Matlab-based-Permanent-Magnet-Synchronous-Motor-Ve

1Matlab-basedPermanentMagnetSynchronousMotorVectorControlSimulationZhonghuiZhangPostgraduatetutorofelectricpowersystemandautomationprofessionofNanChanguniversity,Fullprofessor.Nanchang,Jiangxi,330031,[e-mail]electricpowersystemandautomationprofessionofNanChanguniversity.Nanchang,Jiangxi,330031,[e-mail]—ProposedpermanentmagnetsynchronousmotorbasedonMATLAB(PMSM)vectorcontrolsystemmodelofsimulation.AndtakethemodelforsimulationexperimentinMatlab/Simulinkenvironment.Thesimulationresultindicatedthatthecontrollingsystemhadabetterdynamicresponseandregulatorcharacter.Andvalidateitscontrolalgorithmforatheoreticalbasisthatdesignanddebuggingpermanentmagnetsynchronousmotorcontrolsystem.Keywords-PMSM；Thevectorcontrols；Matlab/SimulinkI.FOREWORDComparedwithotherformsofmotor,permanentmagnetsynchronousmotor(PMSM)hasbetterdynamicperformance,smallersizeandhigherefficiency.Inrecentyears,withtherapiddevelopmentofelectricpowerelectronicstechnical,rareearthpermanentmagneticmaterialsandtheincreasinglysophisticatedresearchinpermanentmagnetmotor.PMSMiswidelyusedinnationaldefense,agricultureanddailylife.[1]PMSMisamultivariable,nonlinearandhighcouplingsystem.Theoutputtorqueandstatorcurrentpresentacomplicatedfunctionrelation.Magneticfieldcanbedecoupledtogetagoodcontrolperformance:Itwasnoslipfrequencycurrent,lessaffectedbytherotorparameters,easiertoimplementvectorcontrol.Therefore,themodelofPMSMvectorcontrolhasbecomeawidespreadconcern.ThispaperanalyzesthemathematicalmodelofpermanentmagnetsynchronousmotorbasedontheuseofpowerfulsimulationwithMatlabmodelingcapabilities.IntheMatlab/SimulinktocreateasimulationmodelofPMSMcontrolsystemcanbeprovideeffectivemeansandtoolsforanalysisanddesignoftheservocontrolsystem.II.PMSMMATHEMATICALMODELA.BasicModelThepermanentmagnetsynchronousmotormainlyfromstatorandrotortwopartconstitute.Three-phasestatorwindingsproducearotatingmagneticfieldthroughthethree-phaseAC.Rotorisusuallyequippedwithhigh-performancepermanentmagnetinsurfaceorinsideofferromagneticmaterials.Suchasneodymiumironboronorrareearthmagneticmaterialstoobtainastrongmagneticfield,etc.Andtherotormagneticfieldtodistributeforthesineorlooklikeasinewaveform.Theinteractionbetweenthestatorandrotormagneticfieldgeneratedtorquewhenthestatorthree-phaseinverterwithaccesstoelectricitygeneratedinthemotorrotatingmagneticfield.Thenthetorquepushsynchronizationoftherotortothestatormagneticfieldrotationspeedtoachievethepurposeoffrequencycontrol.Inordertofacilitateanalysis,themotortomakethefollowingassumptions:thestatorwindingthree-phasesymmetrical,uniformairgap,ignoringtheendeffect;neglectedmagneticsaturationandironloss,magneticcircuitislinear;converterprovidesanidealthree-phasepower,ignoringhigherharmonics;ignoretherotorshaftfriction.Motorvoltagebalanceequationisgivenby:⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡+⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡dtddtddtdRRRUcUbUacbacbaiiiψψψ000000(1.1)Motorfluxbalanceequationisgivenby:⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−+⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡)240cos()120cos(cos0000000cos240cos120cos120cos0cos240cos240cos120cos0cosofrofrfrcbaooooooooocbaiiiLLLθψθψθψψψψ（1.2)Torqueexpressionisgivenby:[]⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−=)240cos()120cos(cosofrofrfrcbaeddTiiiθψθψθψθλ(1.3)Equationofmotionforthemotorisgivenby:leTTdtdwJ−=(1.4)TypeofUa,Ub,Ucforthethree-phasestatorwindingvoltage.ia,ib,icforthethree-phasestatorwindingcurrent.ψa,ψb,ψcforthethree-phasestatorwindingflux.R,L,ψfrarethestatorwindingsofeachphaseofresistance,inductance,theequivalentrotorfieldflux.TLisloadtorque.λ,J,ωarethemotorpolenumber,rotorinertia,therotorelectricalangularvelocity.TheACpermanentmagnetsynchronousmotorisamulti-variablecoupledandnonlineartime-varyingsysteminlasttype.Directuseoftraditionallinearcontroltheorycannotachieveeffectivecontrolofit.Therefore,itmustbepossibletotransformandsimplifytheuseofclassicalcontroltheoryregulatordesign.2B.Coordinatetransformationandfield-orientedcontrolFigure1showsthecoordinatesystemofpermanentmagnetsynchronousmotorstatorandrotor.Inordertoeffectivelyapplythefieldorientedcontroltheory,firstlyletthethreephasesystemintoatwo-phaseorthogonalsystem,thenpinwheeltwo-phaseorthogonalsystemforangleθinordertocontroldirectaxisandquadratureaxis.Figure1.CoordinatesystemofpermanentmagnetsynchronousmotorVoltagetransformationissimilartocurrenttransformationandcurrenttransformationisaexampleinthetext.Statorcurrenttothecurrenttwo-phaseorthogonaltransformationbetweenthefollowing:⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡iiiiiiooooooocbaβα21240sin240cos21120sin120cos210sin0cos32（1.5）⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡iiiiiicbaooooooo212121240sin120sin0sin240cos120cos0cos32βα（1.6）Sincethestatorthree-phasecurrent0=++cbaiii，Therefore,zerosequencecurrentcomponent03/)(0=++=cbaiiiicanbeneglected.Thestatorcurrentoforthogonalcoordinatesystemtransformationforrotortwo-phaseoforthogonalcoordinatesystemisgivenby:⎥⎥⎦⎤⎢⎢⎣⎡⎥⎦⎤⎢⎣⎡=⎥⎥⎦⎤⎢⎢⎣⎡iiiiqdθθθθβαcossinsincos(1.7)⎥⎥⎦⎤⎢⎢⎣⎡⎥⎦⎤⎢⎣⎡−=⎥⎥⎦⎤⎢⎢⎣⎡iiiiqdβαθθθθcossinsincos(1.8)Theformula(1.5)to(1.8)intoformula(1.1)to(1.3)finishingavailable:⎥⎦⎤⎢⎣⎡−+⎥⎦⎤⎢⎣