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

JournaloftheFranklinInstitute338(2001)781809Enhancedrobuststabilityanalysisoflargehydrauliccontrolsystemsviaabifurcation-basedprocedureGregoryG.Kremer*DepartmentofMechanicalEngineering,OhioUniversity,254StockerCenter,Athens,OH45701-2979,USAReceived14August2001AbstractBecauseoftheirsizeandcomplexity,theinitialdesignofmanyhydraulicsystemsisbasedprimarilyonsteadystatemodels.Nonlinearsystemdynamiccharacteristicsarenormallycheckedbysimulationand/orprototypetestingofthenaldesignconguration,butevenatthisstageonlythenominalsystemdesignandalimitednumberofotherpossiblesystemscanbeanalyzedduetotheexcessivecostofeachsystemanalysis.Exhaustiveparametricstudiesthatverifytheperformanceandstabilityofallpossiblesystemsaregenerallynotpractical.Thedeciencyassociatedwiththisanalysislimitationisthathydrauliccontrolsystemsthatarepredictedtobestablesometimesexhibitnonlinearpressureoscillationsofunacceptablylargemagnitude.Thispaperdocumentsthedevelopmentanddemonstrationofabifurcation-basedanalysisprocedurethatfocusesonpotentialmodesofoscillationratherthanonanalyzingallpossiblesystemstoyieldapracticallyrigorousrobuststabilityanalysisoflargenonlinearsystems.Additionalcontributionsofthisresearchinclude:(1)proposedsolutionstothemainissuesthatcomplicatetherobuststabilityanalysisoflargenonlinearsystems,(2)demonstrationoftheuseoftheresultsfromabifurcationanalysistoinformandenableanecientnonlinearanalysis,and(3)adetaileddescriptionofthepossiblenonlinearresponsesforalargeautomatictransmissionhydraulicsystemwitha9-dimensionalstatespaceanda24-dimensionalparameterspace.r2001TheFranklinInstitute.PublishedbyElsevierScienceLtd.Allrightsreserved.Keywords:Nonlinearsystems；Nonlineardynamics；Hydrauliccontrolsystems；Robustness；Stability；Hopfbifurcation；Limitcycle；Perioddoublingbifurcation；Participationfactor*Tel.:+1-740-593-1561；fax:+1-740-593-0476.E-mailaddress:(G.G.Kremer).0016-0032/01/$20.00r2001TheFranklinInstitute.PublishedbyElsevierScienceLtd.Allrightsreserved.PII:S0016-0032(01)00031-X1.IntroductionHydrauliccontrolsystemspresentinreal-worldapplicationssuchasautomatictransmissionsandpositioncontrollersarecomposedofalargenumberofpressurechambers(volumesofuidatasinglepressureseparatedfromotherchambersbyvalveportsorxedorices)andnumerousmechanicalcomponents(i.e.valves,pumpsandaccumulators).Themathematicalmodelsforthesehydraulicsystemsthereforehavealargestatespacecomposedofthevalveposition,valvevelocityandchamberpressurestatevariablesandalargeparameterspacecomposedofthesystemdesignparameters.Althoughthesehydraulicsystemshavebeenstudiedextensivelyovertheyears,thecurrentstate-of-the-artanalysisprocedures(numericalsimulationsandrules-of-thumbbasedonlinearizedanalysis)stillhavesomesignicantlimitations.Onesuchlimitationisthatwithnumericalsimulationsitispracticallyinfeasibletodoacompleteparametricanalysisofthelargemathematicalmodelsthatarenecessarytoadequatelydescriberealhydraulicsystems1.Generallyspeaking,aparameterspacewithdimensionoffourorgreaterisclassiedaslargebecauseitssizeprohibitsacomprehensiverobustnessanalysisFforcontextnotethatthedimensionoftheparameterspaceforarealhydraulicsystemisofteninthehundredsandnearlyalwaysexceeds20.Thesizeofthestatespaceisnotasignicantlimitingfactorforrobuststabilityanalysisbutitisacomplicatingfactorbecausesystemmodelswithalargestatespacearemorelikelytoexhibitanumberofdierentresponsemodesforparametercombinationswithinthepossibleparameterspace,includingcomplexnonlinearbehaviorssuchaslimitcycles,2-frequencytori,NomenclaturediriaunitvectorthatdenesadirectioninparameterspaceDscalardistanceparameterJJacobianmatrixlieigenvalueoftheJacobianMatrix,(i1；y；n)vieigenvectoroftheJacobianMatrix,associatedwithliNASnonasymptoticallystableresponsePmparameterspacesubsetofRmrestrictedbasedonparameterlimitsRmreal,m-dimensionalspacexistatevariable(i1；y；n),x=statevectormibifurcationparameter(i1；y；m),m=parametervectorSubscriptseequilibriumvaluenomvalueforthenominalsystemovalueatthebifurcationpointcvalueattheclosestbifurcationpointG.G.Kremer/JournaloftheFranklinInstitute338(2001)781809782andchaos.Thepossibleparameterspacereferstothem-dimensionalspacePmconsistingofallpossiblecombinationsofvaluesforthesystemparameters,wherethepossiblerangeofeachparameterisdeterminedbyitstolerancerangeoritsuncertaintyrange.Thedeciencyassociatedwiththeinabilityofcurrentanalysismethodstohandlelargesystemsisthathydrauliccontrolsystemsthatarepredictedtobestablesometimesexhibitnonlinearpressureoscillationsofsucientlylargeamplitudetoseriouslydegradesystemperformance2.Animprovedmethodforquantifyingthestabilityrobustnessoflargehydraulicsystemsusingabifurcation-basedprocedureisthetopicofcurrentresearch.Bifurcation-basedprocedureshavebeenusedbyanumberofresearcherstoanalyzethestabilityofvarioustypesofsystems35,andKremerandThompson1haveshownthatananalysisprocedurebasedonthecomputationoftheclosestHopfbifurcationcanecientlyquantifythestabilityrobustnessofahydraulicpositioncontrolsystemwithalarge(7-dimensional)parameterspace.Severalimportantissuesfortherobuststabilityanalysisoflargesystemswereaddressedinthatwork,includingnormalizationsfordealingwithnonhomogeneousparameterspacesandtheuseoftolerancerangelimitsinaparameteranalysis.Anumberofadditionalissuesmustbeaddressedtohandlethegeneralcaseoflargenonlinearsystems,includingthedevelopmentofproceduresfordealingwiththepossibilityofmultipleoscillatorymodes(whereamodeisdenedasanoscillationwithauniquefrequencyandmodeshape),determiningthephysicalmeaningofeachoscillatorymode,andguaranteeingthatresultsarenotjustvalidlocallybutalsoglobally.Thepurposeofthispaperisto:(1)investigatethemainissuesthatcomplicatetherobuststabilityanalysisoflargenonlinearsystems,(2)developanddemonstrateabifurcation-basedanalysisprocedurethatincombinationwithtargetednumericalsimulationsyieldsapracticallyrigorousrobuststabilityanalysisoflargenonlinearsystems,and(3)demonstratetheuseofresultsfromabifurcationanalysistoinformandenableanecientnonlinearanalysisofthesystem.Followingthisintroductorysectionarebackgroundsectionscoveringnonlinearsystemresponses(Section2)andbifurcation-basedrobuststabilityanalysis(Section3).Thebulkofthepaperthenfocusesonissuesthatcomplicatetheanalysisoflargenonlinearsystems(Section4),adescriptionoftheenhancedanalysisprocedure(Section5),anexampleapplicationofthenewanalysisprocedure(Section6),andconcludingremarks(Section7).ThelargesystemusedasanexamplethroughoutthispaperisshowninFig.1；itisasubmodelofanautomatictransmissionhydraulicsystemwitha9-dimensionalstatespaceanda24-dimensionalparameterspace.ThismodelisdiscussedandanalyzedinSection6.2.NonlinearsystemresponsesForanalysispurposes,mostphysicalsystemscanbemodeledasaninterconnec-tionofcomponentsbasedonlumpedparametermodelingassumptions.ForG.G.Kremer/JournaloftheFranklinInstitute338(2001)781809783example,thepressure-regulatinghydraulicsystemshowninFig.1canbemodeledasaseriesofpressurechambersconnectedbyowpassagessuchasvalveportsandoworices.Theequationsofmotionforthevalvesandthecontinuityequationsforthepressurechamberscomprisethemathematicalmodelofthelumpedparametersystem.Thesetofordinarydierentialequationsinthemathematicalmodelarecommonlyrepresentedinstatevectorformxfx；m；1wherexARnarethestatevariablesandmARmarethesystemparameters.ForexampleseeSection6wherethemodelcorrespondingtothehydraulicsystemshowninFig.1isrepresentedinstatevectorform