BACKSTEPPING BASED FUZZY LOGIC CONTROL OF ACTIVE V

1BACKSTEPPINGBASEDFUZZYLOGICCONTROLOFACTIVEVEHICLESUSPENSIONSYSTEMSJ.Campos,F.L.Lewis,L.Davis,andS.Ikenaga,AutomationandRoboticsResearchInstituteTheUniversityofTexasatArlington7300JackNewellBlvd.S,Ft.Worth,[e-mail]9,1999ResearchSupportedby:TexasATPGrant003656-027,NSFGrantECS-9521673andAROGrant39657-MA.Keywords:fuzzycontrol,activesuspensioncontrol,backsteppingtechnique.AbstractInthispaper,wepresentabacksteppingbasedfuzzylogic(FL)schemefortheactivecontrolofvehiclesuspensionsystemsusingthetwo-degreesoffreedomor1/4carmodel.Thefulldynamicsofanovelhydraulicstrutareconsidered.Theservo-valvedynamicsarealsoincluded.Afuzzylogicsystemisusedtoestimatethenonlinearhydraulicstrutdynamics.Thebacksteppingfuzzylogicschemeisshowntogivesuperiorperformanceoverpassivesuspensionandactivesuspensioncontrolusingconventionalproportional-integral-derivative(PID)schemes.TheFLsystemisadaptedinsuchawayastoestimateon-linetheunknownhydraulicdynamicsandprovidethebacksteppingloopwiththedesiredservo-valvepositioningsothattheschemebecomesadaptive,guaranteeingboundedtrackingerrorsandparameterestimates.Arigorousproofofstabilityandperformanceisgivenandasimulationexampleverifiesperformance.Unlikestandardadaptivebacksteppingtechniques,nolinear-in-the-parametersassumptionsareneeded.21.IntroductionThestudyofridequalityevaluatesthepassenger'sresponsetoroad/terrainirregularitieswiththeobjectiveofimprovingcomfortandroadisolationwhilemaintainingwheel/groundcontact.Rideproblemsmainlyarisefromvehiclevibrations,whichmaybeinducedbyavarietyofsourcesincludingexternalfactors,suchasroadwayroughnessoraerodynamicsforces,ortheymaybeinternallygeneratedbyforcesproducedbyvehiclesubsystems,suchastheengine,powertrain,orthesuspensionmechanisms.Suspensionsystemdesignsaremostlybasedonrideanalysis.Vehiclesuspensionsusingvarioustypesofsprings,dampers,andlinkageswithtailoredflexibilityinvariousdirectionshavebeendevelopedoverthelastcenturysincethebeginningoftheautomobileage.Thesimplestandmostcommontypesofsuspensionsarepassiveinthesensethatnoexternalsourcesofenergyarerequired.Withthedevelopmentofmoderncontroltheoryandtheconcomitantdevelopmentofinexpensiveandreliableelectronicdevicesithasbecomeclearthatincreasedperformanceistheoreticallypossibleforsuspensionswhichcansenseaspectsofvehiclemotionandproduceforcesormotionsthroughactuatorsinwaysimpossibleforconventionalpassivesuspensions.Inautomobileindustryactiveandsemi-activesuspensionshaverecentlyattractedincreasedattentionsbecausetheycanimprovevehicleridecomfortandroadhandlingperformance.Themainadvantageofemployinganactivesuspensionistheassociatedadaptationpotential:thesuspensioncharacteristiccanbeadjustedwhiledriving,tomatchtheprofileoftheroadbeingtraversed.Anactivesuspensionsystemshouldbeabletoprovidedifferentbehavioralcharacteristics3dependinguponvariousroadconditionsandbeabletodosowithoutgoingbeyonditstravellimits.Itisnotpossibletodecreasebodymotionsatthewheelfrequency0wusingcontrolinputsappliedonlybetweenthesprungandunsprungmasses,asinallstandardstrutgeometries.Thisisduetothefactthatusingsuchcontrolinputs,thesystemhasapole-zerocancellationat0warisingfromanuncontrollablemode.Itisnotdifficulttoimproveperformancebelowthewheelfrequency0w.Thismaybeaccomplishedbyrollingoffthespringconstantatlowfrequencies(LF)orusingskyhookdamping[5,10].Itisdifficulttoimprovebodymotionatfrequenciesabovethewheelfrequency0wwithoutusingcomplexcontrollerssuchasbackstepping[2,9,24]ormechanicalmodificationstothevehiclethatincludehangingextradampersoffthewheels.However,in[5,10]itwasshownthatrollingoffthedampingconstantsathighfrequenciescaneasilymitigatemotionsabovethewheelfrequency.Includingthedynamicsofthehydraulicsystemconsistingoffluids,valves,pumps,etc,complicatestheactivesuspensioncontrolproblemevenfurthersinceitintroducesnonlinearitiestothesystem.Ithasbeennotedthatthehydraulicdynamicsandfastservo-valvedynamicsmakecontrolsdesignverydifficult.In[8]itisshownthattheactuatordynamicssignificantlychangethevibrationalcharacteristicsofthevehiclesystem.Itisshownin[3]thatusingaforcecontrollooptocompensateforthehydraulicdynamicscandestabilizethesystem.Thisfullnonlinearcontrolproblemofactivesuspensionshasbeeninvestigatedusingseveralapproachesincludingoptimalcontrolbasedonalinearizedmodel[8],adaptivenonlinearcontrol[1,2],andadaptiveH8controlusingbackstepping[9].Theseschemesuselinearapproximationsforthehydraulic4dynamicsortheyneglecttheservo-valvemodeldynamicsinwhichacurrentorvoltageiswhatultimatelycontrolstheopeningofthevalvetoallowflowofhydraulicfluidtoorfromthesuspensionsystem.Anonlinearbacksteppingapproachincludingtheservo-valvedynamicshasbeenproposedin[24],inwhichanonlinearfilterwhoseeffectivebandwidthdependsonthemagnitudeofthesuspensiontravelisused.Duringthepastseveralyears,therehasbeengreatsuccessinthedesignofnonlinearcontrolsystemduetothedevelopmentofthebacksteppingtechnique[17].Integratorbacksteppingisusedtodesigncontrollersforsystemswithknownnonlinearitiesnotsatisfyingmatchingconditions.Adaptivebacksteppingdesigncanbeuse