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StudyonNeuralNetworksControlAlgorithmsforAutomotiveAdaptiveSuspensionSystemsL.J.Fu,J.G.CaoSchoolofAutomobileEngineering,ChongqingInstituteofTechnology,XingshengRoadNo.04Yangjiaping,Chongqing,China400050E-mail:Abstract-Thesemi-activesuspension,whichconsistsofpassivespringandactiveshockabsorberinthelightofdifferentroadconditionsandautomobilerunningconditions,isthemostpopularautomotivesuspensionbecauseactivesuspensioniscomplicatedinstructureandpassivesuspensioncannotmeetthedemandsofvariousroadconditionsandautomobilerunningconditions.Inthispaper,aneurofuzzyadaptivecontrolcontrollerviamodelingofrecurrentneuralnetworksofautomotivesuspensionispresented.Themodelingofneuralnetworkshasidentifiedautomotivesuspensiondynamicparametersandprovidedlearningsignalstoneurofuzzyadaptivecontrolcontroller.Inordertoverifycontrolresults,amini-busfittedwithmagnetorheologicalfluidshockabsorberandneurofuzzycontrolsystembasedonDSPmicroprocessorhasbeenexperimentedwithvariousvelocityandroadsurfaces.Thecontrolresultshavebeencomparedwiththoseofopenlooppassivesuspensionsystem.Theseresultsshowthatneuralcontrolalgorithmexhibitsgoodperformancetoreductionofmini-busvibration.I.INTRODUCTIONThemainfunctionsofautomotivesuspensionsystemaretoprovidesupporttheweightofautomobile,toprovidestabilityanddirectioncontrolduringhandlingmaneuversandtoprovideeffectiveisolationfromroaddisturbances.Thesedifferenttasksleadtoconflictingdesignrequirements.Thesemi-activesuspension,whichconsistsofpassivespringandactiveshockabsorberwithcontrollabledampingforceinthelightofdifferentroadconditionsandautomobilerunningconditions,isthemostpopularautomotivesuspensionbecausetheactivesuspensioniscomplicatedinstructureandconventionalpassivesuspensioncannotmeetthedemandsofdifferentroadconditionsandautomobilerunningconditions.Simi-activesuspensionwithvariablemagnetorheological(MR)fluidshockabsorbershassomeadvantagesinreducingautomobilevibrationatrelativelowcastandpower.Sofar,thereareanumberofcontrolmethodsthathavebeendevelopedforsemi-activesuspension,startwithskyhookmethoddescribedbyKarnoopp,etal.lThismethodattemptstomaketheshockabsorberexertaforcethatisproportionaltotheabsolutevelocitybetweensprungmasses.SomeinvestigationsuseC.R.Liao,B.ChenSchoolofAutomobileEngineering,ChongqingInstituteofTechnology,XingshengRoadNo.04Yangjiaping,Chongqing,China400050E-mail:chenbao(linearsuspensionmodel,whichislinearizedaroundtheoperationalpoints,andcontrolalgorithmarederivedusinglinearmodels,suchasLQGandrobustcontrol2,3.Thesecontrolmethodscannotmakeafullexploitationofsemi-activesuspensionresourcesbecauseofautomotivesuspensionisinherentnon-linearperformance.Inordertoimproveperformanceofnonlinearsuspensionsystem,someintelligentcontroltechniques,suchasfuzzylogiccontrol,neuralnetworkscontrolandneurofuzzycontrol,havebeenrecentlyappliedtononlinearsuspensioncontrolbyresearchers4,5.Inthispaper,aneurofuzzyadaptivecontrolcontrollerisappliedtocontrolsuspensionvibrationviamodelingofrecurrentneuralnetworksofautomotivesuspensionandcontinuouslyvariableMRshockabsorbers.Thecontrollerstructuresdesignandneurofuzzycontrolalgorithmsarepresentedinsection2.Arecurrentneuralnetworksdynamicsmodelingofsuspensionareshownrespectivelyinsection3.Thecontrolsystemexperimentationsaregiveninsection4andsomeconclusionsarefinallydrawninsection5.HI.NEUROFUZZYADAPTIVECONTROLALGORITHMSFORAUTOMOTIVESUSPENSIONSTheneurofuzzycontrolsystempresentedinthispaper,showninFigure1,iscomposedofaneurofuzzynetworkandarecurrentneuralnetworkmodelingofmini-bussuspension.Theneurofuzzynetworkisdefinedasadaptivecontroller,whichhasfunctionoflearningandcontrol.Thefunctionofrecurrentneuralnetworkistoidentifymini-bussuspensionmodelparameters.y(t)andyd(t)aresystemactualoutputandsystemdesireoutputrespectivelyinFigure1.xl(t)issystemerrorofsystemactualoutputbetweensystemdesireoutput,x2(t)issystemerrorrateofsystemactualoutputbetweensystemdesireoutput.xi(t)andx2(t)aredefinedasfellows:xI(t)e(t)=y(t)-Yd(t)(1)X2(t)=e(t)=e(t+1)-e(t)(2)0-7803-9422-4/05/$20.00C2005IEEE1795Fig.1.structureofneuralnetworkscontrolsystemforsuspensionnetworkscontrolsystem.Theglobalsetsoflinguisticvariablesaredefinedrespectivelyasfellows:-=-E,E,1=-AtJuU-U,U.Theneurofuzzycontrollerhasfourlayersne-urons,inwhichthefirstandthesecondlayerscorrespondtothefuizzyrulesif-part,thethirdlayercorrespondstotheinferenceandtheforthlayercorrespondstothefuzzyrulesthen-part.Thesetsxl,x2anduarerespectivelydivinedintosevenfuzzysubsetsofwhichfuzzysetsX1,X2Uarecomposedasfallowsrules:X1=NB,NM,NS,ZE,PS,PM,PBX2=NB,NM,NS,ZE,PS,PM,PBU=NB,NM,NS,ZE,PS,PM,PBInthispaper,theGaussianmembershipfunctionareusedinelementsoffuzzysetsX1X2andtheelementsoffuzzysetUisdefinedasfollowingmembershipfunctionci(u)J0(otherwise)0(3)=I(3)k=1,2,3.49j=13,23,3.74949Layer4:(4)-(3)wkand0(4)=I(4)/0(3)k=1k=1Wherexl(t)x2(t)aretheinputsofneuralnetworks,wkisweightofneuralnetwork,0(4)iStheoutputofneuralnetworksinwhich0(4)=U,ai,b,jarethecentralvaluesofGaussianmembershipfunction.Learningalgorithmsoftheneuralnetworkscontrollerisbasedongradientdescentbymeansoferrorsignalback-propagationmethod.Theerrorback-propagationalgorithm.saccomplishsynapticweightadjustmentthroughminimizationofcostfunction5.m.ALGORITHMFORRECURRENTNEURALNETWORKSSUSPENSIONDYNAMICALMODELINGArecurrentneuralnetworkdesignedtoapproximatetotheactualoutputofsuspensiony(t)isthree-layerneuralnetworkwithonelocalfeedbackloopinthehiddenlayer,whosearchitecturesareshowninFigure3.Thepropertythatisofprimarysignificanceforrecurrentneuralnetworkistheabilityofthenetworktolearnfromitsenvironmentandtoimproveitsperformancesbymeansofprocessofadjustmentsappliedtoitsweights.TherecurrentnetworkwithinputsignalII(t)=u(t)andI2(t)=y(t-1)hasoutputy(t)bylocalfeedbackloopneuroninthehiddenlayerwhoseoutputsumisSj(t)correspondingtotheneuronjth.(3)Fig.2.schematicofneuralnetworkscontrollerforadaptivesuspensionWhereU*Eu.Theinput/outputispresentedasfollowsaccordingtoFigure2.Layer1:I(1)x(t)andO)xi(t)i=1,2Layer2:I-2)(t)-ai)2/b2andO.epx()i=1,2j=1,2,3.7Layer3:I13)=tu(X2Q)IandFig.3.schematicofneuralnetworksmodelingofsuspensionsystem(4)Sy()=,w.*i(t)+WJD_Xj(t-_1)i1=(i(t)+wjXj(t_lqyj(t)=1wxi(t)j=l(5)(6)1796wherewI,wareweightoftherecurrentneuralnetwork,Xj(t)isoutputofneuronwithlocalfeedbackloopneuroninthehiddenlayer,p,qareinputneuronnumberandfeedbackneuronnumberrespectively.Theactivationfunctionforbothinputneuronsandoutputneuronsislinearfunction,whiletheactivationforneuronsinthehiddenlayerissigmoidfunction.heobjectivefunctionE(t)canbedefmedinthetermsoftheerrorsignale(t)as:E(t)=_y(t)-.y(t)2=1e2(t)(7)22Thatis,E(t)istheinstantaneousvalueoftheerrorenergy.Thestep-by-stepadjustmentstothesynapticweightsofneuronarecontinueduntilthesystemreachsteadystate,i.e.thesynapticweightsareessentiallystabilized.DifferentiatingE(t)withrespecttoweightvectorwyields.aE(t)_8=-e(t)0Y()(8)Fromexpression(1),(2)and(3),differentiatingA(t)0DIwithrespecttotheweightvectorw1w,-,w,-Yrespectivelyyields.aS(t)=x(t)As(t)woax1Q)-(WaXI(t)aWjJaWjFrom(4),(5)and(6),analyzingvalueofsynapticweightisdeterminedbyw(t+1)=w(t)+q*e(t)89(t)(12)whereqtheleaning-rateparameter,Adetailedconvergenceanalysisoftherecurrenttrainingalgorithmisrathercomplicatedtoacquiretheleaning-rateparametervalue.Accordingtoexpression(13),theweightvectorwforrecurrentneuralnetworkcanbeadjusted.WeestablishatheLyapunovfunctionasfollowsV(t)=1/2*e2(t),whosechangevalueAV(t)canbedeterminedaftersometiterations,inthesensethat(13)Wehavenoticedthattheerrorsignale(t)aftersometiterationscanbeexpressedasfollowsfromexpression(13)and(14),ae(t)ao(t)ae(t)ae(t)-,Aw=-qe(t)=77e(t),theawOwawOwLyapunovfunctionincrementcandeterminedaftersometiterationsasfollows(14)Mtt)=-q-&(t)+v2.e(t)-=-V(t)where(t)22jt16(t)2A=10()lpq2-5l0(t)ll2ql2-77O220w(9)?7maxa(t)29ifqf2,thenAV(t)O,wax1(t)DandaWjx1(t)uxiyieldsrespectivelyrecurrentformulas.ax1(t)a-fS(t)FX.x(tt1)1ax1(O)=,WjD=axi(t)aNiafS(t)+wat-i)&4LaNiax1(o)(11)avn=0Havingcomputedthesynapticadjustment,theupdatednamelytherecurrenttrainingalgorithmisconvergent.IV.ROADTESTANDRESULTSANALYSESTomakeademonstrationthevalidityofneuralcontrolalgorithmproposedinthepaper,anexperimentalmini-bussuspensionwithMRfluidshockabsorberhasbeenmanufacturedinChina.Themini-busadaptivesuspensionsystemconsistsofaDSPmicroprocessor,8accelerationsensors,4MRfluidshockabsorbers,and1controllableelectriccurrentpowerwithinputvoltage12V.TheDSPmicroprocessorreceivessuspensionvibrationsignalinputfromaccelerometersmountedrespectivelysprungmassandun-sprungmass.Inaccordancewithvibrationsignalandcontrolschemeinthispaper,theDSPmicroprocessoradjustsdampingofadaptivesuspensionbyapplicationcontrolsignaltothecontrollableelectriccurrentpowerconnectedtoelectromagneticcoilinMRfluidshockabsorbers.MagneticfieldproducedbytheelectromagneticcoilinMRfluidshockabsorberscandvarydampingforceinbothcompressionandreboundbyadjustmentofflow1797II,&V(t)=12(t+1)-e2(t2behaviorsofMRfluidsindampingchannels.Raodtestonmini-busadaptivesuspensionbasedneuralnetworkscontrolpresentedinthispaperarecarriedoutinDclassroadsurfacesrespectivelyinrunningvelocity30,40,50km/h.Duringroadtest,experimentalmini-busrunseachtestconditionataconstantspeed.Thetestexperimentsofadaptivesuspensionwithneuralnetworksandpassivesuspensionsystemwerecarriedoutrepeatedlyundersameroadsurfaceandrunningvelocity.TestresultslistedinTable1haveshownthattheadaptivesuspensionwithneuralnetworkscanreducevibrationpowerspectraldensitiesofbothsprungmassandun-sprungmass.Figure4isthemin-bussuspensionvibrationpowerspectraldensitiesofbothsprungmassandun-sprungmasswithpassiveandadaptivesuspensionsystembyDclassroadsurface.Itisclearthatneuralnetworkscontrolimprovesperformancesofmini-bussuspensionwithmainlyimprovementsoccurringaboutsprungmassresonancepeak.Thepowerspectraldensitiesindicatethattheadaptivesuspensionsystemwithneuralnetworkscontrolcanreducemini-busvibrationgreatlycomparedwithpassivesuspension.Ifexcellentfizzycontrolrulesandrationalmodelingofshockabsorberandsuspensioncanbeobtained,theadaptivesuspensionsystemwithneuralnetworkscontrolwillimprovefartherridecomfortandroadholdingandhandlingstabilityofautomobileinthefuture.TABLEImin-bussuspensionroadtestresults:sprungmassandun-sprungmassaccelerationr.m.s.Values(Dclassroad)Speed30(1km/h)40(1m/h)50(kmlh)PassiveControlreducePassiveControlreducePassiveControlreduce|mass10.37560.325213.40.41400.344916.70.46940.396615.5masspg1.60111426610.91.89751.660312.52.34682.065212.0massIC,-4a|1-#,-t0ri-0110.1.lo1Fry-0Qgco1okaId-ela.r10f1FrcqvOFig.4.min-bussuspensionvibrationpowerspectraldensitiesofsprungmass(left)andun-sprungmass(right)withcontrolandpassive(runningspeed40km/h)V.CONCLUSIONSInthispaper,anewrecurrentneuralnetworks-orientedsuspensionmodelandneurofuzzycontrolschemesforthemini-bussuspensionsystemwereinvestigated.Upontherequirementofusing8accelerationsensors,aDSPcontrollerwithgainschedulingwasdeveloped.ConsideringthecomplexityoftheMRfluidshockabsorber,theactuatordynamicshasbeenincorporatedduringthehardware-in-the-loopsimulations.Itwasdemonstratedthattheadaptivecontrolsystemcould1798achieveacompetitivecontrolperformancebyadoptingtheneurofuzzycontrolschemesandrecurrentneuralnetworks-orientedsuspension.Becausethecontrollawdesign,thegainschedulingstrategy,andthehardware-in-the-loopsimulationmethoddevelopedinthispaperarerestrictedto