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StudyonNeuralNetworksControlAlgorithmsfor AutomotiveAdaptiveSuspensionSystems L.J.Fu,J.G.Cao SchoolofAutomobileEngineering,Chongqing InstituteofTechnology, XingshengRoadNo.04Yangjiaping, Chongqing,China400050 E-mail:flj Abstract-Thesemi-activesuspension,whichconsistsof passivespringandactiveshockabsorberinthelightof differentroadconditionsandautomobilerunningconditions,is themostpopularautomotivesuspensionbecauseactive suspensioniscomplicatedinstructureandpassivesuspension cannotmeetthedemandsofvariousroadconditionsand automobilerunningconditions.Inthispaper,aneurofuzzy adaptivecontrolcontrollerviamodelingofrecurrentneural networksofautomotivesuspensionispresented.Themodeling ofneuralnetworkshasidentifiedautomotivesuspension dynamicparametersandprovidedlearningsignalsto neurofuzzyadaptivecontrolcontroller.Inordertoverify controlresults,amini-busfittedwithmagnetorheologicalfluid shockabsorberandneurofuzzycontrolsystembasedonDSP microprocessorhasbeenexperimentedwithvariousvelocity androadsurfaces.Thecontrolresultshavebeencompared withthoseofopenlooppassivesuspensionsystem.These resultsshowthatneuralcontrolalgorithmexhibitsgood performancetoreductionofmini-busvibration. I.INTRODUCTION Themainfunctionsofautomotivesuspensionsystemare toprovidesupporttheweightofautomobile,toprovide stabilityanddirectioncontrolduringhandlingmaneuvers andtoprovideeffectiveisolationfromroaddisturbances. Thesedifferenttasksleadtoconflictingdesignrequirements. Thesemi-activesuspension,whichconsistsofpassive springandactiveshockabsorberwithcontrollabledamping forceinthelightofdifferentroadconditionsandautomobile runningconditions,isthemostpopularautomotive suspensionbecausetheactivesuspensioniscomplicatedin structureandconventionalpassivesuspensioncannotmeet thedemandsofdifferentroadconditionsandautomobile runningconditions.Simi-activesuspensionwithvariable magnetorheological(MR)fluidshockabsorbershassome advantagesinreducingautomobilevibrationatrelativelow castandpower.Sofar,thereareanumberofcontrol methodsthathavebeendevelopedforsemi-active suspension,startwithskyhookmethoddescribedby Karnoopp,etal.lThismethodattemptstomaketheshock absorberexertaforcethatisproportionaltotheabsolute velocitybetweensprungmasses.Someinvestigationsuse C.R.Liao,B.Chen SchoolofAutomobileEngineering,Chongqing InstituteofTechnology, XingshengRoadNo.04Yangjiaping, Chongqing,China400050 E-mail:chenbao( linearsuspensionmodel,whichislinearizedaroundthe operationalpoints,andcontrolalgorithmarederivedusing linearmodels,suchasLQGandrobustcontrol2,3.These controlmethodscannotmakeafullexploitationof semi-activesuspensionresourcesbecauseofautomotive suspensionisinherentnon-linearperformance.Inorderto improveperformanceofnonlinearsuspensionsystem,some intelligentcontroltechniques,suchasfuzzylogiccontrol, neuralnetworkscontrolandneurofuzzycontrol,havebeen recentlyappliedtononlinearsuspensioncontrolby researchers4,5. Inthispaper,aneurofuzzyadaptivecontrolcontrolleris appliedtocontrolsuspensionvibrationviamodelingof recurrentneuralnetworksofautomotivesuspensionand continuouslyvariableMRshockabsorbers.Thecontroller structuresdesignandneurofuzzycontrolalgorithmsare presentedinsection2.Arecurrentneuralnetworks dynamicsmodelingofsuspensionareshownrespectivelyin section3.Thecontrolsystemexperimentationsaregivenin section4andsomeconclusionsarefinallydrawninsection 5. HI.NEUROFUZZYADAPTIVECONTROLALGORITHMSFOR AUTOMOTIVESUSPENSIONS Theneurofuzzycontrolsystempresentedinthispaper, showninFigure1,iscomposedofaneurofuzzynetwork andarecurrentneuralnetworkmodelingofmini-bus suspension.Theneurofuzzynetworkisdefinedasadaptive controller,whichhasfunctionoflearningandcontrol.The functionofrecurrentneuralnetworkistoidentifymini-bus suspensionmodelparameters.y(t)andyd(t)aresystem actualoutputandsystemdesireoutputrespectivelyinFigure 1. xl(t) issystemerrorofsystemactualoutputbetween systemdesireoutput,x2(t)issystemerrorrateofsystem actualoutputbetweensystemdesireoutput. xi(t)and x2(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/$20.00C2005IEEE 1795 Fig.1.structureofneuralnetworkscontrolsystemforsuspension networkscontrolsystem.Theglobalsetsoflinguistic variablesaredefinedrespectivelyasfellows: - =-E,E, 1=-AtJuU-U,U.Theneurofuzzycontrollerhas fourlayersne-urons,inwhichthefirstandthesecondlayers correspondtothefuizzyrulesif-part,thethirdlayer correspondstotheinferenceandtheforthlayercorresponds tothefuzzyrulesthen-part.Thesetsxl, x2and uare respectivelydivinedintosevenfuzzysubsetsofwhichfuzzy setsX1,X2Uarecomposedasfallowsrules: X1=NB,NM,NS,ZE,PS,PM,PB X2=NB,NM,NS,ZE,PS,PM,PB U=NB,NM,NS,ZE,PS,PM,PB Inthispaper,theGaussianmembershipfunctionareused inelementsoffuzzysets X1 X2andtheelementsof fuzzysetUisdefinedasfollowingmembershipfunction ci(u)J0(otherwise) 0(3)=I(3)k=1,2,3 .49 j=13,23,3 .7 4949 Layer4:(4)-(3)wkand0(4)=I(4)/0(3) k=1k=1 Wherexl(t)x2(t)aretheinputsofneuralnetworks, wkisweightofneuralnetwork, 0(4) iStheoutputof neuralnetworksinwhich0(4)=U, ai,b,j arethecentral valuesofGaussianmembershipfunction.Learning algorithmsoftheneuralnetworkscontrollerisbasedon gradientdescentbymeansoferrorsignalback-propagation method.Theerrorback-propagationalgorithm.saccomplish synapticweightadjustmentthroughminimizationofcost function5. m.ALGORITHMFORRECURRENTNEURALNETWORKS SUSPENSIONDYNAMICALMODELING Arecurrentneuralnetworkdesignedtoapproximateto theactualoutputofsuspension y(t) isthree-layerneural networkwithonelocalfeedbackloopinthehiddenlayer, whosearchitecturesareshowninFigure3.Thepropertythat isofprimarysignificanceforrecurrentneuralnetworkisthe abilityofthenetworktolearnfromitsenvironmentandto improveitsperformancesbymeansofprocessof adjustmentsappliedtoitsweights.Therecurrentnetwork withinputsignal II(t)=u(t) andI2(t)=y(t-1)has outputy(t)bylocalfeedbackloopneuroninthehidden layerwhoseoutputsumis Sj(t) correspondingtothe neuronjth. (3) Fig.2.schematicofneuralnetworkscontrollerforadaptivesuspension WhereU*Eu.Theinput/outputispresentedasfollows accordingtoFigure2. Layer1:I(1)x(t)andO)xi(t)i=1,2 Layer2:I-2)(t)-ai)2/b 2 and O.epx()i=1,2j=1,2,3.7 Layer3: I13)= t u(X2Q)I and Fig.3.schematicofneuralnetworksmodelingofsuspensionsystem (4)Sy()=,w.*i(t)+WJD _Xj(t-_1) i1= (i(t)+wjXj(t_l q yj(t)=1wxi(t) j=l (5) (6) 1796 wherewI,wareweightoftherecurrentneural network, Xj(t)is outputofneuronwithlocalfeedback loopneuroninthehiddenlayer,p,qareinputneuron numberandfeedbackneuronnumberrespectively.The activationfunctionforbothinputneuronsandoutput neuronsislinearfunction,whiletheactivationforneurons inthehiddenlayerissigmoidfunction. heobjectivefunctionE(t)canbedefmedinthetermsof theerrorsignale(t)as: E(t)= _y(t)-.y(t)2=1e2(t) (7) 22 Thatis,E(t)istheinstantaneousvalueoftheerror energy.Thestep-by-stepadjustmentstothesynapticweights ofneuronarecontinueduntilthesystemreachsteadystate, i.e.thesynapticweightsareessentiallystabilized. DifferentiatingE(t)withrespecttoweightvectorw yields. aE(t)_ 8 =-e(t)0Y() (8) Fromexpression(1),(2)and(3),differentiatingA(t) 0DI withrespecttotheweightvectorw1 w,- ,w,-Yrespectively yields. aS(t) =x(t) As(t) woax1Q) -( W aXI(t) aWj J aWj From(4),(5)and(6),analyzing valueofsynapticweightisdeterminedby w(t+1)=w(t)+q*e(t)89(t)(12) whereqtheleaning-rateparameter,Adetailed convergenceanalysisoftherecurrenttrainingalgorithmis rathercomplicatedtoacquiretheleaning-rateparameter value.Accordingtoexpression(13),theweightvectorw forrecurrentneuralnetworkcanbeadjusted.Weestablisha theLyapunovfunctionasfollowsV(t)=1/2*e2(t), whosechangevalueAV(t)canbedeterminedaftersome titerations,inthesensethat (13) Wehavenoticedthattheerrorsignale(t)aftersomet iterationscanbeexpressedasfollowsfromexpression(13) and(14), ae(t)ao(t)ae(t)ae(t) - ,Aw=-qe(t)=77e(t),the awOwawOw Lyapunovfunctionincrementcandeterminedaftersomet iterationsasfollows (14) Mtt)=-q- &(t)+v2.e(t)- =-V(t) where (t) 2 2jt1 6(t) 2 A=10()lp q 2-5l0(t)ll2 ql2-77O 220w (9) ?7maxa(t) 29 if qf2, thenAV(t)O, w ax1(t) D and aWj x1(t) uxi yieldsrespectivelyrecurrentformulas. ax1(t)a-fS(t)FX.x(tt1)1 ax1(O)= ,WjD = axi(t) aNi afS(t) +w a t-i) &4 LaNi ax1(o) (11) avn =0 Havingcomputedthesynapticadjustment,theupdated namelytherecurrenttrainingalgorithmisconvergent. IV.ROADTESTANDRESULTSANALYSES Tomakeademonstrationthevalidityofneuralcontrol algorithmproposedinthepaper,anexperimentalmini-bus suspensionwithMRfluidshockabsorberhasbeen manufacturedinChina.Themini-busadaptivesuspension systemconsistsofaDSPmicroprocessor,8acceleration sensors,4MRfluidshockabsorbers,and 1controllable electriccurrentpowerwithinputvoltage12V.TheDSP microprocessorreceivessuspensionvibrationsignalinput fromaccelerometersmountedrespectivelysprungmassand un-sprungmass.Inaccordancewithvibrationsignaland controlschemeinthispaper,theDSPmicroprocessor adjustsdampingofadaptivesuspensionbyapplication controlsignaltothecontrollableelectriccurrentpower connectedtoelectromagneticcoilinMRfluidshock absorbers.Magneticfieldproducedbytheelectromagnetic coilinMRfluidshockabsorberscandvarydampingforce inbothcompressionandreboundbyadjustmentofflow 1797 II ,&V(t)= 12 (t+1)-e2(t 2 behaviorsofMRfluidsindampingchannels. Raodtestonmini-busadaptivesuspensionbasedneural networkscontrolpresentedinthispaperarecarriedoutinD classroadsurfacesrespectivelyinrunningvelocity 30,40,50km/h.Duringroadtest,experimentalmini-busruns eachtestconditionataconstantspeed.Thetestexperiments ofadaptivesuspensionwithneuralnetworksandpassive suspensionsystemwerecarriedoutrepeatedlyundersame roadsurfaceandrunningvelocity.TestresultslistedinTable 1haveshownthattheadaptivesuspensionwithneural networkscanreducevibrationpowerspectraldensitiesof bothsprungmassandun-sprungmass. Figure4isthemin-bussuspensionvibrationpower spectraldensitiesofbothsprungmassandun-sprungmass withpassiveandadaptivesuspensionsystembyDclass roadsurface.Itisclearthatneuralnetworkscontrol improvesperformancesofmini-bussuspensionwithmainly improvementsoccurringaboutsprungmassresonancepeak. Thepowerspectraldensitiesindicatethattheadaptive suspensionsystemwithneuralnetworkscontrolcanreduce mini-busvibrationgreatlycomparedwithpassive suspension.Ifexcellentfizzycontrolrulesandrational modelingofshockabsorberandsuspensioncanbeobtained, theadaptivesuspensionsystemwithneuralnetworkscontrol willimprovefartherridecomfortandroadholdingand handlingstabilityofautomobileinthefuture. TABLEI min-bussuspensionroadtestresults: sprungmassandun-sprungmassaccelerationr.m.s.Values(Dclassroad) Speed30(1km/h)40(1m/h)50(kmlh) PassiveControlreducePassiveControlreducePassiveControlreduce |mass10.37560.325213.40.41400.344916.70.46940.396615.5 mass pg1.60111426610.91.89751.660312.52.34682.065212.0 mass IC,-4a |1- #,-t 0 ri-0110.1. lo1 Fry- 0Qgco1okaId-e la.r10f1 Frcqv O Fig.4.min-bussuspensionvibrationpowerspectraldensitiesofsprungmass(left) andun-sprungmass(right)withcontrolandpassive(runningspeed40km/h) V.CONCLUSIONS Inthispaper,anewrecurrentneuralnetworks-oriented suspensionmodelandneurofuzzycontrolschemesforthe mini-bussuspensionsystemwereinvestigated.Uponthe requirementofusing8accelerationsensors,aDSP controllerwithgainschedulingwasdeveloped. ConsideringthecomplexityoftheMRfluidshock absorber,theactuatordynamicshasbeenincorporated duringthehardware-in-the-loopsimulations.Itwas demonstratedthattheadaptivecontrolsystemcould 1798 achieveacompetitivecontrolperformancebyadoptingthe neurofuzzycontrolschemesandrecurrentneural networks-orientedsuspension.Becausethecontrollaw design,thegainschedulingstrategy,andthe hardware-in-the-loopsimulationmethoddevelopedinthis paper