Vehicle Dynamics汽车动力学 Lecture_11_Anti-lock braking

1/17/20201VehicleSystemDynamicsProfessorYou-QunZhaod-mgsinFvvr(1/c)________(m/c)s+1Kp+(Ki/s)+++-1/17/20202Lecture11ReviewandOutlineReviewofPreviousLectureTiremodelsBrakingsimulationLinearBrushMagicformulaToday’stopicsTractioncontrolsystemsIntroductionModelingandsimulationLinearcontrollerRulebasedcontrollerSlidingmodecontrollerVehicledynamics(orvehiclestability)control1/17/20203TractionControlSystemTractioncontrolsystems(TCS)includeananti-lockbrakingsystem(ABS)andananti-spinaccelerationsystemControlbrake/tractionforcetopreventwheellock-uporspin1/17/20204EarlyDevelopmentofABSABS(AntilockBrakingSystems)gobacktoatleast1908,whenJ.E.Francisdevelopedarailcarversion.ToavoidflatspotsItissoonnoticedtrainswithABSstoppedfasterRobertBoschGmbHreceivedapatentin1936foranABSsystem.In1948,BoeingB-47cameequippedwithanABS(byHydroAire).Controlisbang-bangtype(dumppressuretozerothenrebuild).FullymodulatingABSwerefirstdevelopedinthe1950’s(GoodyearandHydroAire)Ford:1954experimentalLincolnKelsey-Hayes:1968rear-wheelonlysystemGM(ACElectronics)”1971OldsToronadorear-wheelonlyChrysler(usesBendixsystem):1971Imperial4-wheelABS1/17/20205HowABS/TCSworksABS(AntilockBrakingSystems)ActivecontrolofwheelbrakepressurewhendriverbrakingexceedsthelimitsoftheroadTCS(TractionControlSystems)Activecontrolofbrakepressureand/orenginetorquewhendriveraccelerationexceedsthelimitsoftheroadTractioncontrolsystem(TCS)typicallyreferstobothanti-lockandanti-spincontrol1/17/20206StableandUnstableSlipRegions1/17/20207BenefitsofABS/TractionControl–MaintainStability–MaintainSteerability–MinimizeStoppingDistance–ReducedDriverWorkload1/17/20208VehicleControlObjectives(ABSexample)I.StoppingDistance-Maximizelongitudinalforces-Findpeak-CycleefficientlyII.Stability-undertorquedisturbances-Maximizerearlateralforcecapability-NobrakingatrearIII.Steerability-Maximizefrontlateralforcecapability-NobrakingatfrontClearly,thereisatrade-off!1/17/20209SimulationModel1/17/202010SimulationModel)]([(Rotationaldynamicsofawheel:wherewisthewheelrotationalvelocity,Jwisthewheelinertia,Teistheenginetorque,Tbisthebrakingtorque,rwisthewheelradius,Fxisthetractive(orbrakingwhennegative)force,andTw(w)isawheelfrictiontorquewhichisafunctionofwheelrotationalspeedmFNmgfmguuACuxwwd/]sincos)(5.0[2Vehiclelongitudinaldynamics:Tireforcemodel:Fx=mFzwvwwvwvvwvdrivenbraking1/17/202011StateSpaceSimulationModelwwzwzwwz])([)/()](sincos))(5.0([22211mmx1vx2wWhereT=(Te-Tb)andTheoutputequation(controlledvariable)is=(x2-x1)/x1forbraking,=(x2-x1)/x2foracceleratingDefinestatevariables:Nonlinearstateequations:SimplifiedABS/TCScontrolproblem:findproperT=Te-Tbtoachievewheelslipregulation.1/17/202012StateSpaceSimulationModel1/17/202013Ex.6.3VehicleBrakingSimulationw/oABS(usesEx.6.1polynomialformcurve)00.20.40.60.81-505101520VehicleBrakingTime(sec)xForwardspeedWheelspeed%Ex6_3.mti=0.0;tf=1.0;xi=[20.0,20.0];tol=1.0e-4;trace=1;[t,x]=ode45('Ex6_3a',ti,tf,xi,tol,trace);plot(t,x);title('VehicleBraking');xlabel('Time(sec)');ylabel('x');grid;legend('Forwardspeed','Wheelspeed')%AseparatefileEx6_3a.mfunctionxdot=Ex6_3a(t,x);%Definethesimulationparameters:m=1400;rho=1.202;Cd=0.5;A=1.95;g=9.81;Theta=0.0;bw=0.0;f=0.01;uw=0.0;fw=0.0;Iw=2.65;rw=0.31;Nw=4;Fz=3560.0;%Definethemu-lambdapolynomialcoefficients:c=[-68.593,238.216,-324.819,219.283,-75.58,12.088,-0.0068];ifx(1)=x(2),lambda=(x(2)-x(1))/x(1);elselambda=(x(2)-x(1))/x(2);end;al=abs(lambda);ifal1.0,al=1.0;end;mu=sign(lambda)*c*[al^6;al^5;...al^4;al^3;al^2;al;1];%DefinethetorqueinputT=Te-Tb;Te=0.0;Tb=1000.0;T=Te-Tb;%Definethestateequations:ifx(1)0.0,x(1)=0.0;end;ifx(2)0.0,x(2)=0.0;end;xdot=[(-(0.5*rho*Cd*A)*(uw+rw*x(1))^2+Nw*Fz*mu-f*m*g*cos(Theta)-m*g*sin(Theta))/(m*rw);(fw*Fz-bw*x(2)-Fz*rw*mu+T)/Iw];ifx(1)=0.0,xdot(1)=0.0;end;ifx(2)=0.0,xdot(2)=0.0;end;1/17/202014LinearABSController+-rKDs1s1sa11a12k2a22++++--++a21k1d1d2TbTe+-Tbx1x2++a11CdArwx10mNwFzmrwm0x10a12NwFzmrwm0x20a21FzrwIwm0x10a22bwIwFzrwIwm0x20b1Iwd1x10x20x102d2x201x10•Equilibrium•Linearization•Linearcontrollerdesign(integralplusstatefeedback)1/17/202015Ex.6.4VehicleBrakingw/LinearABS00.51-1001020WheelSlipw/LinearABSTime,t(sec)(a)00.20.40.6-9.567-9.566-9.565-9.564x106ABStorquevariationTime,t(sec)(c)00.20.40.6-0.02-0.015-0.01-0.0050WheelSlipw/ABSTime,t(sec)(d)linearcontrollerdesignisnoteffectiveforthisapplicationsincethenominaloperatingpointisnotanequilibrium1/17/202016Rule-basedABS/TCSControlDT=0.0IFTHENELSEENDIF|(t)|minTHENDT=sgn()|T(t-1)|ENDIF|(t)|maxTHENDT=-sgn()|T(t-1)|ENDT(t)=T(t-1)+DTwvwvwwvv12Rule-basedABS/TCSalgorithmsarecommonlyusedinproductionvehicles.Forexampleifwheelsliptoolarge,release(ordecrease)ifwheelsliptoosmall,reapply(orincrease)else,holdthepressureWhatcanbeimproved?