輕型載貨汽車后懸架鋼板彈簧設計【輕型貨車鋼板彈簧懸架的設計】【依維柯歐霸輕卡車型】【說明書+CAD+CATIA】,輕型貨車鋼板彈簧懸架的設計,依維柯歐霸輕卡車型,說明書+CAD+CATIA,輕型載貨汽車后懸架鋼板彈簧設計【輕型貨車鋼板彈簧懸架的設計】【依維柯歐霸輕卡車型】【說明書+CAD+CATIA】,輕型,載貨 Study onNeuralNetworksControlAlgorithms for Automotive Adaptive Suspension Systems L.J.Fu, J.G.Cao SchoolofAutomobileEngineering,Chongqing InstituteofTechnology, XingshengRoadNo.04Yangjiaping, Chongqing,China400050 E-mail: Abstract-The semi-active suspension, which consists of passive spring and active shock absorber in the light of differentroadconditionsandautomobilerunningconditions,is the most popular automotive suspension because active suspension is complicated in structure andpassive suspension cannot meet the demands of various road conditions and automobile running conditions. In this paper, a neurofuzzy adaptive control controller via modeling of recurrent neural networksofautomotive suspensionispresented. Themodeling of neural networks has identified automotive suspension dynamic parameters and provided learning signals to neurofuzzy adaptive control controller. In order to verify controlresults,amini-busfittedwithmagnetorheologicalfluid shock absorber and neurofuzzy control system based on DSP microprocessor has been experimented with various velocity and road surfaces. The control results have been compared with those of open loop passive suspension system. These results show that neural control algorithm exhibits good performancetoreductionofmini-busvibration. I.INTRODUCTION Themainfunctions ofautomotive suspension systemare to provide support the weight of automobile, to provide stability and direction control during handling maneuvers and to provide effective isolation from road disturbances. Thesedifferenttasksleadtoconflictingdesignrequirements. The semi-active suspension, which consists of passive springandactiveshockabsorberwithcontrollabledamping forceinthelightofdifferentroadconditionsandautomobile running conditions, is the most popular automotivesuspension because the active suspension is complicatedin structure and conventional passive suspension cannot meet the demands of different road conditions and automobile running conditions. Simi-active suspension with variable magnetorheological(MR) fluid shock absorbers has someadvantages inreducingautomobile vibration atrelative low cast and power. So far, there are a number of control methods that have been developed for semi-activesuspension, start with skyhook method described by Karnoopp, etal.lThismethodattemptstomaketheshockabsorber exert a force that is proportional to the absolute velocity between sprung masses. Some investigations use C.R.Liao, B.Chen SchoolofAutomobileEngineering,Chongqing InstituteofTechnology, XingshengRoadNo.04Yangjiaping, Chongqing,China400050 E-mail:chenbao( linear suspension model, which is linearized around the operational points, and control algorithm are derivedusing linearmodels, suchasLQGandrobustcontrol 2,3. These control methods cannot make a full exploitation of semi-active suspension resources because of automotive suspension is inherent non-linear performance. In order to improveperformanceofnonlinearsuspensionsystem, some intelligent control techniques, such as fuzzy logic control, neuralnetworks control andneurofuzzy control, havebeen recently applied to nonlinear suspension control by researchers4,5. Inthispaper, aneurofuzzy adaptive control controlleris applied to control suspension vibration via modeling of recurrent neural networks of automotive suspension and continuously variable MR shock absorbers. The controller structures design and neurofuzzy control algorithms are presented in section 2. A recurrent neural networks dynamicsmodelingofsuspensionareshownrespectivelyin section3. The control system experimentations are givenin section4andsomeconclusions arefinallydrawninsection 5. HI.NEUROFUZZYADAPTIVECONTROLALGORITHMSFOR AUTOMOTIVESUSPENSIONS The neurofuzzy control system presented in this paper, shown in Figure 1, is composed ofa neurofuzzy network and a recurrent neural network modeling of mini-bus suspension. Theneurofuzzynetwork is defined as adaptivecontroller, which has function oflearning and control. The functionofrecurrentneuralnetworkistoidentifymini-bus suspension model parameters.y(t) and yd(t) are system actualoutputandsystemdesireoutputrespectivelyinFigure 1. xl(t) is system error of system actual outputbetween system desire output, x2(t) is system error rate ofsystem 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 networks control system .The global sets of linguistic variables are definedrespectively as fellows: - =-E,E, 1=-AtJ u U-U,U. The neurofuzzy controller has fourlayersne-urons, inwhichthefirstandthesecondlayers correspond to the fuizzy rules if-part, the third layercorresponds totheinferenceandtheforthlayercorresponds to the fuzzy rules then-part. The sets xl, x2and u are respectivelydivinedintosevenfuzzysubsetsofwhichfuzzy sets X1, X2 U arecomposedasfallowsrules: 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,theGaussianmembership functionareused in elements of fuzzy sets X1 X2 and the elements of fuzzyset U isdefinedasfollowingmembershipfunction ci(u)J0 (otherwise) 0(3)=I(3) k=1,2,3.49 j=13,23,3.7 49 49Layer4:(4)- (3)wk and 0(4) =I(4)/ 0(3) k=1 k=1 Where xl(t) x2(t) are the inputs of neural networks, wk is weight of neural network, 0(4) iS the output of neuralnetworksinwhich 0(4) =U, ai, b,j arethecentral values of Gaussian membership function. Learning algorithms of the neural networks controller is based on gradientdescentbymeans oferrorsignalback-propagation method. The errorback-propagation algorithm.s accomplish synaptic weight adjustment through minimization of cost function5. m.ALGORITHMFORRECURRENTNEURALNETWORKS SUSPENSIONDYNAMICALMODELING A recurrent neural network designed to approximate to the actual output ofsuspension y(t) is three-layer neural network with one local feedback loop in the hidden layer, whosearchitecturesareshowninFigure3.Thepropertythat isofprimarysignificanceforrecurrentneuralnetworkisthe ability ofthenetworkto learnfromits environment andto improve its performances by means of process of adjustments applied to its weights. The recurrent network with input signal II(t)=u(t) and I2(t)=y(t-1) has output y(t) by local feedback loop neuron in the hidden layer whose output sum is Sj(t) corresponding to the neuronjth. (3) Fig.2.schematicofneuralnetworkscontrollerforadaptivesuspension Where U* E u .Theinput/outputispresentedasfollows accordingtoFigure2. Layer1: I(1)x(t) and O ) xi(t) i=1,2 Layer2: I -2) (t)-ai )2/b 2 and O. epx() i=1,2 j=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)+wj Xj(t_l q yj(t)= 1w xi(t)j=l (5) (6) 1796 where wI , ,w areweightoftherecurrentneural network, Xj(t)is output of neuron with local feedback loop neuron in the hidden layer, p,qare input neuron number and feedback neuron number respectively. The activation function for both input neurons and output neurons is linear function, whilethe activation forneurons inthehiddenlayerissigmoidfunction. heobjectivefunction E(t)canbedefmedinthetermsof theerrorsignal e(t)as: E(t)= _y(t)-.y(t)2 =1e2(t) (7)2 2 That is, E(t) is the instantaneous value of the error energy.Thestep-by-stepadjustmentstothesynapticweights ofneuronarecontinueduntilthe systemreachsteadystate, i.e. the synaptic weights are essentially stabilized. Differentiating E(t)with respect to weight vector w yields.aE(t) _ 8=-e(t)0Y() (8) From expression (1), (2) and (3), differentiating A(t) 0 D Iwithrespecttotheweightvectorw1 w,- ,w,-Y respectively yields. aS(t)=x (t) As(t) wo ax1Q)-( WaXI(t)aWj J aWj From(4),(5)and(6), analyzing valueofsynapticweightisdeterminedby w(t+1)=w(t)+q*e(t)89(t) (12) where q the leaning-rate parameter, A detailed convergence analysis ofthe recurrent training algorithm is rather complicated to acquire the leaning-rate parameter value. According to expression (13), theweightvector w forrecurrentneuralnetworkcanbeadjusted. Weestablisha the Lyapunov function as follows V(t)=1/2*e2(t), whosechangevalue AV(t) canbedeterminedaftersome t iterations,inthesensethat (13) Wehavenoticedthattheerrorsignal e(t) aftersome t iterations canbeexpressedas follows fromexpression (13) and(14),ae(t) ao(t) ae(t) ae(t) - ,Aw=-qe(t) =77e(t) ,theaw Ow aw Ow Lyapunovfunctionincrement candeterminedaftersome t iterationsasfollows (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 ql2-77O 2 20w (9) ?7 maxa(t) 29 if qf2, then AV(t)O, w ax1(t) D andaWj x1 (t) uxi yieldsrespectivelyrecurrentformulas.ax1(t)a-fS (t)FX.x(tt 1) 1 ax1(O)= ,WjD = axi(t)aNi afS(t) +w a t- i) &4 L aNi ax1(o) (11)avn =0 Having computed the synaptic adjustment, the updated namelytherecurrenttrainingalgorithmisconvergent. IV.ROADTESTANDRESULTSANALYSES To make a demonstration the validity ofneural control algorithmproposed inthe paper, an experimental mini-bussuspension with MR fluid shock absorber has been manufactured in China. The mini-bus adaptive suspension system consists of a DSP microprocessor, 8 acceleration sensors, 4 MR fluid shock absorbers, and 1 controllable electric current power with input voltage 12V. The DSP microprocessor receives suspension vibration signal input fromaccelerometers mountedrespectivelysprungmassand un-sprung mass. In accordance with vibration signal and control scheme in this paper, the DSP microprocessor adjusts damping of adaptive suspension by applicationcontrol signal to the controllable electric current power connected to electromagnetic coil in MR fluid shock absorbers. Magnetic fieldproducedby the electromagnetic coilinMRfluidshockabsorbers candvarydampingforce in both compression and rebound by adjustment of flow 1797 I I ,&V(t)= 1 2(t+1)-e2(t2 behaviorsofMRfluidsindampingchannels. Raod test on mini-bus adaptive suspension based neural networkscontrolpresentedinthispaperarecarriedoutinD class road surfaces respectively in running velocity 30,40,50km/h. Duringroadtest,experimentalmini-busruns eachtestconditionataconstantspeed.Thetestexperiments ofadaptive suspension with neural networks and passive suspension system were carried outrepeatedlyunder same roadsurfaceandrunningvelocity.TestresultslistedinTable 1 have shown that the adaptive suspension with neural networks can reduce vibration power spectral densities of bothsprungmassandun-sprungmass. Figure 4 is the min-bus suspension vibration power spectral densities ofboth sprungmass andun-sprungmass with passive and adaptive suspension system by D class road surface. It is clear that neural networks controlimproves performancesofmini-bussuspensionwithmainly improvementsoccurringaboutsprungmassresonancepeak. The power spectral densities indicate that the adaptive suspensionsystemwithneuralnetworks controlcanreduce mini-bus vibration greatly compared with passive suspension. If excellent fizzy control rules and rational modelingofshockabsorberandsuspensioncanbeobtained, theadaptivesuspensionsystemwithneuralnetworkscontrol will improve farther ride comfort and road holding and handlingstabilityofautomobileinthefuture. TABLEI min-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 15.5mass pg 1.6011 14266 10.9 1.8975 1.6603 12.5 2.3468 2.0652 12.0mass IC, -4a |1 -#, -t 0 ri-01 10.1. lo1 Fr y- 0Q gco1okaId -e la.r 10f 1Frcqv O Fig.4.min-bussuspensionvibrationpowerspectraldensitiesofsprungmass(left) andun-sprungmass(right)withcontrolandpassive(runningspeed40km/h) V.CONCLUSIONS In thispaper, anewrecurrentneuralnetworks-oriented suspensionmodelandneurofuzzycontrol schemes forthemini-bus suspension system were investigated. Upon the requirement of using 8 acceleration sensors, a DSP controller with gain scheduling was developed. Considering the complexity of the MR fluid shockabsorber, the actuator dynamics has been incorporated during the hardware-in-the-loop simulations. It wasdemonstrated that the adaptive control system could 1798 achieveacompetitivecontrolperformancebyadoptingthe neurofuzzy control schemes and recurrent neural networks-oriented suspension. Because the control law design, the gain scheduling strategy, and the hardware-in-the-loop simulationmethoddevelopedinthis paper are restricted to a min-bus suspension system with specificparameters, the entire strategy canbeextendedto other semi-active system if suspension parameters are changed.Roadtestresultsshowthatneurofizzycontroller can effectively improve mini-bus ride comfort and road holding. It is feasible to employDSP control to suppress whole vehicle vibration, including in sprung mass vibration and un-sprung mass vibration. The neurofuzzy controllershows somerobustcapabilityandcanminimize influences on suspension model parameters changes, which are important factors to improve control system performance. REFERENCES 1 Kanopp D. (1995) Active and Semi-active Vibration Isolation, Transactions ofASME, JournalofSpecial50thAnniversaryDesign Issue,Vol.117,pp117-125. 2 Chantrnuwathhana,S. andPeng,H. (1999) Adaptive Robust Control for Active Suspension, proceedings of the American Control Conference,SanDiego,California,pp.l702-1706 3Yu,F. andCrolla,D.A.(1998) AnOptimalSelf-TuningControllerfor ActiveSuspension, VehicleSystemDynamics,vol.29,pp.51-654 Zadeh,A., Fahim,A., and El-Gindy,M. (1997) Neural Networks and FuzzyLogicApplicationstoVehicleSystem,InternationalJournalof VehicleDesign,vol.18(2),pp.132-1935 Wuwei Chen, James K. Mills and Le Wu,(2003) Neurofuzzy and FuzzyControlofAutomotiveSemi-ActiveSuspensions,InternationalJournalofVehicleAutonomousSystems,vol.1(2),pp.222-236 1799