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

Study onNeuralNetworksControlAlgorithms forAutomotive Adaptive Suspension SystemsL.J.Fu, J.G.CaoSchoolofAutomobileEngineering,ChongqingInstituteofTechnology,XingshengRoadNo.04Yangjiaping,Chongqing,China400050E-mail:Abstract-The semi-active suspension, which consists ofpassive spring and active shock absorber in the light ofdifferentroadconditionsandautomobilerunningconditions,isthe most popular automotive suspension because activesuspension is complicated in structure andpassive suspensioncannot meet the demands of various road conditions andautomobile running conditions. In this paper, a neurofuzzyadaptive control controller via modeling of recurrent neuralnetworksofautomotive suspensionispresented. Themodelingof neural networks has identified automotive suspensiondynamic parameters and provided learning signals toneurofuzzy adaptive control controller. In order to verifycontrolresults,amini-busfittedwithmagnetorheologicalfluidshock absorber and neurofuzzy control system based on DSPmicroprocessor has been experimented with various velocityand road surfaces. The control results have been comparedwith those of open loop passive suspension system. Theseresults show that neural control algorithm exhibits goodperformancetoreductionofmini-busvibration.I.INTRODUCTIONThemainfunctions ofautomotive suspension systemareto provide support the weight of automobile, to providestability and direction control during handling maneuversand to provide effective isolation from road disturbances.Thesedifferenttasksleadtoconflictingdesignrequirements.The semi-active suspension, which consists of passivespringandactiveshockabsorberwithcontrollabledampingforceinthelightofdifferentroadconditionsandautomobilerunning conditions, is the most popular automotivesuspensionbecause the active suspension is complicatedinstructure and conventional passive suspension cannot meetthe demands of different road conditions and automobilerunning conditions. Simi-active suspension with variablemagnetorheological(MR) fluid shock absorbers has someadvantages inreducingautomobile vibrationatrelative lowcast and power. So far, there are a number of controlmethods that have been developed for semi-activesuspension, start with skyhook method described byKarnoopp, etal.lThismethodattemptstomaketheshockabsorberexert a force that is proportional to the absolutevelocity between sprung masses. Some investigations useC.R.Liao, B.ChenSchoolofAutomobileEngineering,ChongqingInstituteofTechnology,XingshengRoadNo.04Yangjiaping,Chongqing,China400050E-mail:chenbao(linear suspension model, which is linearized around theoperational points, and control algorithm are derivedusinglinearmodels, suchasLQGandrobustcontrol 2,3. Thesecontrol methods cannot make a full exploitation ofsemi-active suspension resources because of automotivesuspension is inherent non-linear performance. In order toimproveperformanceofnonlinearsuspensionsystem, someintelligent control techniques, such as fuzzy logic control,neuralnetworks control andneurofuzzy control, havebeenrecently applied to nonlinear suspension control byresearchers4,5.Inthispaper, aneurofuzzy adaptive control controllerisapplied to control suspension vibration via modeling ofrecurrent neural networks of automotive suspension andcontinuously variable MR shock absorbers. The controllerstructures design and neurofuzzy control algorithms arepresented in section 2. A recurrent neural networksdynamicsmodelingofsuspensionareshownrespectivelyinsection3. The control system experimentations are giveninsection4andsomeconclusions arefinallydrawninsection5.HI.NEUROFUZZYADAPTIVECONTROLALGORITHMSFORAUTOMOTIVESUSPENSIONSThe neurofuzzy control system presented in this paper,shown in Figure 1, is composed ofa neurofuzzy networkand a recurrent neural network modeling of mini-bussuspension. Theneurofuzzynetwork is defined as adaptivecontroller, whichhas function oflearning and control. Thefunctionofrecurrentneuralnetworkistoidentifymini-bussuspension model parameters.y(t) and yd(t) are systemactualoutputandsystemdesireoutputrespectivelyinFigure1. xl(t) is system error of system actual outputbetweensystem desire output, x2(t) is system error rate ofsystemactualoutputbetweensystemdesireoutput. 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 1795Fig. 1.structureofneuralnetworkscontrolsystemforsuspensionnetworks control system .The global sets of linguisticvariables are definedrespectively as fellows: - =-E,E,1=-AtJ u U-U,U. The neurofuzzy controller hasfourlayersne-urons, inwhichthefirstandthesecondlayerscorrespond to the fuizzy rules if-part, the third layercorrespondstotheinferenceandtheforthlayercorrespondsto the fuzzy rules then-part. The sets xl, x2and u arerespectivelydivinedintosevenfuzzysubsetsofwhichfuzzysets X1, X2 U arecomposedasfallowsrules:X1 =NB,NM,NS,ZE,PS,PM,PBX2 = NB,NM,NS,ZE,PS,PM,PBU=NB,NM,NS,ZE,PS,PM,PBInthispaper,theGaussianmembership functionareusedin elements of fuzzy sets X1 X2 and the elements offuzzyset U isdefinedasfollowingmembershipfunctionci(u)J0 (otherwise)0(3)=I(3) k=1,2,3.49 j=13,23,3.749 49Layer4:(4)- (3)wk and 0(4)=I(4)/ 0(3)k=1 k=1Where xl(t) x2(t) are the inputs of neural networks,wk is weight of neural network, 0(4) iS the output ofneuralnetworksinwhich 0(4) =U, ai, b,j arethecentralvalues of Gaussian membership function. Learningalgorithms of the neural networks controller is based ongradientdescentbymeans oferrorsignalback-propagationmethod. The errorback-propagation algorithm.s accomplishsynaptic weight adjustment through minimization of costfunction5.m.ALGORITHMFORRECURRENTNEURALNETWORKSSUSPENSIONDYNAMICALMODELINGA recurrent neural network designed to approximate tothe actual output ofsuspension y(t) is three-layer neuralnetwork with one local feedback loop in the hidden layer,whosearchitecturesareshowninFigure3.Thepropertythatisofprimarysignificanceforrecurrentneuralnetworkistheability ofthenetworkto learnfromits environment andtoimprove its performances by means of process ofadjustments applied to its weights. The recurrent networkwith input signal II(t)=u(t) and I2(t)=y(t-1) hasoutput y(t) by local feedback loop neuron in the hiddenlayer whose output sum is Sj(t) corresponding to theneuronjth.(3)Fig.2.schematicofneuralnetworkscontrollerforadaptivesuspensionWhere U* E u .Theinput/outputispresentedasfollowsaccordingtoFigure2.Layer1: I(1)x(t) and O ) xi(t) i=1,2Layer2: I -2) (t)-ai )2/b 2 andO. epx() i=1,2 j=1,2,3.7Layer3: I13)= t u(X2Q)I andFig.3.schematicofneuralnetworksmodelingofsuspensionsystem(4)Sy()=,w.*i(t)+WJD _ Xj(t-_1)i1=(i(t)+wj Xj(t_lqyj(t)= 1w xi(t)j=l(5)(6)1796where wI , ,w areweightoftherecurrentneuralnetwork, Xj(t)is output of neuron with local feedbackloop neuron in the hidden layer, p,qare input neuronnumber and feedback neuron number respectively. Theactivation function for both input neurons and outputneurons is linear function, whilethe activation forneuronsinthehiddenlayerissigmoidfunction.heobjectivefunction E(t)canbedefmedinthetermsoftheerrorsignal e(t)as:E(t)= _y(t)-.y(t)2 =1e2(t) (7)2 2That is, E(t) is the instantaneous value of the errorenergy.Thestep-by-stepadjustmentstothesynapticweightsofneuronarecontinueduntilthe systemreachsteadystate,i.e. the synaptic weights are essentially stabilized.Differentiating E(t)with respect to weight vector wyields.aE(t)_ 8=-e(t)0Y() (8)From expression (1), (2) and (3), differentiating A(t)0 D Iwithrespecttotheweightvectorw1 w,- ,w,-Y respectivelyyields.aS(t)=x (t)As(t) wo ax1Q)-(WaXI(t)aWj J aWjFrom(4),(5)and(6), analyzingvalueofsynapticweightisdeterminedbyw(t+1)=w(t)+q*e(t)89(t) (12)where q the leaning-rate parameter, A detailedconvergence analysis ofthe recurrent training algorithm israther complicated to acquire the leaning-rate parametervalue. According to expression (13), theweightvector wforrecurrentneuralnetworkcanbeadjusted. Weestablishathe Lyapunov function as follows V(t)=1/2*e2(t),whosechangevalue AV(t) canbedeterminedaftersomet iterations,inthesensethat(13)Wehavenoticedthattheerrorsignal e(t) aftersome titerations canbeexpressedas follows fromexpression (13)and(14),ae(t) ao(t) ae(t) ae(t)- ,Aw=-qe(t) =77e(t) ,theaw “O“w aw O“wLyapunovfunctionincrement candeterminedaftersome titerationsasfollows(14)Mtt)=-q- &(t) +v2.e(t)- =-V(t)where(t) 2 2jt 1 6(t) 2A= 1 0()lp q 2-5l 0(t)ll 2 ql2-77O2 20w(9) ?7 maxa(t) 29 if qf2, then AV(t)O,wax1(t)D andaWjx1 (t)uxiyieldsrespectivelyrecurrentformulas.ax1(t)a-fS (t)FX.x(tt 1) 1ax1(O)=,WjD =axi(t)aNi afS(t) +w a t- i)&4 L aNiax1(o) (11)avn =0Having computed the synaptic adjustment, the updatednamelytherecurrenttrainingalgorithmisconvergent.IV.ROADTESTANDRESULTSANALYSESTo make a demonstration the validity ofneural controlalgorithmproposed inthe paper, an experimental mini-bussuspension withMR fluid shock absorber has beenmanufactured in China. The mini-bus adaptive suspensionsystem consists of a DSP microprocessor, 8 accelerationsensors, 4 MR fluid shock absorbers, and 1 controllableelectric current power with input voltage 12V. The DSPmicroprocessor receives suspension vibration signal inputfromaccelerometers mountedrespectivelysprungmassandun-sprung mass. In accordance with vibration signal andcontrol scheme in this paper, the DSP microprocessoradjusts damping of adaptive suspension by applicationcontrol signalto the controllable electric current powerconnected to electromagnetic coil in MR fluid shockabsorbers. Magnetic fieldproducedby the electromagneticcoilinMRfluidshockabsorbers candvarydampingforcein both compression and rebound by adjustment of flow1797I I,&V(t)= 1 2(t+1)-e2(t2behaviorsofMRfluidsindampingchannels.Raod test on mini-bus adaptive suspension based neuralnetworkscontrolpresentedinthispaperarecarriedoutinDclass road surfaces respectively in running velocity30,40,50km/h. Duringroadtest,experimentalmini-busrunseachtestconditionataconstantspeed.Thetestexperimentsofadaptive suspension with neural networks and passivesuspension system were carried outrepeatedlyunder sameroadsurfaceandrunningvelocity.TestresultslistedinTable1 have shown that the adaptive suspension with neuralnetworks can reduce vibration power spectral densities ofbothsprungmassandun-sprungmass.Figure 4 is the min-bus suspension vibration powerspectral densities ofboth sprungmass andun-sprungmasswith passive and adaptive suspension system by D classroad surface. It is clear that neural networks controlimprovesperformancesofmini-bussuspensionwithmainlyimprovementsoccurringaboutsprungmassresonancepeak.The power spectral densities indicate that the adaptivesuspensionsystemwithneuralnetworks controlcanreducemini-bus vibration greatly compared with passivesuspension. If excellent fizzy control rules and rationalmodelingofshockabsorberandsuspensioncanbeobtained,theadaptivesuspensionsystemwithneuralnetworkscontrolwill improve farther ride comfort and road holding andhandlingstabilityofautomobileinthefuture.TABLEImin-bussuspensionroadtestresults:sprungmassandun-sprungmassaccelerationr.m.s.Values(Dclassroad)Speed 30(1km/h) 40(1m/h) 50(kmlh)Passive Control reduce Passive Control reduce Passive Control reduce| mass 1 0.3756 0.3252 13.4 0.4140 0.3449 16.7 0.4694 0.3966 15.5masspg 1.6011 14266 10.9 1.8975 1.6603 12.5 2.3468 2.0652 12.0massIC, -4a|1 -#, -t0ri-01 10.1.lo1Fr y-0Q gco1okaId -ela.r 10f 1FrcqvOFig.4.min-bussuspensionvibrationpowerspectraldensitiesofsprungmass(left)andun-sprungmass(right)withcontrolandpassive(runningspeed40km/h)V.CONCLUSIONSIn thispaper, anewrecurrentneuralnetworks-orientedsuspensionmodelandneurofuzzycontrol schemes forthemini-bus suspension system were investigated. Upon therequirement of using 8 acceleration sensors, a DSPcontroller with gain scheduling was developed.Considering the complexity of the MR fluid shockabsorber,the actuator dynamics has been incorporatedduring the hardware-in-the-loop simulations. It wasdemonstratedthat the adaptive control system could1798achieveacompetitivecontrolperformancebyadoptingtheneurofuzzy control schemes and recurrent neuralnetworks-oriented suspension. Because the control lawdesign, the gain scheduling strategy, and thehardware-in-the-loop simulationmethoddevelopedinthisp