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

STUDYONNEURALNETWORKSCONTROLALGORITHMSFORAUTOMOTIVEADAPTIVESUSPENSIONSYSTEMSLJFU,JGCAOSCHOOLOFAUTOMOBILEENGINEERING,CHONGQINGINSTITUTEOFTECHNOLOGY,XINGSHENGROADNO04YANGJIAPING,CHONGQING,CHINA400050EMAILFLJCQITEDUCNABSTRACTTHESEMIACTIVESUSPENSION,WHICHCONSISTSOFPASSIVESPRINGANDACTIVESHOCKABSORBERINTHELIGHTOFDIFFERENTROADCONDITIONSANDAUTOMOBILERUNNINGCONDITIONS,ISTHEMOSTPOPULARAUTOMOTIVESUSPENSIONBECAUSEACTIVESUSPENSIONISCOMPLICATEDINSTRUCTUREANDPASSIVESUSPENSIONCANNOTMEETTHEDEMANDSOFVARIOUSROADCONDITIONSANDAUTOMOBILERUNNINGCONDITIONSINTHISPAPER,ANEUROFUZZYADAPTIVECONTROLCONTROLLERVIAMODELINGOFRECURRENTNEURALNETWORKSOFAUTOMOTIVESUSPENSIONISPRESENTEDTHEMODELINGOFNEURALNETWORKSHASIDENTIFIEDAUTOMOTIVESUSPENSIONDYNAMICPARAMETERSANDPROVIDEDLEARNINGSIGNALSTONEUROFUZZYADAPTIVECONTROLCONTROLLERINORDERTOVERIFYCONTROLRESULTS,AMINIBUSFITTEDWITHMAGNETORHEOLOGICALFLUIDSHOCKABSORBERANDNEUROFUZZYCONTROLSYSTEMBASEDONDSPMICROPROCESSORHASBEENEXPERIMENTEDWITHVARIOUSVELOCITYANDROADSURFACESTHECONTROLRESULTSHAVEBEENCOMPAREDWITHTHOSEOFOPENLOOPPASSIVESUSPENSIONSYSTEMTHESERESULTSSHOWTHATNEURALCONTROLALGORITHMEXHIBITSGOODPERFORMANCETOREDUCTIONOFMINIBUSVIBRATIONIINTRODUCTIONTHEMAINFUNCTIONSOFAUTOMOTIVESUSPENSIONSYSTEMARETOPROVIDESUPPORTTHEWEIGHTOFAUTOMOBILE,TOPROVIDESTABILITYANDDIRECTIONCONTROLDURINGHANDLINGMANEUVERSANDTOPROVIDEEFFECTIVEISOLATIONFROMROADDISTURBANCESTHESEDIFFERENTTASKSLEADTOCONFLICTINGDESIGNREQUIREMENTSTHESEMIACTIVESUSPENSION,WHICHCONSISTSOFPASSIVESPRINGANDACTIVESHOCKABSORBERWITHCONTROLLABLEDAMPINGFORCEINTHELIGHTOFDIFFERENTROADCONDITIONSANDAUTOMOBILERUNNINGCONDITIONS,ISTHEMOSTPOPULARAUTOMOTIVESUSPENSIONBECAUSETHEACTIVESUSPENSIONISCOMPLICATEDINSTRUCTUREANDCONVENTIONALPASSIVESUSPENSIONCANNOTMEETTHEDEMANDSOFDIFFERENTROADCONDITIONSANDAUTOMOBILERUNNINGCONDITIONSSIMIACTIVESUSPENSIONWITHVARIABLEMAGNETORHEOLOGICALMRFLUIDSHOCKABSORBERSHASSOMEADVANTAGESINREDUCINGAUTOMOBILEVIBRATIONATRELATIVELOWCASTANDPOWERSOFAR,THEREAREANUMBEROFCONTROLMETHODSTHATHAVEBEENDEVELOPEDFORSEMIACTIVESUSPENSION,STARTWITHSKYHOOKMETHODDESCRIBEDBYKARNOOPP,ETALLTHISMETHODATTEMPTSTOMAKETHESHOCKABSORBEREXERTAFORCETHATISPROPORTIONALTOTHEABSOLUTEVELOCITYBETWEENSPRUNGMASSESSOMEINVESTIGATIONSUSECRLIAO,BCHENSCHOOLOFAUTOMOBILEENGINEERING,CHONGQINGINSTITUTEOFTECHNOLOGY,XINGSHENGROADNO04YANGJIAPING,CHONGQING,CHINA400050EMAILCHENBAOCQITEDUCNLINEARSUSPENSIONMODEL,WHICHISLINEARIZEDAROUNDTHEOPERATIONALPOINTS,ANDCONTROLALGORITHMAREDERIVEDUSINGLINEARMODELS,SUCHASLQGANDROBUSTCONTROL2,3THESECONTROLMETHODSCANNOTMAKEAFULLEXPLOITATIONOFSEMIACTIVESUSPENSIONRESOURCESBECAUSEOFAUTOMOTIVESUSPENSIONISINHERENTNONLINEARPERFORMANCEINORDERTOIMPROVEPERFORMANCEOFNONLINEARSUSPENSIONSYSTEM,SOMEINTELLIGENTCONTROLTECHNIQUES,SUCHASFUZZYLOGICCONTROL,NEURALNETWORKSCONTROLANDNEUROFUZZYCONTROL,HAVEBEENRECENTLYAPPLIEDTONONLINEARSUSPENSIONCONTROLBYRESEARCHERS4,5INTHISPAPER,ANEUROFUZZYADAPTIVECONTROLCONTROLLERISAPPLIEDTOCONTROLSUSPENSIONVIBRATIONVIAMODELINGOFRECURRENTNEURALNETWORKSOFAUTOMOTIVESUSPENSIONANDCONTINUOUSLYVARIABLEMRSHOCKABSORBERSTHECONTROLLERSTRUCTURESDESIGNANDNEUROFUZZYCONTROLALGORITHMSAREPRESENTEDINSECTION2ARECURRENTNEURALNETWORKSDYNAMICSMODELINGOFSUSPENSIONARESHOWNRESPECTIVELYINSECTION3THECONTROLSYSTEMEXPERIMENTATIONSAREGIVENINSECTION4ANDSOMECONCLUSIONSAREFINALLYDRAWNINSECTION5HINEUROFUZZYADAPTIVECONTROLALGORITHMSFORAUTOMOTIVESUSPENSIONSTHENEUROFUZZYCONTROLSYSTEMPRESENTEDINTHISPAPER,SHOWNINFIGURE1,ISCOMPOSEDOFANEUROFUZZYNETWORKANDARECURRENTNEURALNETWORKMODELINGOFMINIBUSSUSPENSIONTHENEUROFUZZYNETWORKISDEFINEDASADAPTIVECONTROLLER,WHICHHASFUNCTIONOFLEARNINGANDCONTROLTHEFUNCTIONOFRECURRENTNEURALNETWORKISTOIDENTIFYMINIBUSSUSPENSIONMODELPARAMETERSYTANDYDTARESYSTEMACTUALOUTPUTANDSYSTEMDESIREOUTPUTRESPECTIVELYINFIGURE1XLTISSYSTEMERROROFSYSTEMACTUALOUTPUTBETWEENSYSTEMDESIREOUTPUT,X2TISSYSTEMERRORRATEOFSYSTEMACTUALOUTPUTBETWEENSYSTEMDESIREOUTPUTXITANDX2TAREDEFINEDASFELLOWSXITETYTYDT1X2TETET1ET20780394224/05/2000C2005IEEE1795FIG1STRUCTUREOFNEURALNETWORKSCONTROLSYSTEMFORSUSPENSIONNETWORKSCONTROLSYSTEMTHEGLOBALSETSOFLINGUISTICVARIABLESAREDEFINEDRESPECTIVELYASFELLOWSE,E,1ATJUUU,UTHENEUROFUZZYCONTROLLERHASFOURLAYERSNEURONS,INWHICHTHEFIRSTANDTHESECONDLAYERSCORRESPONDTOTHEFUIZZYRULESIFPART,THETHIRDLAYERCORRESPONDSTOTHEINFERENCEANDTHEFORTHLAYERCORRESPONDSTOTHEFUZZYRULESTHENPARTTHESETSXL,X2ANDUARERESPECTIVELYDIVINEDINTOSEVENFUZZYSUBSETSOFWHICHFUZZYSETSX1,X2UARECOMPOSEDASFALLOWSRULESX1NB,NM,NS,ZE,PS,PM,PBX2NB,NM,NS,ZE,PS,PM,PBUNB,NM,NS,ZE,PS,PM,PBINTHISPAPER,THEGAUSSIANMEMBERSHIPFUNCTIONAREUSEDINELEMENTSOFFUZZYSETSX1X2ANDTHEELEMENTSOFFUZZYSETUISDEFINEDASFOLLOWINGMEMBERSHIPFUNCTIONCIUJ0OTHERWISE03I3K1,2,349J13,23,374949LAYER443WKAND04I4/03K1K1WHEREXLTX2TARETHEINPUTSOFNEURALNETWORKS,WKISWEIGHTOFNEURALNETWORK,04ISTHEOUTPUTOFNEURALNETWORKSINWHICH04U,AI,B,JARETHECENTRALVALUESOFGAUSSIANMEMBERSHIPFUNCTIONLEARNINGALGORITHMSOFTHENEURALNETWORKSCONTROLLERISBASEDONGRADIENTDESCENTBYMEANSOFERRORSIGNALBACKPROPAGATIONMETHODTHEERRORBACKPROPAGATIONALGORITHMSACCOMPLISHSYNAPTICWEIGHTADJUSTMENTTHROUGHMINIMIZATIONOFCOSTFUNCTION5MALGORITHMFORRECURRENTNEURALNETWORKSSUSPENSIONDYNAMICALMODELINGARECURRENTNEURALNETWORKDESIGNEDTOAPPROXIMATETOTHEACTUALOUTPUTOFSUSPENSIONYTISTHREELAYERNEURALNETWORKWITHONELOCALFEEDBACKLOOPINTHEHIDDENLAYER,WHOSEARCHITECTURESARESHOWNINFIGURE3THEPROPERTYTHATISOFPRIMARYSIGNIFICANCEFORRECURRENTNEURALNETWORKISTHEABILITYOFTHENETWORKTOLEARNFROMITSENVIRONMENTANDTOIMPROVEITSPERFORMANCESBYMEANSOFPROCESSOFADJUSTMENTSAPPLIEDTOITSWEIGHTSTHERECURRENTNETWORKWITHINPUTSIGNALIITUTANDI2TYT1HASOUTPUTYTBYLOCALFEEDBACKLOOPNEURONINTHEHIDDENLAYERWHOSEOUTPUTSUMISSJTCORRESPONDINGTOTHENEURONJTH3FIG2SCHEMATICOFNEURALNETWORKSCONTROLLERFORADAPTIVESUSPENSIONWHEREUEUTHEINPUT/OUTPUTISPRESENTEDASFOLLOWSACCORDINGTOFIGURE2LAYER1I1XTANDOXITI1,2LAYER2I2TAI2/B2ANDOEPXI1,2J1,2,37LAYER3I13TUX2QIANDFIG3SCHEMATICOFNEURALNETWORKSMODELINGOFSUSPENSIONSYSTEM4SY,WITWJD_XJT_1I1ITWJXJT_LQYJT1WXITJL561796WHEREWI,WAREWEIGHTOFTHERECURRENTNEURALNETWORK,XJTISOUTPUTOFNEURONWITHLOCALFEEDBACKLOOPNEURONINTHEHIDDENLAYER,P,QAREINPUTNEURONNUMBERANDFEEDBACKNEURONNUMBERRESPECTIVELYTHEACTIVATIONFUNCTIONFORBOTHINPUTNEURONSANDOUTPUTNEURONSISLINEARFUNCTION,WHILETHEACTIVATIONFORNEURONSINTHEHIDDENLAYERISSIGMOIDFUNCTIONHEOBJECTIVEFUNCTIONETCANBEDEFMEDINTHETERMSOFTHEERRORSIGNALETASET_YTYT21E2T722THATIS,ETISTHEINSTANTANEOUSVALUEOFTHEERRORENERGYTHESTEPBYSTEPADJUSTMENTSTOTHESYNAPTICWEIGHTSOFNEURONARECONTINUEDUNTILTHESYSTEMREACHSTEADYSTATE,IETHESYNAPTICWEIGHTSAREESSENTIALLYSTABILIZEDDIFFERENTIATINGETWITHRESPECTTOWEIGHTVECTORWYIELDSAET_8ET0Y8FROMEXPRESSION1,2AND3,DIFFERENTIATINGAT0DIWITHRESPECTTOTHEWEIGHTVECTORW1W,W,YRESPECTIVELYYIELDSASTXTASTWOAX1QWAXITAWJJAWJFROM4,5AND6,ANALYZINGVALUEOFSYNAPTICWEIGHTISDETERMINEDBYWT1WTQET89T12WHEREQTHELEANINGRATEPARAMETER,ADETAILEDCONVERGENCEANALYSISOFTHERECURRENTTRAININGALGORITHMISRATHERCOMPLICATEDTOACQUIRETHELEANINGRATEPARAMETERVALUEACCORDINGTOEXPRESSION13,THEWEIGHTVECTORWFORRECURRENTNEURALNETWORKCANBEADJUSTEDWEESTABLISHATHELYAPUNOVFUNCTIONASFOLLOWSVT1/2E2T,WHOSECHANGEVALUEAVTCANBEDETERMINEDAFTERSOMETITERATIONS,INTHESENSETHAT13WEHAVENOTICEDTHATTHEERRORSIGNALETAFTERSOMETITERATIONSCANBEEXPRESSEDASFOLLOWSFROMEXPRESSION13AND14,AETAOTAETAET,AWQET77ET,THEAW“O“WAWO“WLYAPUNOVFUNCTIONINCREMENTCANDETERMINEDAFTERSOMETITERATIONSASFOLLOWS14MTTQTV2ETVTWHERET22JT16T2A10LPQ25L0TLL2QL277O220W97MAXAT29IFQF2,THENAVTO,WAX1TDANDAWJX1TUXIYIELDSRESPECTIVELYRECURRENTFORMULASAX1TAFSTFXXTT11AX1O,WJDAXITANIAFSTWATI4LANIAX1O11AVN0HAVINGCOMPUTEDTHESYNAPTICADJUSTMENT,THEUPDATEDNAMELYTHERECURRENTTRAININGALGORITHMISCONVERGENTIVROADTESTANDRESULTSANALYSESTOMAKEADEMONSTRATIONTHEVALIDITYOFNEURALCONTROLALGORITHMPROPOSEDINTHEPAPER,ANEXPERIMENTALMINIBUSSUSPENSIONWITHMRFLUIDSHOCKABSORBERHASBEENMANUFACTUREDINCHINATHEMINIBUSADAPTIVESUSPENSIONSYSTEMCONSISTSOFADSPMICROPROCESSOR,8ACCELERATIONSENSORS,4MRFLUIDSHOCKABSORBERS,AND1CONTROLLABLEELECTRICCURRENTPOWERWITHINPUTVOLTAGE12VTHEDSPMICROPROCESSORRECEIVESSUSPENSIONVIBRATIONSIGNALINPUTFROMACCELEROMETERSMOUNTEDRESPECTIVELYSPRUNGMASSANDUNSPRUNGMASSINACCORDANCEWITHVIBRATIONSIGNALANDCONTROLSCHEMEINTHISPAPER,THEDSPMICROPROCESSORADJUSTSDAMPINGOFADAPTIVESUSPENSIONBYAPPLICATIONCONTROLSIGNALTOTHECONTROLLABLEELECTRICCURRENTPOWERCONNECTEDTOELECTROMAGNETICCOILINMRFLUIDSHOCKABSORBERSMAGNETICFIELDPRODUCEDBYTHEELECTROMAGNETICCOILINMRFLUIDSHOCKABSORBERSCANDVARYDAMPINGFORCEINBOTHCOMPRESSIONANDREBOUNDBYADJUSTMENTOFFLOW1797II,VT12T1E2T2BEHAVIORSOFMRFLUIDSINDAMPINGCHANNELSRAODTESTONMINIBUSADAPTIVESUSPENSIONBASEDNEURALNETWORKSCONTROLPRESENTEDINTHISPAPERARECARRIEDOUTINDCLASSROADSURFACESRESPECTIVELYINRUNNINGVELOCITY30,40,50KM/HDURINGROADTEST,EXPERIMENTALMINIBUSRUNSEACHTESTCONDITIONATACONSTANTSPEEDTHETESTEXPERIMENTSOFADAPTIVESUSPENSIONWITHNEURALNETWORKSANDPASSIVESUSPENSIONSYSTEMWERECARRIEDOUTREPEATEDLYUNDERSAMEROADSURFACEANDRUNNINGVELOCITYTESTRESULTSLISTEDINTABLE1HAVESHOWNTHATTHEADAPTIVESUSPENSIONWITHNEURALNETWORKSCANREDUCEVIBRATIONPOWERSPECTRALDENSITIESOFBOTHSPRUNGMASSANDUNSPRUNGMASSFIGURE4ISTHEMINBUSSUSPENSIONVIBRATIONPOWERSPECTRALDENSITIESOFBOTHSPRUNGMASSANDUNSPRUNGMASSWITHPASSIVEANDADAPTIVESUSPENSIONSYSTEMBYDCLASSROADSURFACEITISCLEARTHATNEURALNETWORKSCONTROLIMPROVESPERFORMANCESOFMINIBUSSUSPENSIONWITHMAINLYIMPROVEMENTSOCCURRINGABOUTSPRUNGMASSRESONANCEPEAKTHEPOWERSPECTRALDENSITIESINDICATETHATTHEADAPTIVESUSPENSIONSYSTEMWITHNEURALNETWORKSCONTROLCANREDUCEMINIBUSVIBRATIONGREATLYCOMPAREDWITHPASSIVESUSPENSIONIFEXCELLENTFIZZYCONTROLRULESANDRATIONALMODELINGOFSHOCKABSORBERANDSUSPENSIONCANBEOBTAINED,THEADAPTIVESUSPENSIONSYSTEMWITHNEURALNETWORKSCONTROLWILLIMPROVEFARTHERRIDECOMFORTANDROADHOLDINGANDHANDLINGSTABILITYOFAUTOMOBILEINTHEFUTURETABLEIMINBUSSUSPENSIONROADTESTRESULTSSPRUNGMASSANDUNSPRUNGMASSACCELERATIONRMSVALUESDCLASSROADSPEED301KM/H401M/H50KMLHPASSIVECONTROLREDUCEPASSIVECONTROLREDUCEPASSIVECONTROLREDUCE|MASS1037560325213404140034491670469403966155MASSPG160111426610918975166031252346820652120MASSIC,4A|1,T0RI01101LO1FRY0QGCO1OKAIDELAR10F1FRCQVOFIG4MINBUSSUSPENSIONVIBRATIONPOWERSPECTRALDENSITIESOFSPRUNGMASSLEFTANDUNSPRUNGMASSRIGHTWITHCONTROLANDPASSIVERUNNINGSPEED40KM/HVCONCLUSIONSINTHISPAPER,ANEWRECURRENTNEURALNETWORKSORIENTEDSUSPENSIONMODELANDNEUROFUZZYCONTROLSCHEMESFORTHEMINIBUSSUSPENSIONSYSTEMWEREINVESTIGATEDUPONTHEREQUIREMENTOFUSING8ACCELERATIONSENSORS,ADSPCONTROLLERWITHGAINSCHEDULINGWASDEVELOPEDCONSIDERINGTHECOMPLEXITYOFTHEMRFLUIDSHOCKABSORBER,THEACTUATORDYNAMICSHASBEENINCORPORATEDDURINGTHEHARDWAREINTHELOOPSIMULATIONSITWASDEMONSTRATEDTHATTHEADAPTIVECONTROLSYSTEMCOULD1798ACHIEVEACOMPETITIVECONTROLPERFORMANCEBYADOPTINGTHENEUROFUZZYCONTROLSCHEMESANDRECURRENTNEURALNETWORKSORIENTEDSUSPENSIONBECAUSETHECONTROLLAWDESIGN,THEGAINSCHEDULINGSTRATEGY,ANDTHEHARDWAREINTHELOOPSIMULATIONMETHODDEVELOPEDINTHISPAPERARERESTRICTEDTOAMINBU