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Multi-motor Drive System Based on Adjacent Coupling Error Strategy

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    Multi-motor Drive System Based on

    Adjacent Coupling Error Strategy 344JournalofOonghuaUniversity(Eng.Ed.)Vo1.26,No.4(2009) MultimotorDriveSystemBasedonAdjacentCouplingErrorStrategy LIYan(李艳),HEYong(f~I),LIHui-rain(李慧敏)

    CollegeofMechanicalEngineering,DonghUniwersit3-.Shanghai201620,China

    Abstract:Anewcontrolstrategynamedadjacentcoupling errorstrategyisproposedtomulti?motordrivesystem.The adjacentcouplingerrorcontrolschemeisdeveloped consideringthetrackingspeederrorinonemotorandthe synchronouserroramongadjacentmotorssimultaneously.In thestrategy,duetonon?lineareffectsofthetwomentioned errorstothemotioncontrolofmotorf.anadaptivefuzzy logiccontrollerisdesignedtodecidethecontrolvariableof themotordrivesystem.Themulti-motordrivesystemis modeledandsimulatedbySIMULDl(.Thesimulated

    researchesshowthattheproposedstrategyimprovesthe synchronization,stabilization,andconvergenceofthe multi?motorsystem.

    Keywords:multiDlotorsynchronouscontrol;adjacent

    couplingP,?rstrategy:adaptivefuzzycontTvller;hi-

    closedlooPcontrolsystem

    CLCnumber:TP73.2Documentcode:A

    ArticleID:16725220(2009)04034406

    Introduction

    Themotioncontrolofmulti.motorforhighprecision andhighspeedmachiningisbecomingacriticalproblemin

    modernmanufacturing.especiallyinpapermaking, printinganddyeing,andtextile,

    Themulti.motor'synchronoussystemcanbedividedinto tWOkinds:master-slavesynchronizationandcoupling synchronization.Masterslaveconfigurationhasthesimplest topologybutitisinherentlylackofstiffnessresultsinall appropriatetechniqueformultimotorsynchronization.

    IncouplingsynchrOnationtherearesynchronous coefficientsforthecoordinationofthemultipledrive shafts.Themosttypicalsynchronizationtechniquesin couplingcontrolarecrOSScouplingtechnique,biaxialcross

    coupledcontrolmethod,electronic(virtua1)lineshafting,

    andtherelativecouplingstrategy;..Crosscoupling controloffersgoodspeedsynchronizationandeasy implement,yetwithlimitationwhenarelativeangleisa chfconsideration.Theelectronic(virtua1)line-shafting methodachievesthesimplepracticalconfigurationbuta partialfunctioningfromtherelativeanglepointofview. Relativecouplingmakesthebestperformancewiththe mostcomplexityaswel1.

    Inpracticalapplication,thecoupling(compensating) lawisdifficulttodecide.Thecontrolexpressionswilllead tothecomplexdesignedcontroller,andhugeon-line calculatingwork.Inaddition,thepresentstrategiesare aimedatthesynchronous~ontroloftwomotors.Itis difficulttoapplycouplingrulesintheapplicationsofmulti- motorsystem(n?3).

    Unlikeotherclassicalcontrolschemes,thefuzzylogic controlisamodel-freeapproachanddoesnotrequirea mathematicalmodelofthecontrolledsystem.Itisproved

    tobehighlyeffectiveincontrollingsystemswhosedetailed andaccuratemathematicaldescriptionsarenot availablec"sj.Thereareresearchestryingtodesign controllersformotioncontrolincorporatingfuzzy logic~6-z03.

    Althoughfuzzylogiccontrolintroducesagoodwayto dealwithcomplicated,nonlinear,andi11definedsysterns,

    itsuffersfromadrawbackofthe"parametertuning"for thecontroller.Hence.aneffectivemethodisneededfor tuningthemembershipfunctionsandrules,tominimizethe outputerrorormaximizethepe,rformancemeasureL. Inthispaper,anadaptivefuzzysynchronous

    controllerisdevelopedbasedontheadjacentcouplingerror controlstrategy,andtheadaptiverulesaregiven.The resultsofsimulationsandexperimentsareallshownthat fuzzycontrol|eriseffectNeintheadjacentcouplingerror controlstrategyinthemultimotorsynchronoussystem.

    Innextsection,anadjacentcouplingerrorstrategyis developedforanalyzingtheeffectsoftrackingspeederror andsynchronizationerrortosystemmotion.With modelingthemulti-motordrivesystem,thesimulatework isdone,andthelastpartgivesconclusionsofthe researches.

    1AdjacentCouplingErrorStrategy

    Foran,pmotordrivecontrolsystem,thetracking speederrorisdefinedas:

    Receireddate:20090213

    Foundationitem:NationalNaturalScienceFoundationofChina(No.60774023)

    *CorrespondenceshouldbeaddressedtoLIYan,E-mail:liyaab,@dhu.edu.ca

    JournalofDonghuaUniversity(Eng.Ed.)Vo/.26,No.4(2009)345

e(t)=(f)xf(t),(1)

    where,(t)isthedesiredvelocityoftheithmotor, xf(t)istherealvelocityoftheithmotor.The synchronizationproportionalcoefficientissupposeda1. Toobtainthepropersynchronizationmotionamong motors,ej(t)Oisrequiredalongwith:

    e1(t)=e2(t)::e(t).(2)

    So,thesynchronousspeederrori(t)isdenotedas

    follows!:

    El(t)=e1(t)e2(,)

    e2(t)e3(t)

    .(3)'

    I.''.

    I(,):e()e1(,)

    Ifforal1motors.therearee,(f)=0,thenthe performancedenotedasEq.(2)isachieved. FromRefs.[11123,thesynchronouscontrol

    strategybasedontheminimtimcorrelativemotoris proposed.Thatis,thecontroltorqueofamotorshould ensurethestabilizationandtheconvergenceofthetracking speederroraboutitself,andthesynchronousspeederrors aboutitsadjacentmotors.

    Avariablenamedadjacentcouplingerrore(t)is introduced,whichincludesl(t)andei(r)inone equationsimultaneously.Thene(t)isdefinedasfollows: e(f)=e2(f)+I[2(r)一:1(r)]dr,(4)

    where,(,)istheSHInoftheef(t)andthecumulate deviationofthetwoadjacentsynchronottsspeederror e_.1(t)and(t).Hereisapositivecoupling

    coefficientforthelatter.Ifisgivenlarge,thenthe

    weightofthesynchronousspeederrorislargetoo. Contro1function"j(t)isalsodefinedasfollowsto couplingthemotionsofneighbormotorilandmotor

    i+1tomotorisimultaneously,thatis,

    u(f)=f(f).(f)+[sj(f)ej+1(t)3+Aei(f)=

    jf(,)+(t)+[ef(f)Et(,)]+

    A(,)J:(r)_1(dr).(5)

    FromEq.(5),"(,)includestheaccelerationof feedbackrotorspeed,adjacentcouplingerror,andits accelerationerror.Sobothtrackingspeederrorand synchronousspeederrorsareconsideredinuf(t). Similarto.Aistheweightsettobalancethe trackingspeederrorsandthesynchronousspeed errors.WhenAisgivenlarge,theadjacentcoupling errorwillobtainthebiggerweightinthecontrol function".(t).Withanalyzingtheinfluencesofthe twotypesoferrors,thecorrelatedmotionsamong motorsw'l1beachieved.

    FurtherconversionofEq(5)ismadeasfollows: "(t)=E:(r)+E(r)+E(t),(6)

    here:

    E(f):(,),

    E;(r):(f)+p[?(f)一:](t)]=(f),

    E(f)=Ae;(f)=Ae(,)+AJ8l(r)e,l(r)]dr,J0

    (7)

    where,E(t)istheaccelerationoffeedbackrotorspeed; E;(r)istheaccelerationofadjacentcouplingerror,which includesthebothtrackingspeederrorandsynchronous speederrorsofmotori;andE;(t)istheadjacentcoupling error.WiththeadjacentcouplingerrorE;(t)andits

    accelerationerrorE;(f),thecontrolinputvariableof motoriwillbeobtainedtocontrolthemotordriverand motions.Further,thecorrelationmotionofmulti.motor systernwillbeachieved.

    2DesignoftheAdaptiveFuzzyLogic

    Controller

    Accordingtotheaboveanalysis,thedesignedadaptive fuzzylogiccontrollerofmotorisshownasFig.1.Inthe figure,thestructureofthemotorcontrolsystemisgiven accordingtoEqs(17).ThethreeinputvariablesE(),

    E(),andE(s),aredesignedastheinputsofthefuzzy controllertoobtainthecontrolinputM.(s)ofthemotori withtheadjacentcouplingalgorithm.

    Fig.1Structureoftheadjacenterrorcouplingcontrolmethodwithfuzzylogic

    Withtheoptimizationoffuzzyinference,

    fuzzification,anddefuzzificationstrategiesbyfuzzylogic controller,theoutput,thatis,thecontrolinputofbi

    closeloopcontrolsystemofmotori(".(s))is obtained,andthenthebicloseloopmotorcontrolsystem

    isoptimized.

    Inthedesignofthefuzzylogiccontroller,theinput andoutputvariableswillbedeterminedfirstly.Fromthe 346JournalofDonghuaUniversity(Eng.Ed.)Vo/.26,No.4(2009) aboveanalysisandEq.(6),theoutputis"(s).The inputsareobtainedfromtheerrorvariablesE(f),E: (f),andEj(t).

    Thefuzzycontrolrulesareestablishedbythedynamic characteristicsofsystem.Thatis,thesimpledynamic characteristicsofoscillating,underdampedandover

    dampedresponsesarefirstlyusedtoprovidethebasis

    controlinformation.Thenwiththerea1.timecontrol characteristics,anadaptivelawisdesignedtooptimizethe parametersofthefuzzycontroller.Thefuzzyrulesare showninTabIe1.

    Table1Therulesofthefuzzycontroller

    ,

    2(f)

    NBNMNSZEPSPMPB

    NBNBNBNBNBNMNSZE

    NMNBNBNMNMNSZEPS

    NSNBNMNMNSZEPSPM

    ZENBNMNSZEPSPMPB

    PSNMNSZEPSPMPMPB

    PMNSZEPSPMPMPBPB

    PBZEPSPMPBPBPBPB

    Basedonthefuzzycontroller,anadaptivelawforthe fuzzycontrollerisfurtherdesignedtooptimizethefuzzy rulesinFig.2.Byanadaptivelaw,thefuzzyparameters canbetunedinrealtimebasedoiltheapproachThe feedbackcontroIlawcanbeillustratedasfollows. ——

    E

    

    ,

    Fuzzylogic

    controllerI

    ],

    adaptivelaw

    Fig.2Structureoftheadaptivefuzzylogiccontroller Theadaptivelawisdepictedthat,accordingtothe

    actualconditionsinmulti-motorsdriveintextile manufacturingmachine,whenthereislargersynchronous speederrors,thesynchronouscontrolispreferentially optimized.WhentherekeeDwithintheallowableerrorsof thesynchronousspeed,thetrackingspeederroris preferentiallyoptimized.

    Specifically.Aandistwoundeterminedparameters thataredifficulttocalculateinthisresearchAsnotedand analyzed.Aandallinfluencethesynchronousspeed error.Intheadaptivelaw.iftheproductofthemis bigger,thenthesynchronouscontrolispreferentially optimized.AndifAisbiggerindividually,thenthe trackingspeederrorispreferentiallyoptimized.Andvice versa.TheadaptivefuzzyrulesareshowninTable2. Table2Theadaptivelawoftheadaptivefuzzycontroller 7~(t

    \\)NNNANBNMNSZEPSPMPB

    NBNBNBNBNBNBNSZE

    NMNBNBNBNSNSZEPS

    NSNBNSNSNSZEPSPM

    ZENBNMNSZEPSPMPB

    PsNMNSZEPSPMPMPB

    PMNSZEPSPMPMPBPB

    PBZEPSPMPBPBPBPB

    WiththefuzzyadaptiverulesshowninTable2,the controlinput(t)isoptimized,andtheithmotordrive systemwillbeoptimized.Andfurther,thewholemulti? motordrivesystemwillbeoptimizedtoo.

    Theoutputofthefuzzycontrollerisdenotedas follows:

u(t):"f(f)+yi(f),(8)

    where"(r)istherevisedcontrolinputintheithmotor drivesystem,y(f)istherevisingfactor,and"i(f)is thecontrolinputwithoutoptimizationbytheadaptive law.

    3SimulationResearch

    Fodemonstrateandverifythecontrolperformanceof theproposedcontrolalgorithmindifferentconditions,the threeDCmotorsynchronouscontrolsystemisexampledto simulatethecontrolalgorithm.Thestructureofabi.closed loopDCspeedcontrolsystemisshowninFig.3.The parametersofthethreeDCmotorinthesystemareshown inTable3

    Table3Parametersofthethree13(2motorinthesystem JournalofDonghuaUniversity(Eng.Ed.)Vol.26,No.4(2009)347 FromFig.3,thebiclosedloopDCspeedcontrol

    s~temincludesACvoltagesourcemodule,SCRuniversal bridgemodule,synchronizedsixpulsegenerator,DC

    machinemodule,andbi.close-loopcontrolmodule.The paraaneterssuchaSrotatespeedn,armaturecurrentJa, fieldcurrent1f,andelectromagnetictorqueTare observedbyfourscopesrespectively.

    I'hediagramofmultimotorsynchronouscontroI

    systemisshowninFig.4.Thes~temincludestwoparts, thatis,motorcontrols~temandtheadjacentcoupling errorcontrolstrategy.Themotorcontrolsystemisdetailed inFig.3.Thediagramoftheadjacentcouplingerror controlstrategyisshowninFig.5,andthestrategyis detailedintheprecedingpartofthepaper.

    E

    Fig3Diagramofbi-closeloopcontrolsystemofmotori Fig.4Diagramofmultimotorsynchronouscontrol~stem 348JournalofDonghuaUniversity(En9.Ed.)Vo1.26,No.4(2009) e3

    Fig.5DiagramofadjacentCOtlplingerrorstrategy ThesimulationiscarriedoutusingMATLABpackage. TwOsimulationtestsareconductedundertheconditionsof freeloaddisturbancesandloaddisturbances. (1)Simulationundermotormotionsfreeload disturbances

    Thetrackingspeederrorsandsynchronousspeed errorsunderthesamegivenstepinputsareshowninFigs. 68.Fromthecurves,thetrackingspeederrorsare convergedtozeroin0.6S,andthesynchronousspeed errorsareconvergedtozeroin0.8S.Fromthefigures, inthestartingprocess,themaximumsynchronouserroris 5.0rad/s,andthesynchronouscontrolaccuracyis O.5%.

    :

    \

    Fig6RotatespeedCHIVESundernoloadtorquedisturbance ,

    ?

    ,

    ,

    ,

    2.5

    O

    

    2.5

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