Study on Neural Networks Control__ Algorithms for Automotive Adaptive Suspension Systems.pdf

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 l Thismethodattemptstomaketheshock absorberexertaforcethatisproportionaltotheabsolute velocitybetweensprungmasses Someinvestigationsuse C R Liao B Chen SchoolofAutomobileEngineering Chongqing InstituteofTechnology XingshengRoadNo 04Yangjiaping Chongqing China400050 E mail chenbao linearsuspensionmodel whichislinearizedaroundthe operationalpoints andcontrolalgorithmarederivedusing linearmodels suchasLQGandrobustcontrol 2 3 These controlmethodscannotmakeafullexploitationof semi activesuspensionresourcesbecauseofautomotive suspensionisinherentnon linearperformance Inorderto improveperformanceofnonlinearsuspensionsystem some intelligentcontroltechniques suchasfuzzylogiccontrol neuralnetworkscontrolandneurofuzzycontrol havebeen recentlyappliedtononlinearsuspensioncontrolby researchers 4 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 AtJ uU 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 function 5 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 I 13 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 1w xi t j l 5 6 1796 wherew I w areweightoftherecurrentneural 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 aw O waw O w 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 ll 2 ql 2 77 O 220w 9 7maxa t 29 if q f 2 thenAV t O w ax1 t D and aWj x1 t uxi yieldsrespectivelyrecurrentformulas ax1 t a f S t FX x tt1 1 ax1 O WjD axi t aNi afS t w a t i 4 LaN i 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 paperarerestricted