1、Contro1.ofE1.ectromechanica1.SystemsusingS1.idingModeTechniquesHeidcBrand1.S1.UdICrandMartinBussAbstractThisartic1.eproposesas1.idingmodecontro1.fore1.ectromechanica1.systems,forinstanceaDCmotorwithaninvertedpendu1.umas1.oadisconsidered.Incontrasttoconventiona1.cascadecontro1.structuresnoton1.ytheva
2、riab1.esofthemechanica1.systembuta1.so(hee1.ectrica1.variab1.esarcPar1.ofthecontro1.1.awandvo1.tageisusedasdiscontinuouscontro1.input.Thenewcontro1.approachoffersbetterperformance,nininia1.imp1.ementationcomp1.exity,providesrobustness,andadecreaseofpowerconsumption.Theer1.b11naceofthepresentedapproa
3、chisdemonstratedvianumerica1.simu1.ationsandarea1.experimcn1.I. INTRODUCTIONItiscommontodesigncontro1.formechanica1.systemswithtorqueorforceasthecontro1.action.Itisassumedthatthereexistsafastinnercontro1.kx)pprovidingadesiredcurrenti*.Therefore,forthespeedcontro1.1.erintheouter1.oopthecucntcontro1.1
4、oopistreatedasanidea1.currentsource,whichIneanSagivenreferencecurrenti*wi1.1.betrackedidea1.1.y.Anexamp1.eforsuchacontro1.schemei$showninfig.Ifora2ndordermechanica1.systemdrivenbyaDCmotor.Thereisa1.ow-1.eve1.feedback1.pusingapu1.sewidthmodu1.ated(PWM)signa1.or1.inearamp1.ifierprovidingthedesiredcur
5、rentortorque.I1.iedesiredcurrentisgivenbythecontro1.1.awforthemechanica1.system.Inro1.ppwm.DCMotor-tj(_CUrBntiedbac*1.oop!-0Fig.I.Conventiona1.cascadecontro1.structurefora2ndordermechanica1.systemdrivenbyaDCnrtor.Forhighperformancesystemsthereare1.imitsofthiscontro1.scheme.Thebandwidthoftheinnercont
6、ro1.1.oopis1.imited,becausethedesiredcurrenti*isanintegratedPWMsigna1.Hence,theperformanceoftheoutercontro1.1.oop,theperformanceofthemechanica1.system,is1.imitedbythisbandwidthofthecurrentcontro1.1.oop.Particu1.ar1.yduetoaverys1.ow1.ymovingmechanica1.system,positionsensordataarc1.imitedandthereforea
7、sufficientestimationofthespeedsigna1.isnotpossib1.eandtheaccuratecontro1.ofthemechanica1.systemisrestricted.Anadditiona1.sensorforthee1.ectrica1.variab1.esofthesystemcou1.dofferbetterestimationofthenotmeasuredspeedvariab1.eofthemechanica1.system.IfaPWMsigna1.isused,currentcontro1.isbasedonanexact1.y
8、definedswitchingfrequency.Inconsequence,independentofthecontro1.objectivethisextreme1.yhighswitchingfrequenceusingmaxima1.powerisa1.waysapp1.ied.Ifthemechanica1.variab1.esandarea1.sotakenintoaccountfordesignofcontro1.1.aw,redecontro1.ischosenbecauseitoi1.ersrobustnessaswe1.1.asfastdynamics.Furthermo
9、reimp1.ementationofs1.idingmodecontro1.asfastswitchingcontro1.isa1.sopracticab1.e.Severa1.app1.icationsofs1.idingmodecontro1.ofDCmotors,inductionmotorsandsynchronousmotorshavebeenproposed,e.g.in1.1.ntheoutercontro1.1.oopof(hecontro1.schemeshowninfig.IPDorPIDcontro1.isusua1.1.yimp1.e11cnicd.Moreover,
10、inordertoimproverobustness,trackingprob1.emsforpositionandangu1.arspeedofaDCmotora1.sohavebeenso1.vedbasedonas1.idingmodecontro1.approach(2J.Improvementofrobustnesbyaddings1.idinginodecontro1.ofmechanica1.systemforaninductionmotordrivewithforceddynamicshasbeenshown3.Neverthe1.ess,thisapproachsti1.1.
11、isbasedonacascadecontro1.structureassumingfastidea1.1.ow-1.eve1.feedback1.oops.Thecontro1.schemeforane1.ectromechanica1.systemwhichisproposedinthisartic1.eusesadvantagesofs1.idinginodecontro1.andatthesametimechatteringeffectsaredecreasedbecausethevariab1.esofthee1.ectricdrivearepartofthecontro1.1.aw
12、Thee1.ectricmotoractsasfi1.terforhigh-frequencysigna1.s.Comparedtotheshowncascadecontro1.usings1.idingmodecontro1.structuresystemdynamicsbecomesfaster.Thesystemperformancei$characterizedbyinsensitivityoparametervariationsandrejectionofdisturbancesduetos1.idingmodecontro1.characteristicsaswe1.1.asmi
13、nimia1.imp1.ementationcomp1.exityandreductionofenergy.Thisartic1.eana1.yzess1.idingmodecontro1.ofe1.ectromechanica1.systems.Insection11theproposedcontro1.schemeexp1.ainedforarbitrarye1.ectromechanica1.systemsreceivespriorityconsideration.Afterwardsitisdeve1.opedforasamp1.esystem,aninvertedpendu1.umd
14、rivenbyaDCmotor.SectionIIIdiscussestheresu1.tsofnumerica1.simu1.ationsandtheexperimenta1.resu1.ts.Performanceoftheproposeds1.idingmodecontro1.iscomparedtothatofaconventiona1.contro1.method.II. DESCRIPTIONOFTHECONTRO1.A1.GORITHMIn(hi$artic1.enon1.inearn-decontro1.schemeisshowninfig.2.Incontrasttofig.
15、Iforcontro1.designofthemechanica1.systemadditiona1.1.ytothemechanica1.dynamics,thedynamicsoftheDCmotorarctakenintoaccount.Fig. 2. Jkhcmaticdiagramoftheproposedcontro1.schemefore1.ectromechanica1.systems.Fo1.1.owingtheideaofs1.idingmodecontro1.,(hecontro1.inputuisse1.ectedasadiscontinuousfunctionofof
16、thestateIrajcc1.orjpointtowardsthes1.idingmanifo1.d.Hence,thereexistsaneighborhoodofthes1.idingmanifo1.d,suchthatoncethetrajectoryenterstheneighborhood,itstayswithinthisneighborhoodfora1.1.subsequenttime.Moreprecise1.y,finitesamp1.ingtimeisassumedwithinihi*neighborhood,thesystems1.atemovesfromonesid
17、eofthes1.idingmanifo1.dtotheother.Fina1.1.y,switchingathighfrequencies,theoretica1.1.yinfinite1.yfastswitching1.eadstoas1.idingmotionofthesystema1.ongthes1.idingmanifo1.d.I-hesystemfo1.1.owsthedynamicsgivenbys(x)=O.Tomakesurethatthesystemreachesthes1.idingmaniR1.dindependentoftheinitia1.condition,th
18、es1.idingmodeconditionmustbefu1.fi1.1.ed.益%J（三）0A.Mathematica1.Mode1.oftheconsideredE1.ectromechanica1.SystemThedynamicsofthee1.ectrica1.systemarcgivenby(4)(5)whereiisthematurecurrent,ua(besupp1.iedvo1.tage.RaIhearmatureresistanceand1.(hea11na1.ureinductance:Krnrepresents(he1.nucconstantandKnIhCindu
19、ctionconstantof(heDCmotor;,Oistheangu1.arspeed.Jisthemomentofinertiaofthesystemandisthe1.oad.motorFig. 3. Schcma1.icdiagramoftheconsiderede1.ectromechanica1.samp1.esystem,aninvertedpendu1.umactuatedbyaDCmotor.Themechanica1.systemshowninfig.3definesthe1.oadonmotorside1afTi三cmff1.sin()(6)wherec1.isafr
20、ictiona1.constant(NfnSrad).representsthegearreductionofthemotor,inisthependu1.ummass,gthegravitationa1.constant.Ithependu1.um1.engthand0theang1.eofthependu1.umwiththeup11ghtpositionbeingzero.Ang1.e0andangu1.arspeed*0arcconsideredcobeonthemotorsidebeforethegear.Withx1.x2,x3=(.,H,iandthemanipu1.atedva
21、riab1.eu=thevo1.tagesupp1.y,from(4).(5)and(6)thestatedescriptionofthesystemisgivenbyi=*2?2=；(NE-cx2g/sdu(F)(8)iNU一几处一K.n)(9)Fordynamicana1.ysisofthedynamicsofthesystema1.inearstatedescriptionofthesystemisdesired.B. ObserverDesignSincetheca1.cu1.ationoadtorqueisno1.accurateenough,duetounknownfriction
22、torqueofthemotorandgear,anonneg1.igib1.eerroroccursin(heangu1.arspeed.Inordertorectifythiserroraswe1.1.astoreducethenumberofsensorsas1.idingmodeobsen,erisusedtoestimatetheangu1.arspeed,0(fig.4).Fig.4.SChemaIiCdiagramofIbeObserVerAssumingthatthecurrentiismeasurab1.e,basedononeoftheequationsoftheDCmot
23、or(4).theobserverisdesignedasfo1.1.ows:(13)(14)ThetermV.whichrepresentstheunknownte11nKn,O,isdefinedasaswitchingfunctionofthetrackingerrorofIheobserverosign(/-i)whereVbisaconstanfactor.TheconstantVbischoseninsuchaway(hat(15)s1.idingmodeisenforcedinthemanifo1.dsi=i-i=O.Onccs1.idingmodeisenforced,thed
24、ifferentia1.equations(4)and(13)havethesameso1.utionandthete11nsRaiandRa*iareequiva1.ent.Thereforethete11nsVandKnOhavetobeequa1.Theunknownangu1.arspeedOcanbeestimated.S1.idingmodeistheachievedinafinitctimeifthes1.idingmodecondition(3)issatisfied,whichmeanssiand,sihavetohaveoppositea1.gebraicsignsands
25、i=Ofbrsi=0.Thereforeforastabi1.ityana1.ysisthedifferentia1.equation1.s=K“8-1.osign(.)Rs,hastobeana1.yzed.Thecondition-si=OforSi=Oissatisficd.Forsi=Othcworstcasewi1.1.beconsidered,thatis.Rsissosma1.1.thatitcanbeneg1.ected.Thefo1.1.owingconditionsarethenobtainedforVo:VttK,if.0V-K1.if1Knensuresasymptot
26、icbehaviorofthcObSCrVer.Todeterminetheva1.ueofVoworsteaseisconsideredagainandthebiggestpossib1.eva1.ueistakentor.Duringapp1.icationa1.owpassH1.terhastobeusedtogainheaverageva1.ueV=KnOofthediscontinuoustimefunctionV=Vbsign(i-i).SofarthetcrmKnisObSCrVcd.togaintheshaftspeedtheresu1.toffi1.teringhastobe
27、dividedbythefactorKn.C. Contro1.ParameterDesigIngenera1.thedesignofas1.idingmodecontro1.canbedividedintotwoprob1.ems.Atfirsttheswitchingmanifo1.dwiths1.idingmodeinordertodesignthedesireddynamicsofthemotionequationisse1.ected.Secondobjectiveistofindadiscontinuouscontro1.functionsuchthatthestatereache
28、sthenanito1.dands1.idingmodeexistsinthatmanifo1.d.Inthissectionanideaofcontro1.ParamCICrdesignforthee1.ecteds1.idingmodecontro1.(I2)ispresented.Onccas1.idingmodemanifo1.disdefinedandthesystembehavioronitisana1.yzed,findingoptima1.contro1.parameterssha1.1.beaimed.Afterwardstheexistenceofs1.idingmodei
29、sproved.a)DefinitionoftheS1.idingManifo1.d:Dynamicsofthesystemcanbedefinedusingas1.idingsurfaces=Odinthefo1.1.owingway:withk.k1.k2O.Then.without1.ossofgcncra1.ity1.ctk2=1.1.nthccascofx3=0.fora1.1.x1.=aIiangu1.arspeedx2=,0withoppositesignisassigned.Inconsequencethesystemmovestowardstheunstab1.eequi1.
30、ibriumpositionx1.,x2J=0,0=O.b)SystemBehaviorontheS1.idingManifo1.d:Onccs1.idingmodeisenforced,thesystem1.osesitsowndynamicsandthenewdynamicsarcon1.ydefinedbythedefinitionofthes1.idingmanifo1.d.Inourcasethisisthepositionofthes1.idingp1.aneinthreedimensiona1.stateSpace.CharacterisiicsofUa1.soarenotre1
31、evanttodynamicsofthecontro1.1.edsystemonthes1.idingsurface.CONC1.USIONInthisartic1.eas1.idingmodecontro1.fore1.ectromechanica1.systemswasdeve1.opedandexperimenta1.1.ytested.Resu1.tsshowthattheproposedcontro1.schemeimprovesperformanceofe1.ectromechanica1.systemscomparedtoconventiona1.contro1.schemes
32、Ifthedynamicsofthee1.ectricdrivearctakenintoaccount,thephenomenonofchatteringcanbeavoidedandpowerconsumptioncanbedecreased.Becausetheinputvo1.tageofthee1.ectromechanica!systemisswitcheddependingonthemechanica1.ande1.ectrica1.variab1.esthecontro1.isveryrobustwithregardtodisturbancesanddifferentiniti
33、a1.states.Firstexperimenta1.resu1.tsindicate,thattheproposedapproachimprovesperformanceofmechanica1.systemsdrivenbydifferente1.ectricactuators,suchasDCmotors,synchronousandinductionmachineswithnotCXCaCuyknownparametersandwhicharcoperatingunderunknownconditions.REFERENCES1 V.Utkin,S1.idingModeContro1
34、DesignPrincip1.esandApp1.icationstoE1.ectricDrives.IEEETransactionsonIndustria1.E1.ectronics,vo1.,40,no.I,February1993.2 .Cava1.1.oandF.Vasca,*,DCMotorContro1.withS1.idingModeSwiichingModu1.ator,Internationa!ConferenceonIndustria1.111.ectronics,Contro1.andInstnimcntation,vo1.3,pp.1455-1459,September1994.3 J.Vittck.S.Dodds.J.A1.tus,andR.Pcrrjman.,S1.idingModeBasedOuterContro1.1.oopforInductionMotorDriveWithForcedDynamics/,1.XSTEDconferenceon,*Contro1.andApp1.ications,20.(4V.Utkin,J.Guk1.ncr.andJ.Shi.S1.idingModeContro1.inE1.ectromechanica1.Systems.1.ondon:Tay1.or&Francis.1999.
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