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外文翻译--通过分叉程序强化大型液压控制系统的稳定性分析 英文版【优秀】.pdf

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外文翻译--通过分叉程序强化大型液压控制系统的稳定性分析 英文版【优秀】.pdf

JournaloftheFranklinInstitute3382001781–809EnhancedrobuststabilityanalysisoflargehydrauliccontrolsystemsviaabifurcationbasedprocedureGregoryG.KremerDepartmentofMechanicalEngineering,OhioUniversity,254StockerCenter,Athens,OH457012979,USAReceived14August2001AbstractBecauseoftheirsizeandcomplexity,theinitialdesignofmanyhydraulicsystemsisbasedprimarilyonsteadystatemodels.Nonlinearsystemdynamiccharacteristicsarenormallycheckedbysimulationand/orprototypetestingofthefinaldesignconfiguration,butevenatthisstageonlythenominalsystemdesignandalimitednumberofotherpossiblesystemscanbeanalyzedduetotheexcessivecostofeachsystemanalysis.Exhaustiveparametricstudiesthatverifytheperformanceandstabilityofallpossiblesystemsaregenerallynotpractical.Thedeficiencyassociatedwiththisanalysislimitationisthathydrauliccontrolsystemsthatarepredictedtobestablesometimesexhibitnonlinearpressureoscillationsofunacceptablylargemagnitude.Thispaperdocumentsthedevelopmentanddemonstrationofabifurcationbasedanalysisprocedurethatfocusesonpotentialmodesofoscillationratherthanonanalyzingallpossiblesystemstoyieldapracticallyrigorousrobuststabilityanalysisoflargenonlinearsystems.Additionalcontributionsofthisresearchinclude1proposedsolutionstothemainissuesthatcomplicatetherobuststabilityanalysisoflargenonlinearsystems,2demonstrationoftheuseoftheresultsfromabifurcationanalysistoinformandenableanefficientnonlinearanalysis,and3adetaileddescriptionofthepossiblenonlinearresponsesforalargeautomatictransmissionhydraulicsystemwitha9dimensionalstatespaceanda24dimensionalparameterspace.r2001TheFranklinInstitute.PublishedbyElsevierScienceLtd.Allrightsreserved.KeywordsNonlinearsystemsNonlineardynamicsHydrauliccontrolsystemsRobustnessStabilityHopfbifurcationLimitcyclePerioddoublingbifurcationParticipationfactorTel.17405931561fax17405930476.Emailaddresskremerohiou.eduG.G.Kremer.00160032/01/20.00r2001TheFranklinInstitute.PublishedbyElsevierScienceLtd.Allrightsreserved.PIIS001600320100031X1.IntroductionHydrauliccontrolsystemspresentinrealworldapplicationssuchasautomatictransmissionsandpositioncontrollersarecomposedofalargenumberofpressurechambersvolumesoffluidatasinglepressureseparatedfromotherchambersbyvalveportsorfixedorificesandnumerousmechanicalcomponentsi.e.valves,pumpsandaccumulators.Themathematicalmodelsforthesehydraulicsystemsthereforehavealargestatespacecomposedofthevalveposition,valvevelocityandchamberpressurestatevariablesandalargeparameterspacecomposedofthesystemdesignparameters.Althoughthesehydraulicsystemshavebeenstudiedextensivelyovertheyears,thecurrentstateoftheartanalysisproceduresnumericalsimulationsandrulesofthumbbasedonlinearizedanalysisstillhavesomesignificantlimitations.Onesuchlimitationisthatwithnumericalsimulationsitispracticallyinfeasibletodoacompleteparametricanalysisofthelargemathematicalmodelsthatarenecessarytoadequatelydescriberealhydraulicsystems1.Generallyspeaking,aparameterspacewithdimensionoffourorgreaterisclassifiedaslargebecauseitssizeprohibitsacomprehensiverobustnessanalysisFforcontextnotethatthedimensionoftheparameterspaceforarealhydraulicsystemisofteninthehundredsandnearlyalwaysexceeds20.Thesizeofthestatespaceisnotasignificantlimitingfactorforrobuststabilityanalysisbutitisacomplicatingfactorbecausesystemmodelswithalargestatespacearemorelikelytoexhibitanumberofdifferentresponsemodesforparametercombinationswithinthepossibleparameterspace,includingcomplexnonlinearbehaviorssuchaslimitcycles,2frequencytori,NomenclaturediriaunitvectorthatdefinesadirectioninparameterspaceDscalardistanceparameterJJacobianmatrixlieigenvalueoftheJacobianMatrix,i¼1ynvieigenvectoroftheJacobianMatrix,associatedwithliNASnonasymptoticallystableresponsePmparameterspacesubsetofRmrestrictedbasedonparameterlimitsRmreal,mdimensionalspacexistatevariablei¼1yn,xstatevectormibifurcationparameteri¼1ym,mparametervectorSubscriptseequilibriumvaluenomvalueforthenominalsystemovalueatthebifurcationpointcvalueattheclosestbifurcationpointG.G.Kremer/JournaloftheFranklinInstitute3382001781–809782andchaos.ThepossibleparameterspacereferstothemdimensionalspacePmconsistingofallpossiblecombinationsofvaluesforthesystemparameters,wherethepossiblerangeofeachparameterisdeterminedbyitstolerancerangeoritsuncertaintyrange.Thedeficiencyassociatedwiththeinabilityofcurrentanalysismethodstohandlelargesystemsisthathydrauliccontrolsystemsthatarepredictedtobestablesometimesexhibitnonlinearpressureoscillationsofsufficientlylargeamplitudetoseriouslydegradesystemperformance2.Animprovedmethodforquantifyingthestabilityrobustnessoflargehydraulicsystemsusingabifurcationbasedprocedureisthetopicofcurrentresearch.Bifurcationbasedprocedureshavebeenusedbyanumberofresearcherstoanalyzethestabilityofvarioustypesofsystems3–5,andKremerandThompson1haveshownthatananalysisprocedurebasedonthecomputationoftheclosestHopfbifurcationcanefficientlyquantifythestabilityrobustnessofahydraulicpositioncontrolsystemwithalarge7dimensionalparameterspace.Severalimportantissuesfortherobuststabilityanalysisoflargesystemswereaddressedinthatwork,includingnormalizationsfordealingwithnonhomogeneousparameterspacesandtheuseoftolerancerangelimitsinaparameteranalysis.Anumberofadditionalissuesmustbeaddressedtohandlethegeneralcaseoflargenonlinearsystems,includingthedevelopmentofproceduresfordealingwiththepossibilityofmultipleoscillatorymodeswhereamodeisdefinedasanoscillationwithauniquefrequencyandmodeshape,determiningthephysicalmeaningofeachoscillatorymode,andguaranteeingthatresultsarenotjustvalidlocallybutalsoglobally.Thepurposeofthispaperisto1investigatethemainissuesthatcomplicatetherobuststabilityanalysisoflargenonlinearsystems,2developanddemonstrateabifurcationbasedanalysisprocedurethatincombinationwithtargetednumericalsimulationsyieldsapracticallyrigorousrobuststabilityanalysisoflargenonlinearsystems,and3demonstratetheuseofresultsfromabifurcationanalysistoinformandenableanefficientnonlinearanalysisofthesystem.FollowingthisintroductorysectionarebackgroundsectionscoveringnonlinearsystemresponsesSection2andbifurcationbasedrobuststabilityanalysisSection3.ThebulkofthepaperthenfocusesonissuesthatcomplicatetheanalysisoflargenonlinearsystemsSection4,adescriptionoftheenhancedanalysisprocedureSection5,anexampleapplicationofthenewanalysisprocedureSection6,andconcludingremarksSection7.ThelargesystemusedasanexamplethroughoutthispaperisshowninFig.1itisasubmodelofanautomatictransmissionhydraulicsystemwitha9dimensionalstatespaceanda24dimensionalparameterspace.ThismodelisdiscussedandanalyzedinSection6.2.NonlinearsystemresponsesForanalysispurposes,mostphysicalsystemscanbemodeledasaninterconnectionofcomponentsbasedonlumpedparametermodelingassumptions.ForG.G.Kremer/JournaloftheFranklinInstitute3382001781–809783example,thepressureregulatinghydraulicsystemshowninFig.1canbemodeledasaseriesofpressurechambersconnectedbyflowpassagessuchasvalveportsandfloworifices.Theequationsofmotionforthevalvesandthecontinuityequationsforthepressurechamberscomprisethemathematicalmodelofthelumpedparametersystem.Thesetofordinarydifferentialequationsinthemathematicalmodelarecommonlyrepresentedinstatevectorformx¼fðxmÞð1ÞwherexARnarethestatevariablesandmARmarethesystemparameters.ForexampleseeSection6wherethemodelcorrespondingtothehydraulicsystemshowninFig.1isrepresentedinstatevectorform.SinceminEq.1isanmdimensionalvectoroffreeparameters,thestateequationdoesnotdescribeasinglesystembutratheranmparameterfamilyofsystems,withthenominalsystemsignifiedbymnomTheequilibriumstatexeforaparticularsystemmioccursphysicallywhenthestatevariableshaveconstantvalues,ormathematicallywhenthederivativesofallstatevariablesareequaltozero,i.e.whenx¼fðxemiÞ¼0ThefirstorderTaylorserieslinearizationofthisautonomoussystemaboutitsequilibriumpointisx¼JxwhereJ¼qfðxmÞqxC12C12xeistheJacobianmatrix.Ifallofthedifferentialequationscomprisingthestateequationarelinearthenbehaviorofthesystemmodelwillbelinear.However,ifoneormoretermsinthestateequationarenonlinearthenthesystemresponsewillnotadheretothelinearFig.1.ASimplifiedmodelofanautomatictransmissionhydraulicsystem.G.G.Kremer/JournaloftheFranklinInstitute3382001781–809784

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