外文翻译-新型直动式压电电液伺服阀复合控制方法

中文3450字附二：外文翻译HighPreciseControlMethodforaNewTypeof

PiezoelectricElectro—hydraulicServoValveAbstract:Anewtypeofpiezoelectricelectro-hydraulicservovalvesystemwasproposed.Andthenmultilayerpiezoelectricactuatorbasedonnewpiezoelectricceramicmaterialwasusedastheelectricity-machineconverteroftheproposedpiezoelectricelectro-hydraulicservovalve.Theproposedpiezoelectricelectro-hydraulicservovalvehasascendantperformancecomparedwithconventionalones.Butthesystemisofhighnonlinearityanduncertainty,itcannotachievefavorablecontrolperformancebyconventionalcontrolmethod.Todevelopanefficientwaytocontrolpiezoelectricelectro—hydraulicservovalvesystem.Ahigh—precisefuzzycontrolmethodwithhysteresisnonlinearmodelinfeedforwardloopwasproposed.Thecontrolmethodisseparatedintotwoparts:afeedforwardloopwithPreisachhysteresisnonlinearmodelandafeedbackloopwithhigh-precisefuzzycontro1.ExperimentalresultsshowthatthehysteresisloopandthemaximumoutputhysteresisbythePIDcontrolmethodare4.22%and2.11pm,respectively；thehysteresisloopandthemaximumoutputhysteresisbytheproposedcontrolmethodrespectivelyare0.74%and0.37pm,respectively；themaximumtrackingerrorbythePIDcontrolmethodforsinewavereferencesignalisabout5.02%,themaximumtrackingerrorbytheproposedcontrolmethodforsinewavereferencesignalisabout0.85%.control.Keywords:piezoelectricelectro一hydraulicservovalve；hysteresisnonlinearity；Preisachmodel；fuzzycontrolIntroductionElectro—hydraulicservosystemiswidelyappliedinindustrialdomainnowadays.forexample.robotdrive,machinebuilding,architecturalengineering.Theelectro-hydraulicservovalveisthekerneloftheelectro-hydraulicservosystem,anditsperformancehasdecisiveeffectOfthewholesystem.Theconventionaldrivemodeofelectro.hydraulicservovalvehaslowerresolutionandnarrowerworkbandwidth,whichrestrictstheapplicationsoftheelectro-hydraulicservovalve.Theproposedpiezoelectricelectro-hydraulicservovalveadoptsmultilayerpiezoelectricactuatoraselectricity-machineconverter.ThisHewtypeofpiezoelectricelectro-hydraulicservovalvehasbetterdynamicperformancethanthatofconventionalones.Atpresent,withtheresearchandthedevelopmentofnew-typeactuatorbasedonnewtypematerials,itispossibletomakethenewelectricity-machineconverterwithhighfrequency.Newmaterialsincludepiezoelectricceramicmaterials,magnetostrjctivematerials,shapememoryalloys.Thereinto,multilayerpiezoelectricactuatorsbasedonnewpiezoelectricceramicmaterialshavemanymeritssuchassmallcubage,highresolution,highfrequencyandlargedriveforce.Hence,theyarewidelyusedinthemicro-positiondeviceofmachinetoolsandotherprecisionmachines[1-6].However,theyalsohavemanyshortcomings,forexample,hysteresisnonlinearitymodelinfeedforwardloopwasproposed.Workprincipleandcharacteristicofnew-typeofpiezoelectric

electro-hydraulicValveBecausethepullingforcecapacityofmultilayerpiezoelectricactuatorisverypoor,itcannotmaketheslidevalveoftheelectro,hydraulicservovalvebidirectionallvmove.Twomultilayerpiezoelectricactuatorswereadoptedtosolvethisproblem[7-8].Theshortcomingofthismethodishighcostandsystemisdifficulttocontro1.Utilizingtherestoringforceofaleafspring,onemultilayerpiezoelectricactuatorcanrealizebidirectionalmovementoftheslidevalveinthispaper.Whenthevoltageimposedonmultilayerpiezoelectricactuator1sincreased,multilayerpiezoelectricactuatorwillelongateanddrivetheslidevalvetomovetowardstheleft,whichmakestheleafspringdeform.Onthecontrary,whenthevoltageimposedonmultilayerpiezoelectricactuatorisreduced,multilayerpiezoelectricactuatorwillbeshortenedandthendrivetheslidevalvemovetowardstherightbytheactionoftherestoringforceoftheleafspring.Thestructureofnewtypeofpiezoelectricelectro—hydraulicservovalveisshowninFig.1.FigJStructureofnewtypeofpiezoelectricclcctm-hydraulLcv^lveI—Displacement$ensor；2—LeafSpring；3—Extensionrod；Fig.2FigJStructureofnewtypeofpiezoelectricclcctm-hydraulLcv^lve4—Slidevidvc;5—MultilayerpiczaclcctricactuatorEcctm-hydrauiicsepvalvesysLcmTheinput-outputcharacteristicofthenewtypeofpiezoelectricelectro-hydraulicservovalvesystemindicatesthatithashysteresisnonlinearitywithnonlocalmemory(seeFig.2).AtanyreachablepointL(Ua,Ya)ininput-outputdiagram,thenumberofalternativecurvethatdescribesthefuturepathofhysteresisnonlinearitywithnonlocalmemoryisinfinite.Namely,thefutureoutputofthesystemdependsnotonlyonthecurrentoutputYaandfutureinput,butalsoonthepasthistoryofinputvalue’sextremum.Hence,theoutputresponseofnewtypeofpiezoelectricelectro-hydraulicservovalvetoanappliedinputvoltagebecomesunpredictable.Inthesystem,thereexistothernonlinearitiessuchasforceoffrictionandworkdeadzoneofvalve,furthermore,dampingcoefficientandoiltemperaturearealsochangedwithtime.Thenonlinearityanduncertaintyhaveseriouslyeffectsonthepositionprecision.Toimprovetheperformanceofthenewtypeofpiezoelectricelectro-hydraulicservovalvesystem,avalidcontrolmethodisneededControlalgorithmAtpresent,conventionalPIDcontrolleriswidelyappliedinindustrialcontroldomainbecauseofitssimplecontrolstructure,easydesignandinexpensivecost.However,conventionalPIDcontrollerisdifficulttoachievegoodcontrolperformanceinthenewtypeofpiezoelectricelectro,hydraulicservovalvesystembecausethecontrolobjecthashighnonlinearityanduncertainty.Fuzzycontrollershowsgoodresultsinthecaseofcontrollinghighnonlinearsystems.However,conventionalfuzzycontrollerisessentiallyakindofnonlinearPDcontroller,thereexistssteadystateerror,whichcannotmeetthedemandofhighpreciseofthesystem.Inthispaper,ahigh-precisefuzzycontrolalgorithmwithPreisach

hysteresisnonlinearmodelinfeedforwardloopwasproposed.TheblockdiagramofthecombinedcontrolisshowninFig.3.ThecontrolsystemiscomposedofafeedforwardloopbasedonPreisachmodelandafeedbackloopofhighprecisefuzzycontroller.Ul(istheoutputoffeedforwardloopbasedonPreisachmode1.Asalinearterm,itisselectedfromaPreisachfunctiontablebasedonthegivenpositionvalue.U2(istheoutputofthehighprecisefuzzycontroller.ThesumU(t)offeedforwardcontrolvoltagefandfeedbackcontrolvoltageU2(t),asultimatecontrolvoltage,isactedonnewtypepiezoelectricelectro-hydraulicservovalve.3.1FeedforwardloopbasedonPreisachmodelTheopenloopresponseofthenewtypepiezoelectricelectro-hydraulicservovalvesystemunderanarbitraryandnon-cyclicinputsignalisshowninFig.2.Thisphenomenonappearsashysteresisnonlinearitywithnonlocalmemory,whichcanbepredictedbyPreisachmode1.ThenumericalformofPreisachmodelcanbewrittenasfoliows:f(t)=ffu(a,P)u(t)ddS+roFeedforwardLoopbasedonPreisachhy$&esismodelFig*3BlockdiagramofcombinedcontrolFeedforwardLoopbasedonPreisachhy$&esismodelEqn.(1)canbeusedtocalculatetheresponseofthenewtypeofpiezoelectricelectro-hydraulicservovalvesubjecttoaknownarbitraryinputvoltagesequence.Aseriesoffirstorderfunctionsrofthenewtypeofpiezoelectricelectro-hydraulicservovalveareakPkexperimentallydetermined.Theprocedureisasfollows.ThespacebetweenzeroandsaturationvoltageUsisdividedintonequipartitions,andthevoltageofeveryequantpointiskUs/n,wherek=-0,1,2,n.VoltageisappliedfromzerotoeveryequantpointkUs/n,andthendecreasedtozero.Inthisprocess,thepositionoutputvaluesofthenewtypeofpiezoelectricelectro-hydraulicservovalvearerecordedatreveryequantpointbetweenzeroandsaturationvoltageUs,therewith,andthePreisachfunctionakpktableareobtained(seeFig.4),

60w/VFig*4Hysteresiscurvfebydifferentfrequencyvoltage)yu(t)dd(d，(2)〔dt60w/V)yu(t)dd(2)Basedonthedrivervoltagerangeofthenewtypeofpiezoelectricelectro.hydraulicservovalve,thecoordinatespaceisselectedas0<U<l50Vand0<U§,<150VFromFig.4,thelimittriangleisdividedintoseveralsquaresandtriangles.Decreasingthesizeofthesquaresandtrianglesisexpectedtoincreasetheaccuracyofthemode1,however,itwillspendmassivecomputationaltime.Basedontheexperiments,nisselectedas5,namely,thesizeofeachofsidesofthesquaresandtrianglesisselectedas30V.BasedonthegivenpositionvalueandthenumericalformofthePreisachmodel,『U(t)UP'n-1orYcanbeobtained.Thereby,basedonPreisachfunctiontable,thecontrolvoltageUl(t)isobtainedwhenU§liesontheverticallineorUliesonthehorizontalline.FortheinexistencevoltageinthePreisachfunctiontable.itcanbeobtainedbythelinearinterpolation.Incomparisontoaconventionalfeedbackcontroller,themainadvantageofthismode1-basedfeedforwardcontrolleristhatitcancompensatethehysteresisnonlinearityofthesystemandachievehighlydynamicoperationatthesametime,andnoadditionalsensorisneeded.Thisleadstoaverysimpleandinexpensivecontrolsystem.Themaindrawbackofthefeedforwardcontrollerissensitivetounmodeldataandunconsideredexternaldisturbancessuchastemperaturedrift.Foranewtypeofpiezoelectricelectro—hydraulicservovalvesystemthatneedshighcontrolprecision.mode1.basedfeedforwardcontrollercannotobtaingoodcontroleffect.Thenacompoundcontrolmethodwithfeedforwardandfeedbackcontrolprojectwasproposedinthispape.Inthefeedbackcontrolloop,ahigh—precisefuzzycontrolalgorithmwasadopted.Themethodcanobtaingoodperformance.3.2HighprecisefuzzycontrolConventionalfuzzycontrollerhastwoinputvariables,eand△e,andoneoutputvariable(U),theyareerror,changeoferrorandoutputcontroloffuzzycontroller.Inthenewtypeofpiezoelectricelectro-hydraulicservovalvesystem,thephysicalrangeoftheslidevalvepositionerror(andchangeoferror(△e)are[-x,x]and[-△x,△x],respectively.Thecorrespondingdiscreteuniversesofdiscourseofe,△eanduareE,ECandUrespectively.E,ECandUaredesignedasnormalizedform:{-n,-(n一1),…，0,…，n一1,n}(i=1,2,3)(3)

ke|△easzeroandtheoutputThescalefactorsarek,kandk,respectively.Thenk=n/xk=n/xk=yke|△easzeroandtheoutput<0.5andBasedoncontrolruleofconventionalfuzzycontroller,when[0.5,theconventionalfuzzycontrollerconsiderstheinputseanduisalsozero.However,theinputseand△earenotcertainlyequaltozero.Henceconventionalfuzzycontrollerhascontroldeadzone.Controldeadzoneofconventionalfuzzycontrolleristhemainreasonwhythesteadystateprecisionoflook-uptablealgorithmispoor.Thekeytoimprovingthecontrollingprecisionoffuzzycontrolalgorithmbasedonlook-uptableistoeliminate<0.5andToresolvethisproblem,animprovedfuzzycontrollerisadopted.WhenEorECisnotequalto0,thelook-uptableisadaptedtocalculatingthecontroloutputU;whenEorECareequalto0,InterpolationalgorithmisadoptedtocalculatingthecontroloutputU’insteadofquantization.ThemethodofinterpolationcalculationisshowninFig.5.TheU(I,j),U(i+1,j),andU(i+1,j+1)arefourpointinthelook-uptable,andthevalueofU’canbecalculatedbasedonthem.4.ExperimentalresearchThepositionprecisionofthenewtypeofpiezoelectricelectro-hydraulicservovalvesystemissignificantlyreducedduetotheeffectofnonlinearityanduncertainty.Inthispaper,thehigh-precisefuzzycontrolmethodwithPreisachhysteresisnonlinearmodelinfeedforwardloopwasdevelopedtosolvethisproblem.Todemonstratetheeffectivenessofthisproposedcontrolmethod,aseriesofexperimentswereperformedonthenewtypeofpiezoelectricelectro-hydraulicservovalvesystemundervariousconditions.Theexperimentalsetupwasbuilt.whichconsistedofindustrialcontrolcomputer,hydraulicpressureexperimentalbench,pumpingstation,PESarbitrarywaveformgenerator(ModelAG1200,YokogawaCo.)andmulti-purposeFFTanalyzer(ModelCF-5220,OnosokkiCo.).Theexperimentswereconductedunderahydraulicpressureof7MPa.HydraulicpressureexperimentalbenchwasusedtoprovidetheoperationalenvironmentforthePESV.Pumpingstationwasusedtoprovidetheliquidpressureforhydraulicpressureexperimentalbench.Waveformgeneratorwasusedtoprovidethewaveform.Fourieranalyzerwasusedtoanalyzetheexperimentalresult.Industrialcontrolcomputerwasusedtoreceivethepositionfeedbacksignalsandprovidecontrolvoltagebasedontheproposedcontrolmethod.Theindustrialcontrolcomputerstillincludesa12bitAD/DAcard(ModelPC一63l1,ZhongtaiCo.),apoweramplifierandprogramoftheproposedcontrolmethod.IndustrialcontrolcomputeracceptsthegivensignalfromwaveformgeneratorandpositionfeedbacksignalthroughA/Dconversioninterface,soonafterwards,calculatesthecontrolvoltagesignalbasedontheproposedthecontrolmethodandsendsitthroughD/Aconversioninterfacetoapoweramplifier.Inthepoweramplifier,thecontrolmethodwasamplifiedwithl0timesgainstodrivethepiezoelectricactuatorofthePESVThepositionfeedbacksignalwasalsosenttotheFourieranalyserforanalyzingtheexperimentaldatabesidessendingtoindustrialcontrolcomputerforcalculatingthecontrolvoltage.Firstly,theexperimentsweredoneunderopenloopcontrol,PIDcontrol,andhigh~precisefuzzycontrolmethodwithPreisachhysteresisnonlinearmodelinfeedforward

loop.Thehysteresisloopcurveswereplotted.Fig.6(a)showsthehysteresisloopoutputcurveofthesystemunderopenloopcontrol.Itwascalculatedthathysteresisloopisabout13.08%andthemaximumoutputhysteresisisabout6.64pm.Fig.6(b)showsthehysteresisloopoutputcurveofthesystemunderPIDcontrolmethod.Itwascalculatedthatthehysteresisloopisabout4.22%andthemaximumoutputhysteresisisabout2.11pm.Thiscontrolmethodcanrestrainthenonlineareffectsofthesystem.Fig.6(c)showsthehysteresisloopoutputcurveofthesystemunderthehigh-precisefuzzycontrolmethodwithPreisachhysteresisnonlinearmodelinfeedforwardloop.Itwascalculatedthatthehysteresisloopisabout0.74%andthemaximumoutputhysteresisislessthan0.37pm.Thiscontrolmethodcanvirtuallyeliminatethenonlineareffectsofthesystem.hysteresisandthehighestprecisioncomparedwithopenloopcontrolandPIDcontrol.UsFig.7TrackingcurveusingPIDfeedbackcontrolFig.10ErrorcurveusingUsFig.7TrackingcurveusingPIDfeedbackcontrolFig.10ErrorcurveusingPIDfeedbackcontrolbasedonPreisachmodelfeedforwardFig<9TrackingcurveusingPIDfeedbackcontrolbasedonPreisachmodelfeedforwardFig.11TrackingcurveusinghybridcontrolThecontrolresultsshowthattheproposedcontrolmethodgivestheminimumoutputFig.12ErrorcurveusinghybridcontrolSecondly,thecomparativeexperimentsofthetrackingresultforasinewavereferencesignalunderPIDcontrolmethodandtheproposedcontrolmethodweredone.Fig.7showsthetrackingresultofPIDcontrolmethodforsinewavereferencesigna1.Themaximumtrackingerrorisabout5.02%.Forthepositionpreciserequirement,thistrackingresultcannotbeaccepted.ThemainreasonforthisresultisthehysteresisnonlinearityofthenewtypeofpiezoelectricElectro-hydraulicservovalvesystem.Fig.8showsthetrackingresultoftheproposedcontrolmethodforsinewavereferencesigna1.Themaximumtrackingerrorisabout0.85%.ThetrackingresultsshowthattheproposedcontrolschemegivesfasterandmoreaccurateresponsescomparedwiththoseOfPIDcontro1,andtheycansatisfythehighprecisiondemandofthenewtypeofpiezoelectricelectro-hydraulicservovalvesystem.5.ConclusionsAnewtypeofpiezoelectricelectro-hydraulicservovalvesystemisproposed.Multilayerpiezoelectricactuatorbasedonnewpiezoelectricceramicmaterialsisusedastheelectricity-machineconverteroftheproposedpiezoelectricelectro-hydraulicservovalve.Becauseofhighnonlinearityanduncertaintyoftheproposedpiezoelectricelectro—hydraulicservovalvesystem,theprecisionrequirementsforpositionareinfluencedseriously.Hence.ahigh—precisefuzzycontrolmethodwithPreisachhysteresisnonlinearmodelinfeedforwardloopwasproposed.Theproposedcontrolmethodcanavailablyeliminatetheinfluenceofthenonlinearityanduncertainty,andimprovetheperformanceofthenewtypeofpiezoelectricelectro—hydraulicservovalvesystem.References[1]K1MJD,NAMSR.Developmentofamicro-depthc0ntrolsystemforanultra-precisionlatheusingapiezo-electricactuator[J].Intemationa1Jouma1ofMachineToo1s&Manufacture,I997,37(4)：495—509⑵KATSUSH1F,M1TSUNOR1U,NAOTAKEMDisplacementControlofpiezoelectricelementbvfeedbackofinducedcharge[J]Nan0fechnology,1998,9(2)：93—98SUNLiming,SUNShao-yun,QUDong-shen,eta1.Micro-drivepositioningsystembased0nPZTanditscontrollJ1_OpticsandPrecisi0nEngineering2004,12(1)：55—59.(inChinesWE1Yan-dingLUYong-gui,CHENZi-chen.Researchonopen-1oopprecisionpositioningcontro1ofamicrodisplacementplatformbasedonpiezoelectricactuators[J].ChineseJouma1ofMechanica1Engineering,2004,40(12)：8l_85.(inChineseZHOUMiao-lei,YANGZhi-gang,GAOWei,etal.Fuzzycontrolofanewtypeofpiezoelectricdirectdriveelectro-hydraulicservovalve[C]//ProceedingsoftheFourthInternationalConferenceonMachineLearningandCybernetics.Guangzhou:IEEEComputerSoc,2005；；819-824YIY0u-pingSEEMANWGAUSMANR,etal.Anewhybrpiezoelectricultrasonicmotorwithtwostator[J]Jouma1ofCentralSouthUniversityofTechno1og2005,12(3)：324—328YOKOTAS,HIRAMOTOK.Ultrahigh.speedelectro-hydraulicservova1vebymakinguseofamultilayeredpiezoelectricdevice(PZT)(compensationofahysteresisbyintroducingasoftwarealgorithm)[J]lTranai0nofJapansocietyofMechanicalEngineersPartB,1991,57(533):182-187LUHao,ZHUCheng-lin,ZENGSi,etal.StudyonthenewkindofElectro-hydraulichigh-speedon-offvalvedrivenbypztcomponentsanditshigh,powerfulandspeedytechnique[J].ChineseJournalofReferencesMechanicalEngineering,2002,38(8)：118-121.(inChinese)GEMUSEJModelinghysteresisinpiezoceramicactuators[J].PrecisionEngineering,1995,17(3)：21l一221L1UShao-jun,HUANGZhong-hua,CHENYi-zhang.Automobileactivesupensiononsystemwithfuzzycontrol[J].JournalofCentalSouthUniversityofTechnology,2004,11(2)：206-209新型直动式压电电液伺服阀复合控制方法摘要：设计了一种新型直动式压电电液伺服阀。该阀采用压电叠堆执行器作为电一机械转换器，提高了电液伺服阀的性能。并针对压电叠堆执行器固有的迟滞和蠕变非线性使得压电型电液伺服系统的输出精度降低，传统的控制方法难以得到很好的控制效果的问题。提出了基于动态Preisach模型的前馈控制和PID反馈控制的一种复合控制方法。实验结果表明，该方法能有效改善新型直动式压电电液伺服阀的输出精度。关键词：自动控制技术；压电电液伺服阀；复合控制；动态Preisach模型；非线性1新型直动式压电电液伺服阀结构弹性回复板2、左端延长杆3、滑阀4、右端延新型直动式压电电液伺服阀主要由位移传感器1、长杆5、压电叠堆执行器6和阀体等部分组成，见图1。当输入电压增加时，压电叠堆执行器伸长推动滑阀向左运动；当输入电压减小时，压电叠堆执行器缩短，由弹性回复板的回复作用力使滑阀向右运动。通过滑阀的运动来控制进油口的开口量，进而控制液体流量以及压力的变化。弹性回复板2、左端延长杆3、滑阀4、右端延2系统特性分析压电叠堆执行器虽然具有诸多优点，但是其输出位移存在非线性，呷要表现为迟滞非线神蠕变非线性两种。迟滞非线性特性是由压电陶瓷晶体极化的偶极矩偏转引起的，表现为压电叠堆执行图2退滞非线性输出特性器在同一输入电压作用下的输出位移并不相同。蠕变非线性是随外加电压变化产生的一种特性，是在恒定电场作用时晶体电畴缓慢排列所表现出来的现象，当施加电压时，压电叠堆执行器的输出位移会在^级时间内产生变化，之后在很长的一段时间内会发生很微小的位移变化。蠕变的位移变化方向总是与施加电压变化方向相一图2退滞非线性输出特性由于压电叠堆执行器的输出通过延长杆直接作用到滑阀上，所以新型直动式压电电液伺服阀滑阀的输出位移也具有迟滞和蠕变非线性。研究新型直动式压电电液伺服阀的特性主要是研究该阀在控制。电压作用下的输出位移以及电压不变时输出位移和时间的关系。图2为新型直动式压电电液伺服阀在三角波作用下的位移输出曲线。图中虚线代表新型直动式压电电液伺服阀的标称输入/输出线

性化关系。可见，新型直动式压电电液伺服阀具有较强的迟滞非线性，输出响应与标称输出相比有很大的偏差。图3是新型直动式压电电液伺服阀在90V电压作用下100S内的位移输出变化曲线，在这段时间内的位移输出的蠕变量约为1.37m。可见，新型直动式压电电液伺服阀的蠕变非线性会对控制精度产生一定的影响。通过对新型直动式压电伺服系统的特性分析可知，由于迟滞非线性和蠕变非线性的存在，系统的输出精度会受到较大的影响，需要采用适当的控制方法来提高系统的输出精度。3控制算法工业上普遍采用的PID控制方法具有结构简单、造价低廉和无需精确建模等优点，在精密定位控制系统中被广泛采用。但是新型直动式压电电液伺服阀存在迟滞和蠕变非线性，用传统3ID控制算法不能取得很好的控制效果。为了满足新型直动式压电电液伺服阀的高精度性能要求，作者提出了基于动态?昨1,4川模型前馈控制和PID反馈控制的复合控制方法。3.1动态Preisach模型古典Preisach模型常被用来对迟滞非线性进行描述，它是由最简单的迟滞算子『"什)叠加构造而成。对新型直动式压电电液伺服阀施加电压u(t)时，输出位移x(t)，而u(t)—x(t)仅发生在第一象限，其迟滞算子“『弗U()的值只能为0或1，因此对古典preisach模型进行修正［6］，得到如下数学形式f(t)=ffu(a,P)u(t)ddPreisach模型的建立过程如下［7,8］：首先建立迟滞环升压和降压曲线的模型，其次建立用来存储每个升程和回程中不同电压处位移值的模型函数表，然后根据实际加压历程以及上面离线建立的模型函数表来查找对应的输出位移值。对于不在模型函数表中的电压可以通过插值的方法来确定实际电压作用下的位移值。该模型的特点是具有全局记忆特性，即能够考虑到电压施加的全部路径对其位移值进行预测知|计算，该模型为一个二重积分，路径对应着积分区域，只要知道电压的施加过程，就可以算出被控对象的输出位移值。M址相反，进行逆控制，即已知位移给定值求所加控制电压大小时，可根据该位移给定值及加压历程来查找Preisach模型函°2040如即舶100数表进行求逆运算，从而得到所需要施加的控制电压。然而，囹4木同明室噌!±作用'的退滞环曲线在针对新型直动式压电电液伺服阀系统进行的实验中发现，当外加电压信号的频率不同时系统输出的迟滞环的斜率是不同的。图4为在0.1Hz和1OHz这两种频率的电压下系统输出的迟滞环曲线。这表明新型直动式压电电液伺服阀的非线性特性是与速率相关的，而修正Preisach模型仅代表静态(与速率无关)的非线性特性，该模型仅仅根据施加某一频率电压时产生的位移值来建立Preisach模型函数表，而当电压的施加频率发生变化时，函数表的值是变化的。因此单纯采用修正Preisach模型会出现控制误差。为了解决这个问题，作者参考文献[9],在修正Preisach模型中引入一表示速率变化的函数，得出新型直动式压电电液伺服阀的动态?昨1、4川模型，该模型的数学形式为(d1

[dJ出新型直动式压电电液伺服阀的动态?昨1、4川模型，该模型的数学形式为(d1

[dJtf(t)=ffu(a,p,XS+)yu(t)dd(2)(d1〔dJt(d1〔dJt是输入变化率的函数，用于描述输入变化率和迟滞环之间的关系。对"函数进行幕级数展开:(3)取前两项，可得下面动态模型:(d1〔t(d1〔tu(a,p)yu(t)ddf(t)=jju(a,pWu(t)dd+jjx0apapS+S+fd1

〔了Jtu(a,p)yu(t)dd(4)=f(t)+jjXS+式中：f(t)=