机械工程师手册,仪器仪表,系统,控制系统,和MEMch14.doc

542CHAPTER14SERVOACTUATORSFORCLOSED-LOOPCONTROLKarlN.ReidCollegeofEngineering,ArchitectureandTechnologyOklahomaStateUniversityStillwater,OklahomaSyedHamidHalliburtonServicesDuncan,Oklahoma1INTRODUCTION5431.1Denitions5431.2Applications5431.3MathematicalModels5442ELECTRICALSERVOMOTORS5443DIRECT-CURRENTSERVOMOTORS5463.1BrusheddcServomotors5463.2BrushlessdcServomotors5524ALTERNATING-CURRENTSERVOMOTORS5574.1Typesofacservomotors5574.2MathematicalModel5595STEPPERMOTORS5625.1Operation5635.2TypesofStepperMotors5645.3MathematicalModelofaPermanent-MagnetStepperMotor5675.4NumericalExample5676ELECTRICALMODULATORS5696.1Direct-CurrentMotorModulators5696.2StepperMotorModulators5737HYDRAULICSERVOMOTORS5747.1Linear-MotionServomotors5747.2Rotary-MotionServomotors5757.3MathemticalModels5768HYDRAULICMODULATORS5828.1ServovalveDesignandOperation5828.2MathematicalModelofaSpool-TypeValve5848.3MathematicalModelsforanElectrohydraulicServovalve5889ELECTROMECHANICALANDELECTROHYDRAULICSERVOSYSTEMS5909.1TypicalCongurationsofElectromechanicalServosystems5909.2TypicalCongurationsofElectrohydraulicServosystems5909.3ComparisonofElectromechanicalandElectrohydraulicServosystems59210STEADY-STATEANDDYNAMICBEHAVIOROFSERVOACTUATORSANDSERVOSYSTEMS59610.1ElectromechanicalServoactuators59610.2ElectromechanicalServosystems60210.3ElectrohydraulicServoactuators60410.4ElectrohydraulicServosystems60610.5HydraulicCompensation61010.6RangeofControlforElectrodydraulicandElectromechanicalServosystems616REFERENCES617BIBLIOGRAPHY618ReprintedfromInstrumentationandControl,Wiley,NewYork,1990bypermissionofthepublisher.Mechanical Engineers Handbook: Instrumentation, Systems, Controls, and MEMS, Volume 2, Third Edition.Edited by Myer KutzCopyright 2006 by John Wiley & Sons, Inc.1Introduction543Figure1(a)Servoactuator(openloop);(b)servosystem(closedloop).1INTRODUCTION1.1DenitionsAservoactuatorisanopen-loopsystemthatcontrolsthelinearorrotarymotionofaloadinresponsetoaninputcommand(Fig.1a).Feedbackmaybeusedwithaservoactuatortoproduceaclosed-loopsystemreferredtoasaservosystem(Fig.1b).Servoactuatorsarenormallyrate-typesystems,inthataninputcommandresultsinanoutputvelocityforsteady-stateoperation.Positionfeedbackmustbeusedwiththerate-typesystemtoproduceaservosystemforpositioncontrol.Ifhigh-accuracyvelocitycontrolisrequired,velocityfeedbackmaybeusedwiththeservoactuator.Or,ifhigh-accuracyforce(ortorque)controlisrequired,force(ortorque)feedbackmaybeused.Thetermservomotordesignatesthevarioustypesofhigherlevelenergyconverterssuchaselectricalandhydraulicmotors.Theservomotorprovidesthemusclefunctionoftheservoactuator.Themodulatorprovidesaconversionofthelow-powerinputcommand(fortheservoactuator)ortheerrorsignal(fortheservosystem)toahigh-poweroutputthatoperatestheservomotor.Thetransducerprovidesthefeedbackinthecaseoftheservo-system.Theinputtotheservoactuatororservosystemcanbeelectronic,mechanical,hy-draulic,orpneumatic.Anddependingontheenergyconversionmedium,servoactuatorscanbeoftheelectromechanical,electrohydraulic,electropneumatic,orhydromechanicaltypes.1.2ApplicationsEarlydevelopmentofservoactuatorsandservosystemswaspredominantlyinelectropneu-matics(intheprocesscontrolindustry).1Withtheadventofmicroprocessorsandthedevel-opmentofhigh-coercive-strengthmagneticmaterials(suchassamariumcobaltandneodium).electromechanicalservosystemsndthelargestapplicationsinmodemindustry.2Table1describestheservocomponents(modulator,servomotor,andtransducer)forthevariousim-plementations.Applicationsrangefromfairlysimpleopen-loopsystemssuchasthehydraulic544ServoactuatorsforClosed-LoopControlTable1ServosystemComponentsSystemTypeModulatorServomotorTransducerElectromechanicalAmplierServomotorac,dcLinear/RotaryPosition,velocity,torqueDriverBrushlessservomotorTranslator/driverSteppermotorElectrohydraulicServovalveHydraulicmotorcylinderPosition,velocityforce,pressuretorqueElectropneumaticServovalveAirmotor,cylinderPosition,velocity,force,pressuretorque,controlsonabackhoetocomplexfeedbacksystemsinroboticsandaerospacevehicles.Figure2showsatypicallinearoutputservosystemdesignedforuseinawidevarietyofmotioncontrolapplications.Athreephasebrushlessmotorismodulatedbyapulse-width-modulatedcontroller(notshowninFig.2;seeRef.3).Aballscrewisusedtoconvertrotarymotiontolinearmotion.Feedbackisprovidedbyatachometer.1.3MathematicalModelsMathematicalmodelsofthevariouscomponentsofaservoactuatorareneededforcomponentselectiontomeetagivensetofperformancespecications.Thesespecicationsmayconsistofmovingagivenloadthroughagivendisplacementorvelocityproleinaspeciedtimeor,equivalently,followingdisplacementorvelocitycommandsgeneratedbyothersubsys-temsorbyanoperator.Themathematicalmodelofacomponentdescribesthesteady-stateand/ordynamicperformancecharacteristicsofthatcomponent.Mathematicalmodelsarepresentedinthischapterforthecomponentstypicallyusedinhigh-performanceservoactua-torsandservosystems.Examplesarepresentedtoillustratetheuseofmathematicalmodelsinthepredictionofsteady-stateanddynamicperformanceofservoactuatorsandservosys-tems.2ELECTRICALSERVOMOTORSElectricalservomotorsmaybeclassiedbythefollowingcharacteristics:1.Typeofpowerdirectcurrent(dc)oralternatingcurrent(ac)2.Typeofmotionexecuted(continuousordiscrete,rotaryortranslatory)3.Typeofcommutation(mechanicalorelectronic)4.Methodofmagneticeldgeneration(permanentmagnetorelectromagnetic)Accordinglytherearedcandacservomotorsofboththepermanent-magnetandeld-woundtypes.Steppermotorsbelongtothediscretemotiontype.Theratheruncommonlinearmotorexecutestranslatorymotion.Brushlessdcmotorsareoftheelectroniccommutationtype.Forthesakeofsimplicity,electricalservomotorsarebroadlyclassiedhereintofourcate-gories:dcandacservomotors,steppermotors,andlinearservomotors.Electricalservomotorsofferseveraladvantagesovertheirhydraulicandpneumaticcoun-terparts.Theseadvantagesinclude(a)compactness(facilitatedbyavailabilityofhigh-coercive-strengthmagneticmaterialssuchassamariumcobaltorneodium),(b)lowcost,(c)2ElectricalServomotors545Figure2(a)Electromechanicalservosystem;(b)crosssectionofanelectromechanicalservosystem.(CourtesyofMoog,Inc.,EastAurora,NY.)546ServoactuatorsforClosed-LoopControlFigure3Conventionalpermanent-magnetmotor.highreliability,(d)cleanliness,(e)easeofcontrolfunctionimplementation,(f)portabilityduetooperationatlowdcvoltagelevels,and(g)largebandwidthduetohightorque/inertiaratios.3DIRECT-CURRENTSERVOMOTORSDirect-currentservomotorsoffercertainadvantagesoveracservomotors.Theseadvantagesarehigherreliability,smallersize,andlowercost.Useofepoxyresinsandimprovedbrushdesignscombinedwithsuperiormagneticmaterialscontributetotheseadvantages.Direct-currentservomotorsarecompatiblewiththyristors(siliconcontrolledrectiers,SCR)andtransistorampliers,whichfacilitatescontrolimplementation.Typicaldcservomotorsrangeinpowerfromfractionalhorsepowertoseveralthousandhorsepower.Conventionalbrusheddcmotorstheoreticallycanbeusedasservomotors.However,inlowerhorsepowerlevels(10hporless)theyarenotpreferred.3.1BrusheddcServomotorsInthedcservomotor,theinteractionoftwomagneticelds(eitheroneorbothgeneratedelectrically)resultsinmechanicalmotionofanarmature.Atypicalpermanent-magnetdcmotorisillustratedinFig.3.Thepermanentmagnetissometimesreplacedbyaeldwindingtogeneratethemagneticeld.Theeldwindingmaybeconnectedinthreedifferentwaystothearmaturewinding:series,shunt,orcompound.Table2summarizesthebasicfeaturesofthevariouscongurationsalongwiththeresultantperformancecharacteristics.Table3showstypicalupperlimitsofdcservomotorperformance.43Direct-CurrentServomotors547Table2dcServomotorClassicationMotorTypeCongurationTypicalSteady-StateCharacteristicsSalientFeaturesPermanentmagnetNopowerrequiredforeldgenerationRunsCoolerTorque-speedcharacteristicsislinearCompactnessStraightseriesLargestartingtorqueSplitseriesAllowsquickreversingShuntLowstartingtorqueFinitespeedatzerotorqueCompoundHighstartingtorqueComplexcircuitryrequiredforreversingTable3UpperLimitsofdcServomotorPerformanceMotorTypeMaximumPower(hp)MaximumSpeed(rmp)Torque/InertiaRatio(rad/s2)MaximumBandwidth(rad/s)Movingcoil0.51450055002002501500Printedcircuit7300040001302201000Permanentmagnet101585030001530100Source:FromRef.4.548ServoactuatorsforClosed-LoopControlFigure4(a)Ironcore;(b)surfacewound.Thesplit-serieseld-woundmotorhastwowindings,oneforeachdirectionofrotation.Amanualswitchisusuallyemployedtoactivatetheappropriatewinding.Thetwowindingsofthecompoundmotorarealwaysexcitedandresultinahighstartingtorquewithgoodlinearity.Alloftheeldwoundmotorsareself-excitedwiththeresidualmagnetism.Permanent-MagnetMotorsPermanent-magnet(PM)motorsarethemostextensivelyusedforservomotorsbecausetheygeneratelessheatandhavehigherefciencyandmorecompactnessthaneld-excitedmo-tors.TherearethreetypesofPMmotorswithmechanicalcommutation:(1)ironcore,(2)surfacewound,and(3)movingcoil.Figure4showstheconstructionofthethreetypes.DetailsoftheadvantagesanddisadvantagesofeachtypemaybefoundinRef.5.3Direct-CurrentServomotors549Figure4(Continued)(c)Movingcoil.(FromRef.5.)Figure5Lumped-parametermodelofapermanentmotor.MathematicalModelofaPermanent-MagnetServomotorComprehensivepresentationsonmathematicalmodelingofdcservomotorsaregiveninRefs.69.Asimplieddynamicmodelispresentedhere.Themathematicalmodelofapermanent-magnetdcmotorisobtainedbylumpingtheinductanceandresistanceofthearmaturewindingasshowninFig.5.Theresultingequationsaregiven:Voltageequations:div穠L穠Ri穠e(1)aaabdte穠K穠(2)bEmTorquebalanceequation:d穠mKi穠J穠B穠穠T穠T(3)TmmmmLdt550ServoactuatorsforClosed-LoopControlTakingLaplacetransformsofEqs.(1)(3)gives,afteralgebraicmanipulation,酠(s)酠G(s)V(s)酠G(s)T(s)酠T(s)(4)m1a2mLwherethetransferfunctionsG1andG2aregivenbyKTG(s)酠(5)1RB(酠s酠1)(酠s酠1)酠KKamemTER(酠s酠1)aeG(s)酠(6)2RB(酠s酠1)(酠s酠1)酠KKamemTEandtheparametersaredenedasfollows:Bm酠viscousdampinginmotor(N酠m酠s/rad)eb酠backelectromotiveforce(emf)(V)i酠currentthrougharmature(A)Jm酠polarmomentofinertiaofarmature(N酠m酠s2/rad)KE酠z酠酠P/60酠motorvoltageconstantorbackemfconstant(V酠s/rad)KT酠z酠酠P/2酠酠motortorqueconstant(N酠m/A)La酠armatureinductance(H)P酠numberofpolesRa酠armatureresistance(酠)s酠Laplaceoperatort酠time(s)酠TmCoulombfrictiontorqueinmotor(N酠m)TL酠externalloadtorqueva酠voltageappliedtoarmature(V)Va(s)酠Laplacetransformofarmaturevoltageva(t)z酠酠numberofconductorsperparallelpathinarmature酠m酠angularpositionofmotorshaft(rad)酠酠magneticuxperpole(Wb)酠e酠La/Ra酠electricaltimeconstant(s)酠m酠Jm/Bm酠mechanicaltimeconstant(s)酠m酠angularvelocityofmotor(rad/s)酠m(s)酠laplacetransformofmotorangularvelocityEquation(4)canbesimpliedifthearmatureinductanceissmall(makingtheelectricaltimeconstant酠enegligible)andtheCoulombfrictionandloadtorqueareassumedzero.Theresultis酠(s)Kmm酠(7)V(s)酠s酠1awhereKTK酠(motorconstant)(8)mRB酠KKamTEand*Someservomotormanufacturersdene酠mdifferently.Forexample,Electro-Craft9denesthemechan-icaltimeconstantas酠m酠(RaJm)/(KTKE).3Direct-CurrentServomotors551RJam(9)RBKKamTEReference9discussescaseswheretheelectricaltimeconstantcannotbeneglected.Theprecedingmathematicalmodelsassumeavoltageinput.Forapplicationswhereacurrentamplierisused,thefollowingapproximatemodelshouldbeused:(s)Kmm(10)I(s)s1mwhereI(s)istheLaplacetransformofthecurrentinputi.ThemotorconstantinthiscaseisKTK(11)mBmInprinciple,themodelsdevelopedcanbeappliedtoallofthedcmotorsofthevarioustypeswiththeappropriateinputconditions.Thesemodelsdescribetheopen-loopresponse.Forclosed-loopsystemswithvelocityorpositionfeedback,anappropriateclosed-looptrans-ferfunctioncanbederivedeasilybymakinguseofthemotordynamicmodel.Anexampleofaclosed-loopsystemisgiveninSection10.2.NumericalExampleForMotomaticPMservomotormodelnumberE350-MG,10thefollowingspecicationsaregiven:KT3.4in.oz/A(0.024Nm/A)KE2.5V/krpm(0.024Vs/rad)Ra12.4Jm2.5104in.ozs2/rad(1.8106Nms2/rad)Bm0.015in.oz/krpm(1.01106Nms/rad)Tm0.5in.oz(3.5103Nm)Tmax2.5in.oz(1.8102Nm)Imax0.75Amax10,500rpmatnoload(1099rad/s)La3.1mHe0.25103sRththermalresistance13C/WThemechanicaltimeconstantcanbecomputedasJm1.75s(12)mBmSinceem,Eq.(7)canbeusedtodeterminethedynamicresponseiftheCoulombfrictionandloadtorqueareneglected.Inthiscase,thetimeconstantisRJam0.037s(13)RBKKamTEandthemotorconstantisKTK0.39krpm/V(40.8rad/Vs)(14)mRBKKamTEThetransferfunctionofEq.7becomes552ServoactuatorsforClosed-LoopControl趠(s)40.8m趠(15)V(s)0.037s趠1aForastepinputof1V,themotorspeedisgivenby140.8趠(s)趠(16)趠趠ms0.037s趠1TheinverseLaplacetransformgivesthestepresponseas趠t/0.037趠(t)趠40.8(1趠e)(17)m3.2BrushlessdcServomotorsThedevelopmentofbrushlessdcservomotorswasanoutgrowthofsemiconductordeviceseventhoughtherstpatentwasobtainedwithvacuumtubetechnology.11Thebasiccon-structionofabrushlessdcmotoreliminatesmechanicalcommutation.Instead,thecommu-tationprocessisaccomplishedelectronicallywithnomovingcontacts.Hence,theproblemsassociatedwithmechanicalcommutationsuchasbrushwearparticles,electromagneticin-terference(EMI),orarcingareeliminated.Eliminationofarcingmakesdcservomotorsexcellentcandidatesforapplicationsrequiringexplosion-proofsafetyclassication.ConstructionTypically,brushlessmotorshaveaninnerrotorandouterstatorandacongurationsuchastheoneshowninFig.6a.However,theotherconguration(i.e.,innerstatorandouterrotor)isalsopossible(seeFig.6b).Theformercongurationwiththeouterstatorcarryingelec-tricalwindingsprovidesexcellentthermaldissipationcharacteristics,sinceboththeironandcopperlossesoccurinthestatorandthestatorisbetterexposedtotheambientforconvectiveheattransfer.Thisfeatureallowsbrushlessmotorstobeoperatedathigherspeedsandhenceprovideshigherpower-to-weightratio.Brushlessdcmotorsrangefrom1to40in.(0.025to1.02m)indiameterwith6in趠oz(4.24趠10趠2N趠m)to1650ft趠lb(2237N趠m)oftorquecapability(seeTable4).Typicalapplicationsincludememorydiskdrives,videotaperecorders,andpositionservosincryo-geniccompressorsandfuelpumps.Therotorsarepermanentmagnetsmadefromoneofthreeprimarymaterials:ceramic,AlNiCo,andrareearth(suchassamariumcobalt).Ceramicrotorsareusedinapplicationswherecostconsiderationisimportant.Rare-earthmagnetsarethemostexpensivebutprovideexceptionalperformance.AlNiComagnetsareofmediumcostandprovidemediummagneticstrengths.OperationThebrushlessmotorisoperatedbygeneratingarotatingmagneticeldthatis90趠(electrical)outofphasewiththerotor.Positionsensorsareusedtodeterminetherotorposition.Thesepositionsensorsareofthreetypes:phototransistor,electromagnetic,andHalleffectgener-ators.CommutationAnelectronicmoduleconsistingoflogiccircuitsandpoweramplicationcircuitsisusedtodrivethemotor.3,4,12,13Thismodulereceivesrotorpositioninformationfromthepositionsensors.Theanglethroughwhichtherotorturnsduringtheringofawindingiscalledtheconductionangle.Figure7showsschematicallyatwo-phasebrushlessmotorwiththedriverelectronics.3Direct-CurrentServomotors553Figure6Crosssectionoftypicalbrushlessdcmotors:(a)innerrotorouterstatortype;(b)innerstatorouterrotortype.(FromRef.5.)Table4BrushlessdcMotorPerformanceDataMagnetTypePower(W)PeakTorque(in.渠oz)ElectricalTimeConstant(s)MechanicalTimeConstant(s)Torque/Inertiaratio(rad/s2)Ceramic25900106000.00020.00160.02210.740041311,400AlNiCo2028065,0000.00010.00300.00650.133046557,500Rareearth25600010316,0000.00010.01400.00240.0291137100,000554ServoactuatorsforClosed-LoopControlFigure7Two-phasebrushlessmotorwithdriverelectronics.Figure8showsthecontrollercircuitforathree-phasebrushlessmotor.Eachphaserequiresapairofswitchesforcommutation.Sincethecostofthemotorisdependentonthenumberofswitches,thereisatendencytokeepthenumberofphasestoaminimum.Typ-ically,three-phasemotorswithsixswitchesareused.Thecurrentthroughthewindingsmaybevariedinasinusoidalorasquare-wavemanner.Thelatterexcitationresultsinasmalltorqueripple(17%averagetopeakforatwo-phasemotorand7%forathree-phasemotor).Ideally,asinusoidaltorquefunctionresultsinaconstanttorque.Butsinusoidaltorquefunctiongenerationistechnicallydifcultanduneconomical.Analternateapproachistodesignthespatialvariationofthemagneticeld(possiblebymeansofhigh-coercive-strengthmagnets)toobtainatrapezoidaltorquefunctionwhiletheinputcurrenthasasquarewave-form(easilygeneratedbysimpletransistorcontrolcircuitry,suchasshowninFig.8).Themotortorqueisthenapproximatelyconstantandisproportionaltothemaximumvalueofcurrentduringeachcycle.Thetrapezoidaltorquegenerationschemealsoresultsinhigherefciency.Thelocationsofthepositionsensorsrelativetotherotorarealignedtoresultinappro-priatetimingforpropercommutation.Whenproperlycommutated,abrushlessmotordu-plicatesthetorquespeedcharacteristicsofabrush-typedcmotor.Thepoweroutputofthebrushlessmotoriseffectivelycontrolledbypulse-widthmod-ulation(PWM)orpulse-frequencymodulation(PFM)methods.Alinear(i.e.,classA)powerampliercanalsobeusedforpowercontrol.However,useofthistypeofamplierproduces3Direct