基于模型参考滑模控制理论的整车安全控制

2032ModelReferenceSlidingModeControlforImprovingVehicleActiveSafetyLIJianfeng,GAOLi&LIUBirong(DepartmentofTrafficEngineering,BeijingInstituteofTechnology,Beijing100081,China)Abstract:Amodelreferenceslidingmodecontrollerwasdesignedtogenerateadditionalyawmomentofthevehicle.Thiscontrollerwasexpectedtomaketheyawratefollowthereferencemodel.Thereferencemodelwasdevelopedbasedontwodegreeoffreedomvehicledynamicstateequation.Theproposedsimulationmodelwasemployedtocalculatetheyawrateandslipangleresponsecharacteristicsofavehicleunderseverecorneringmaneuver,anditshowsthatthesafetyofthevehicleissignificantlyimprovedascomparedtotheuncontrolledone.Keywords:vehicledynamicalmodel;yawrate;slidingmodecontroller1IntroductionDirectyawmomentcontrolisoneoftheadvancedcontrolsystemusedtoimprovetheactivesafetyofroadvehicles[1-4].Underseveralconditions,themasscenterofthevehiclemaybeshiftedtoanundesirablepositionduetotheheavycargo,makingsuchvehicletobeover-steered.Thismeansthatthevehiclerequireadditionalyawmomenttoimproveitssafety.Vehiclesystemisavariableparameterandtimedependedsystemthatnecessitatesthedevelopmentofcontrollerswithspecialcapabilitiesinsolvingtheseproblems.ModelReferenceSlidingModeControl(MRSC)lawhasbeenprovedasuccessfulmethodindynamiccontrolsystems,thegoodtransientperformanceandrobustnesscapabilitiesmadeitapopularchoicefordesigninggeneral-purposenonlinearcontrollers[5][6].Inthispaper,theMRSCtechniqueisusedtotheyawmomentcontrol.Therequiredyawmomentcanbegeneratedbythevehiclebrakingordrivingforcebetweenthewheels.Thereferencemodelisadoptedtogeneratethedesiredvehicleperformance.TheMRSCisdesignedtomaketheactualvehicleresponsefollowtheoutputofreferencemodel.Finally,numericalsimulationswerecarriedouttoinvestigatethedynamicperformanceoftheneuralnetworkcontrollersystem.2VehicleModelforControllerDesignAlinearvehiclemodeloftwodegreeoffreedombasedonlineartiremodelisdevelopedforthedesignofthecontrolsystem.Theequationsgoverningthelateralandyawmotionsinthelinearvehiclemodelcanbeexpressedasfollows)/(2)/(2)(urlcurlcrmurrff(1)zrrrfffMlurlclurlcrI)/(2)/(2(2)Intheaboveequations,mdenotesthemassofthebody,Ithemomentofinertiaconcerningtheyawmotion,thesideslipangle,rtheyawangularacceleration,uthelongitudinalvelocity,thesteeringangleoffrontwheel,fl,rlthedistancesfromthecenterofgravitytothefrontandrearaxlesrespectively,fc,rcthecorneringstiffnesscoefficientsofthefrontandrearwheelsrespectively,zMtheadditionalyawmoment,whichmustbedeterminedfromthecontrollaw.Combiningequations(1),(2),andrareconsideredasthetwostatevariables,thevehiclestateequationispresentedasHBAXXzM(3)WhererX,22211211aaaaA,21bbB,21hhH))/((211muccafr,1))/((2212muclclaffrr,Iclclaffrr)/(221,))/((22222Iuclclaffrr,01b，I/b12,)/(21muchf,Iachf/22Inequation(3),thevehiclesteeringangleisconsideredastheexternaldisturbance.3ControllerDesign3.1ReferenceModelThereferencemodelisdesignedtoacquirethezerosideslipangleatthecenterofgravitywithrespecttoarbitraryfrontsteeringangle.In(3),theyawrateresponsetothesteeringangleisasecondordersystem.Butinthereferencemodeltheyawrateresponseisapproximatedtobethefirstordersystemforavoidingcomplexity[7])1/()(/)(21`SKKssrm(4)Where1Kand2Karesteadystategainandtimeconstantofyawrateresponserespectively.Theycanbedescribedas1211/ahK222/1aK(5)ThenthereferencemodelcanbeexpressedbythestatespaceformmmmmHXAX(6)2033WheremmmrX,2/1000KmA,210KKmH3.2ModelReferenceSlidingmodeControllerDesignThecontrolobjectiveistomaketheactualvehicleresponsetrackingthereferencemodeloutput.Combiningequations(3)and(6),theerrorbetweenthedesiredvaluemXandXactualvaluecanbepresentedmXXE(7)Theperformanceindexofthecontrolsystemcanbeexpressedas0)(limttE(8)Substitutingthetermsattherightsideof(3)and(6))()()(mmmZmMHHXAABXXAE21)(ddMmmZXAABAE(9)Where21eeE,11hd,1212222/ahahd(10)Where1ccanbedesignedbythesystemresponsetime.Theslidingmodecontrollawcanbedesignedas)sgn()()()(11212112221211211112sracddceaaceaacbMmZ(11)Where0isasmallpositivenumber.LetaLyapunovfunctioncandidatebe221SV,combiningcontrollaw(11),itcanbeprovedSV(12)Thereforethecontrollawin(11)willstabilizethesystemandmakethemodeltrackingerrorneartozero.The)(sminthefollowingequationcanbeusedtosubstitute)sgn(sforeliminatingthechattering.)|(|)(sssm(13)Whereisasmallpositivenumber.Notethat(9)doesnotmeetthematchingcondition,thereforethecontrollawisanapproximateway.TheblockdiagramofthecontrolsystemisshowninFig.14SimulationResultsToinvestigatetheeffectivenessoftheintegratedcontrolsystemusingmodelreferenceslidingmodecontrolapproach,computersimulationsareconducted.Thesimulationresultsarecomparedwiththecasewithoutcontrol.Thesimulationresultsareobtainedforaseverecorneringmaneuver.Thevehiclespeedis30m/s.ThesteeringangleinputisshowninFig.2Therealvehicleisreplacedbyacomprehensiveeightdegreeoffreedomdynamicmodel.ParametersoftheactualvehiclemodelusedinthesimulationareshowninTable1.mrVehiclemodelzMrSlidingmodeco