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PiezoelectricElectro—hydraulicServoValve
Abstract:
Anewtypeofpiezoelectricelectro-hydraulicservovalvesystemwasproposed.Andthenmultilayerpiezoelectricactuatorbasedonnewpiezoelectricceramicmaterialwasusedastheelectricity-machineconverteroftheproposedpiezoelectricelectro-hydraulicservovalve.Theproposedpiezoelectricelectro-hydraulicservovalvehasascendantperformancecomparedwithconventionalones.Butthesystemisofhighnonlinearityanduncertainty,itcannotachievefavorablecontrolperformancebyconventionalcontrolmethod.Todevelopanefficientwaytocontrolpiezoelectricelectro—hydraulicservovalvesystem.Ahigh—precisefuzzycontrolmethodwithhysteresisnonlinearmodelinfeedforwardloopwasproposed.Thecontrolmethodisseparatedintotwoparts:
afeedforwardloopwithPreisachhysteresisnonlinearmodelandafeedbackloopwithhigh-precisefuzzycontro1.ExperimentalresultsshowthatthehysteresisloopandthemaximumoutputhysteresisbythePIDcontrolmethodare4.22%and2.11pm,respectively;
thehysteresisloopandthemaximumoutputhysteresisbytheproposedcontrolmethodrespectivelyare0.74%and0.37μm,respectively;
themaximumtrackingerrorbythePIDcontrolmethodforsinewavereferencesignalisabout5.02%,themaximumtrackingerrorbytheproposedcontrolmethodforsinewavereferencesignalisabout0.85%.contro1.
Keywords:
piezoelectricelectro—hydraulicservovalve;
hysteresisnonlinearity;
Preisachmodel;
fuzzycontrol
1Introduction
Electro—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.
2Workprincipleandcharacteristicofnew-typeofpiezoelectricelectro-hydraulicValve
Becausethepullingforcecapacityofmultilayerpiezoelectricactuatorisverypoor,itcannotmaketheslidevalveoftheelectro,hydraulicservovalvebidirectionallvmove.Twomultilayerpiezoelectricactuatorswereadoptedtosolvethisproblem[7-8].Theshortcomingofthismethodishighcostandsystemisdifficulttocontro1.Utilizingtherestoringforceofaleafspring,onemultilayerpiezoelectricactuatorcanrealizebidirectionalmovementoftheslidevalveinthispaper.Whenthevoltageimposedonmultilayerpiezoelectricactuator1sincreased,multilayerpiezoelectricactuatorwillelongateanddrivetheslidevalvetomovetowardstheleft,whichmakestheleafspringdeform.Onthecontrary,whenthevoltageimposedonmultilayerpiezoelectricactuatorisreduced,multilayerpiezoelectricactuatorwillbeshortenedandthendrivetheslidevalvemovetowardstherightbytheactionoftherestoringforceoftheleafspring.
Thestructureofnewtypeofpiezoelectricelectro—hydraulicservovalveisshowninFig.1.
Theinput-outputcharacteristicofthenewtypeofpiezoelectricelectro-hydraulicservovalvesystemindicatesthatithashysteresisnonlinearitywithnonloca1memory(seeFig.2).AtanyreachablepointL(Ua,Ya)ininput-outputdiagram,thenumberofalternativecurvethatdescribesthefuturepathofhysteresisnonlinearitywithnonloca1memoryisinfinite.Namely,thefutureoutputofthesystemdependsnotonlyonthecurrentoutputYaandfutureinput,butalsoonthepasthistoryofinputvalue’sextremum.Hence,theoutputresponseofnewtypeofpiezoelectricelectro-hydraulicservovalvetoanappliedinputvoltagebecomesunpredictable.
Inthesystem,thereexistothernonlinearitiessuchasforceoffrictionandworkdeadzoneofvalve,furthermore,dampingcoefficientandoiltemperaturearealsochangedwithtime.Thenonlinearityanduncertaintyhaveseriouslyeffectsonthepositionprecision.Toimprovetheperformanceofthenewtypeofpiezoelectricelectro-hydraulicservovalvesystem,avalidcontrolmethodisneeded
3Controlalgorithm
Atpresent,conventionalPIDcontrolleriswidelyappliedinindustrialcontroldomainbecauseofitssimplecontrolstructure,easydesignandinexpensivecost.However,conventionalPIDcontrollerisdifficulttoachievegoodcontrolperformanceinthenewtypeofpiezoelectricelectro,hydraulicservovalvesystembecausethecontrolobjecthashighnonlinearityanduncertainty.Fuzzycontrollershowsgoodresultsinthecaseofcontrollinghighnonlinearsystems.However,conventionalfuzzycontrollerisessentiallyakindofnonlinearPDcontroller,thereexistssteadystateerror,whichcannotmeetthedemandofhighpreciseofthesystem.Inthispaper,ahigh-precisefuzzycontrolalgorithmwithPreisachhysteresisnonlinearmodelinfeedforwardloopwasproposed.TheblockdiagramofthecombinedcontrolisshowninFig.3.
ThecontrolsystemiscomposedofafeedforwardloopbasedonPreisachmodelandafeedbackloopofhighprecisefuzzycontroller.Ul(istheoutputoffeedforwardloopbasedonPreisachmode1.Asalinearterm,itisselectedfromaPreisachfunctiontablebasedonthegivenpositionvalue.U2(istheoutputofthehighprecisefuzzycontroller.ThesumU(t)offeedforwardcontrolvoltagefandfeedbackcontrolvoltageU2(t),asultimatecontrolvoltage,isactedonnewtypepiezoelectricelectro-hydraulicservovalve.
3.1FeedforwardloopbasedonPreisachmodel
Theopenloopresponseofthenewtypepiezoelectricelectro-hydraulicservovalvesystemunderanarbitraryandnon-cyclicinputsignalisshowninFig.2.Thisphenomenonappearsashysteresisnonlinearitywithnonlocalmemory,whichcanbepredictedbyPreisachmode1.ThenumericalformofPreisachmodelcanbe
writtenasfoliows:
(1)
Eqn.
(1)canbeusedtocalculatetheresponseofthenewtypeofpiezoelectricelectro-hydraulicservovalvesubjecttoaknownarbitraryinputvoltagesequence.Aseriesoffirstorderfunctions
ofthenewtypeofpiezoelectricelectro-hydraulicservovalveareexperimentallydetermined.Theprocedureisasfollows.
ThespacebetweenzeroandsaturationvoltageUsisdividedintonequipartitions,andthevoltageofeveryequantpointiskUs/n,wherek=-0,1,2,⋯n.
VoltageisappliedfromzerotoeveryequantpointkUs/n,andthendecreasedtozero.Inthisprocess,thepositionoutputvaluesofthenewtypeofpiezoelectricelectro-hydraulicservovalvearerecordedateveryequantpointbetweenzeroandsaturationvoltageUs,therewith,
andthePreisachfunctiontableareobtained(seeFig.4),
(2)
Basedonthedrivervoltagerangeofthenewtypeofpiezoelectricelectro.hydraulicservovalve,thecoordinatespaceisselectedas0≤
≤l50Vand0≤
<
150VFromFig.4,thelimittriangleisdividedintoseveralsquaresandtriangles.Decreasingthesizeofthesquaresandtrianglesisexpectedtoincreasetheaccuracyofthemode1,however,itwillspendmassivecomputationaltime.Basedontheexperiments,nisselectedas5,namely,thesizeofeachofsidesofthesquaresandtrianglesisselectedas30V.
BasedonthegivenpositionvalueandthenumericalformofthePreisachmodel,
or
canbeobtained.Thereby,basedonPreisachfunctiontable,thecontrolvoltageUl(t)isobtainedwhen
liesontheverticallineor
liesonthehorizontalline.FortheinexistencevoltageinthePreisachfunctiontable.itcanbeobtainedbythelinearinterpolation.
Incomparisontoaconventionalfeedbackcontroller,themainadvantageofthismode1-basedfeedforwardcontrolleristhatitcancompensatethehysteresisnonlinearityofthesystemandachievehighlydynamicoperationatthesametime,andnoadditionalsensorisneeded.Thisleadstoaverysimpleandinexpensivecontrolsystem.Themaindrawbackofthefeedforward
controllerissensitivetounmodeldataandunconsideredexternaldisturbancessuchastemperaturedrift.Foranewtypeofpiezoelectricelectro—hydraulicservovalvesystemthatneedshighcontrolprecision.mode1.basedfeedforwardcontrollercannotobtaingoodcontroleffect.Thenacompoundcontrolmethodwithfeedforwardandfeedbackcontrolprojectwasproposedinthispape.Inthefeedbackcontrolloop,ahigh—precisefuzzycontrolalgorithmwasadopted.Themethodcanobtaingoodperformance.
3.2Highprecisefuzzycontrol
Conventionalfuzzycontrollerhastwoinputvariables,eandΔe,andoneoutputvariable(U),theyareerror,changeoferrorandoutputcontroloffuzzycontroller.Inthenewtypeofpiezoelectricelectro-hydraulicservovalvesystem,thephysicalrangeoftheslidevalvepositionerror(andchangeoferror(△e)are[-x,x]and[-Δx,Δx],respectively.Thecorr