraintsarerequiredtosafe-guardthemotorandthepowerelectronics;forinstance,lusionoftheseconstraintsinthecontrolsyaturationconstraintscancausecontroller“windup”problemswhenthecontrollerattemptstoexceedtheseduringoperationandleadtoperformancedegradation,particulaore,formaximumperformancetobeobtained,thereistherequirementtocomwindupwasoriginallyconceivedtodescribetheunrestrictedaccumulationofanintegralcontroller,obhen,thetermhasbeenusedmorebroadly,andisusedtorefertomoregeneralperformancergerclassofundesirablesaturationeffectsincludesnotonlytheaforementioned“integratorwindup”butalsoincludestheperformancedegradationresultingfromsaturationwithmoderncontroldesignsthatdonothaveanexplicitintegralstate,andperformancedegradationwithcoupledmultivariablesystemrofdifferentmethods,whichvarysigniﬁcantlyincomplexityofdesignandimplementation,sthesimplestapproachistousealow-gainlinearcontroller,r,duetolinearity,rnativewayofavoidingsaturationwouldbetouseH∞techniques[1],[2]toproduce(possiblymultivariable)controllerswhichcandistrib-utecontroleffortinamoreefﬁwbacktobothoftheaforementionedapproachesisthat,sincetheyarelinear,theytreatlarge-andsmall-signalbehaviorinexactlythesamewayandthuscannotbeusedtoachievehigh-performancesmall-signalbehavior,anrnativetotheaboveistousemodel-predictive-control[3],[4](MPC)techniquesinwhichthecontrolconstraintsareincorporatedintoanonlineﬁnitehorizonoptimizationprocedure,psethe0093-9994/$26.00©2009IEEE

MARCHANDTURNER:ANTI-WINDUPCOMPENSATORDESIGNSFORNONSALIENTPMSMSPEEDREGULATORS1599problemwithH∞and,particularly,MPCtechniquesisthattheytendtorequiremoreonlinecomputationthanstandardclassicalcroachweconsiderinthispaperisreferredtoasanti-windup(AW)compensationandeone,a“nominal”controllerisdesignn-trollergovernsthecloseetwo,aso-campensatoronlybecomesactiveduringsaturation,andisdesignedtomaintainstabilityoftheclosedloopsystemandminimizethedegradationofperformancewhenviolationofthesatuoftheconstraintsareincludedinthecontrollerandsaturationofthesesoftwarproachallowsforthenominalcontrollertobedesignedtoprovidegoodsmallsignalperformance,andtheAWcompensatordesignedsubsequentlytrbeneﬁtofAWisthatmanycompensatordesignscancommonlybeimplementedasstaticfeedbackgainsordynamicﬁlterswithjustafewstates,and,inmanyways,numberofAWschemesareinexistenceandthereaderisreferredto[5]–[10]cialadvantageofAWisthatitonlymodiﬁestheexistingcontroller’sbehaviorduringandimmediatelyfollowingsaturationeventsUNDERCONSIDERATIONInthispaper,weapplyAWtodealwithviolationofsatura-tionconstraintsintdelT,itsdynamicscanbereproducedquiteaccuratelybythenonsalientmodelof(1)–(4)inthed–qcoordinatesystem[11]diddt=1L[Vd−Rsid+PLsωmiq](1)diqdt=1s

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