汽车系统动力学Matlab.docx

1、汽车系统动力学Matlab汽车系统动力学Matlab作业报告小组成员：一、组内任务分配二、Matlab程序与图形1、不同转向特性车辆在不同车速下的系统特征根m=1000;I=1500;a1=1.15;b1=1.35;Caf=53000;Car=53000;i=1;R=;for uc=10:5:100; D=(I*(Caf+Car)+m*(a12*Caf+b12*Car)/(m*I*uc); S=(a1+b1)2*Caf*Car/(m*I*uc2)+(b1*Car-a1*Caf)/I; P=1 D S; r=roots(P); R(i,1)=r(1,1);R(i,2)=r(2,1);i=i+1;

2、endplot(real(R(:,1),imag(R(:,1),bo);holda2=1.25;b2=1.25;t=1;S=; for uc=10:5:100 P=m 0;0 I;Q=(Caf+Car)/uc,m*uc+(a2*Caf-b2*Car)/uc;(a2*Caf-b2*Car)/uc,(a22*Caf+b22*Car)/uc; R=Caf;a2*Caf; A=-P(-1)*Q; d=eig(A); i=imag(d); r=real(d); S(t,1)=r(1); S(t,2)=i(1); t=t+1;endplot(S(:,1),S(:,2),*)a3=1.35;b3=1.15;

3、 for uc=10:5:100 P=m 0;0 I; Q=(Caf+Car)/uc,m*uc+(a3*Caf-b3*Car)/uc;(a3*Caf-b3*Car)/uc,(a32*Caf+b32*Car)/uc; R=Caf;a3*Caf; A=-P(-1)*Q; d=eig(A); i=imag(d); r=real(d); S(t,1)=r(1); S(t,2)=i(1); t=t+1;endgrid onplot(S(:,1),S(:,2),d);axis(-14 2 0 3);xlabel(实轴(Re);ylabel(虚轴(Im);text(-8,2.8,不足转向);text(0,0

4、.2,过多转向);text(-3,0.2,中性转向)set(gca,FontName,Helvetica,FontSize,10)title(不同转向特性车辆在不同车速下的系统特征根,FontSize,12); 2.1、具有不同转向特性车辆的横摆角速度幅频和相频响应m=1000;I=1500;a1=1.15;a2=1.25;a3=1.35;b1=1.35;b2=1.25;b3=1.15;Caf=53000;Car=53000;D=;C=;M=;uc=20;i=1;for f=0.1:0.1:10 w=2*pi*f; E=1 0;0 1; P=m 0;0 I; R1=Caf;a1*Caf; R2

5、=Caf;a2*Caf; R3=Caf;a3*Caf; Q1=(Caf+Car)/uc m*uc+(a1*Caf-b1*Car)/uc;(a1*Caf-b1*Car)/uc (a12*Caf+b12*Car)/uc; Q2=(Caf+Car)/uc m*uc+(a2*Caf-b2*Car)/uc;(a2*Caf-b2*Car)/uc (a22*Caf+b22*Car)/uc; Q3=(Caf+Car)/uc m*uc+(a3*Caf-b3*Car)/uc;(a3*Caf-b3*Car)/uc (a32*Caf+b32*Car)/uc; A1=-inv(P)*Q1; A2=-inv(P)*Q2;

6、 A3=-inv(P)*Q3; B1=inv(P)*R1; B2=inv(P)*R2; B3=inv(P)*R3; Hw1=-inv(A1-1i*w*E)*B1; Hw2=-inv(A2-1i*w*E)*B2; Hw3=-inv(A3-1i*w*E)*B3; D(i,1)=angle(Hw1(2)*180/pi;D(i,2)=abs(Hw1(2); C(i,1)=angle(Hw2(2)*180/pi;C(i,2)=abs(Hw2(2); M(i,1)=angle(Hw3(2)*180/pi;M(i,2)=abs(Hw3(2); i=i+1;endsubplot(2,1,1)f=0.1:0.1

7、:10;semilogx(f,D(:,2),k,f,C(:,2),r-.,f,M(:,2)grid onset(gca,Xtick,0.1,0.3,1.5,3,10)set(gca,FontName,Helvetica,FontSize,10)legend(不足转向,中性转向,过多转向)title(具有不同转向特性车辆的横摆角速度幅频响应,FontSize,12);xlabel(频率/Hz)ylabel(横摆角速度增益/(/s)/()subplot(2,1,2)f=0.1:0.1:10;semilogx(f,D(:,1),k,f,C(:,1),r-.,f,M(:,1)m=1000;I=1500

8、;a1=1.15;a2=1.25;a3=1.35;b1=1.35;b2=1.25;b3=1.15;Caf=53000;Car=53000;D=;C=;M=;uc=20;i=1;for f=0.1:0.1:10 w=2*pi*f; E=1 0;0 1; P=m 0;0 I; R1=Caf;a1*Caf; R2=Caf;a2*Caf; R3=Caf;a3*Caf; Q1=(Caf+Car)/uc m*uc+(a1*Caf-b1*Car)/uc;(a1*Caf-b1*Car)/uc (a12*Caf+b12*Car)/uc; Q2=(Caf+Car)/uc m*uc+(a2*Caf-b2*Car)/

9、uc;(a2*Caf-b2*Car)/uc (a22*Caf+b22*Car)/uc; Q3=(Caf+Car)/uc m*uc+(a3*Caf-b3*Car)/uc;(a3*Caf-b3*Car)/uc (a32*Caf+b32*Car)/uc; A1=-inv(P)*Q1; A2=-inv(P)*Q2; A3=-inv(P)*Q3; B1=inv(P)*R1; B2=inv(P)*R2; B3=inv(P)*R3; Hw1=-inv(A1-1i*w*E)*B1; Hw2=-inv(A2-1i*w*E)*B2; Hw3=-inv(A3-1i*w*E)*B3; D(i,1)=angle(Hw1

10、(2)*180/pi;D(i,2)=abs(Hw1(2); C(i,1)=angle(Hw2(2)*180/pi;C(i,2)=abs(Hw2(2); M(i,1)=angle(Hw3(2)*180/pi;M(i,2)=abs(Hw3(2); i=i+1;endsubplot(2,1,1)f=0.1:0.1:10;semilogx(f,D(:,2),k,f,C(:,2),r-.,f,M(:,2)grid onset(gca,Xtick,0.1,0.3,1.5,3,10)set(gca,FontName,Helvetica,FontSize,10)legend(不足转向,中性转向,过多转向)ti

11、tle(具有不同转向特性车辆的横摆角速度幅频响应,FontSize,12);xlabel(频率/Hz)ylabel(横摆角速度增益/(/s)/()subplot(2,1,2)f=0.1:0.1:10;semilogx(f,D(:,1),k,f,C(:,1),r-.,f,M(:,1)grid onset(gca,Xtick,0.1,0.3,1.5,3,10) set(gca,FontName,Helvetica,FontSize,10)legend(不足转向,中性转向,过多转向)title(具有不同转向特性车辆的横摆角速度相频响应,FontSize,12);xlabel(频率/Hz)ylabel

12、(横摆角速度相位（）)grid onset(gca,Xtick,0.1,0.3,1.5,3,10) set(gca,FontName,Helvetica,FontSize,10)legend(不足转向,中性转向,过多转向)title(具有不同转向特性车辆的横摆角速度相频响应,FontSize,12);xlabel(频率/Hz)ylabel(横摆角速度相位（）)2.2、具有不同转向特性车辆的侧向加速度和相频响应m=1000;I=1500;a1=1.15;a2=1.25;a3=1.35;b1=1.35;b2=1.25;b3=1.15;Caf=53000;Car=53000;D=;C=;M=;uc=

13、20;L=a1+b1;i=1;for f=0.1:0.1:10 w=2*pi*f; E=1 0;0 1; Vi=w*I*Caf; Rr=L*Caf*Car/uc; Vr1=(L*b1*Caf*Car/uc-m*a1*Caf*uc); Vr2=(L*b2*Caf*Car/uc-m*a2*Caf*uc); Vr3=(L*b3*Caf*Car/uc-m*a3*Caf*uc); Ri1=w*m*a1*Caf; Ri2=w*m*a2*Caf; Ri3=w*m*a3*Caf; Dr1=-w2*m*I+L2*Caf*Car/(uc2)+m*(b1*Car-a1*Caf); Dr2=-w2*m*I+L2*Ca

14、f*Car/(uc2)+m*(b2*Car-a2*Caf); Dr3=-w2*m*I+L2*Caf*Car/(uc2)+m*(b3*Car-a3*Caf); Di1=w*(I*(Caf+Car)+m*(a12*Caf+b12*Car)/uc; Di2=w*(I*(Caf+Car)+m*(a22*Caf+b22*Car)/uc; Di3=w*(I*(Caf+Car)+m*(a32*Caf+b32*Car)/uc; Hay1=1i*w*(Vr1+1i*Vi)/(Dr1+1i*Di1)+uc*(Rr+1i*Ri1)/(Dr1+1i*Di1); Hay2=1i*w*(Vr2+1i*Vi)/(Dr2+1

15、i*Di2)+uc*(Rr+1i*Ri2)/(Dr2+1i*Di2); Hay3=1i*w*(Vr3+1i*Vi)/(Dr3+1i*Di3)+uc*(Rr+1i*Ri3)/(Dr3+1i*Di3); D(i,1)=angle(Hay1)*180/pi;D(i,2)=abs(Hay1); C(i,1)=angle(Hay2)*180/pi;C(i,2)=abs(Hay2); M(i,1)=angle(Hay3)*180/pi;M(i,2)=abs(Hay3); i=i+1;endsubplot(2,1,1)f=0.1:0.1:10;semilogx(f,D(:,2)*(pi/(180*9.8),

16、k,f,C(:,2)*(pi/(180*9.8),r-.,f,M(:,2)*(pi/(180*9.8)grid onset(gca,XTick,0.1 0.3 1 3 10)set(gca,FontName,Helvetica,FontSize,10)legend(不足转向,中性转向,过多转向)title(具有不同转向特性车辆的侧向加速度幅频响应,FontSize,12);xlabel(频率/Hz)ylabel(侧向加速度增益/g/()subplot(2,1,2)f=0.1:0.1:10;semilogx(f,D(:,1),k,f,C(:,1),r-.,f,M(:,1)grid onlegen

17、d(不足转向,中性转向,过多转向)set(gca,XTick,0.1 0.3 1 3 10)set(gca,FontName,Helvetica,FontSize,10)title(具有不同转向特性车辆的侧向加速度幅频响应,FontSize,12);axis(0.1 10 -120 120)xlabel(频率/Hz)ylabel(侧向加速度相位（）)2.3、 ABS控制器设计w0=120;v0=30;Tb=600;ki=4500;kd=5000;Ts=0.05;Iw=12;rd=0.25;uh=0.8;ug=0.6;s0=0.2;m=300;g=9.8;w=;v=;s=;w(1)=120;v(

18、1)=30;s(1)=0;k=0;i=2;while(v00) k=k+1; sb=(v0-rd*w0)/v0; s(i)=sb; if sb0.22 Tb=Tb-kd*Ts; elseif sb0.18 Tb=Tb+ki*Ts; else Tb=Tb; end w0=w0+(Fxb*rd-Tb)/Iw*Ts; w(i)=w0; v0=v0-Fxb/m*Ts; v(i)=v0; i=i+1;endt=0:Ts:Ts*k;subplot(2,1,1)plot(t,v,t,w*rd);grid onlegend(车轮前进速度,车轮线速度);set(gca,FontName,Helvetica,Fo

19、ntSize,10)title(车轮前进速度与车轮线速度关系曲线,FontSize,12);xlabel(时间/（s）);ylabel(速度/（m/s）);axis(0,Ts*k,0,32);subplot(2,1,2)plot(t,s);axis(0,Ts*k,0,1);grid onset(gca,FontName,Helvetica,FontSize,10)title(ABS控制的滑移率时域仿真结果,FontSize,12);xlabel(时间/（s）);ylabel(滑移率);set(gca,Ytick,0:0.2:1)3、扭振系统振型图J1=1.986*10(-3);1.910*10

20、(-3);1.931*10(-3);1.931*10(-3);1.910*10(-3);1.924*10(-3);7.8426*10(-2);2.258*10(-3);2.641*10(-2);2.91*10(-3);2.51*10(-3);1.77*10(-3);7.836*10(-2);3.238;K1=7.95*104;7.95*104;6.95*104;7.95*104;7.95*104;6.90*104; 8.93*103;1.41*104;1.02*104;4.4*103;1.38*104;1.616*102;2.51*102;J=diag(J1);K(1,1)=K1(1);K(1

21、,2)=-K1(1);i=2;for i=2:13; K(i,i-1)=-K1(i-1); K(i,i)=K1(i-1)+K1(i); K(i,i+1)=-K1(i);endK(14,13)=-K1(13);K(14,14)=K1(13);A=inv(J)*K;G,D=eig(A);f=sqrt(D)/(2*pi); m=1; while m=14 G(:,m)=G(:,m)/G(1,m) m=m+1endsubplot(3,2,1)plot(G(:,13)xlabel(质点号);set(gca,FontName,Helvetica,FontSize,10)grid on title(单节点振

22、型图（4.26Hz）,FontSize,12)axis(1 15 -0.2 1.1) subplot(3,2,2) plot(G(:,12)xlabel(质点号);set(gca,FontName,Helvetica,FontSize,10)grid onaxis(1 15 -5 1.2)title(双节点振型图（11.99Hz）,FontSize,12)subplot(3,2,3)plot(G(:,11)xlabel(质点号);set(gca,FontName,Helvetica,FontSize,10)grid onaxis(1 15 -7 1.2)title(三节点振型图 (73.9Hz

23、),FontSize,12)subplot(3,2,4)plot(G(:,10)xlabel(质点号);set(gca,FontName,Helvetica,FontSize,10)grid ontitle(四节点振型图 (147.7Hz),FontSize,12)axis(1 15 -9 37)subplot(3,2,5)plot(G(:,9)xlabel(质点号);set(gca,FontName,Helvetica,FontSize,10)grid onaxis(1 15 -0.2 1.1)title(五节点振型图 (252Hz),FontSize,12)5、福特Granada轿车后悬架

24、单轮模型频率响应函数和系统相应输入功率谱密度mb=317.5;mw=45.4;ks=22000;kt=192000;cs=1500;Go=5*10(-6);Uc=20;n=1;B=;D=;for f=0:0.01:15 w=2*pi*f; Sf=4.47*10(-4)*power(f,-2.5); A=i*cs*w+(ks+kt-w2*mw),-i*cs*w-ks;-i*cs*w-ks,i*cs*w+(ks-mb*w2); C=kt;0; D=-A(-1)*C; B(1,n)=abs(D(2)-D(1); B(2,n)=abs(-D(2)*w2); B(3,n)=abs(kt*(D(1)-1)

25、; B(4,n)=Sf; B(5,n)=B(2,n)2*Sf; B(6,n)=B(1,n)2*Sf; B(7,n)=B(3,n)2*Sf; n=n+1;endf=0:0.01:15subplot(3,2,1)plot(f,B(1,:);xlabel(频率/Hz)ylabel(悬架动行程增益)grid onsubplot(3,2,2);plot(f,B(2,:);grid onxlabel(频率/Hz)ylabel(不舒适性参数增益/(m/s2)/m)subplot(3,2,3);plot(f,B(3,:);grid onxlabel(频率/Hz)ylabel(轮胎动载荷增益/N/m)subpl

26、ot(3,2,4)plot(f,B(6,:);xlabel(频率/Hz)ylabel(悬架动行程功率谱密度/m2/Hz)grid onsubplot(3,2,5);plot(f,B(5,:);grid onxlabel(频率/Hz)ylabel(不舒适性功率谱密度/(m/s2)2/Hz)subplot(3,2,6);plot(f,B(7,:);grid onxlabel(频率/Hz)ylabel(轮胎动载荷功率谱密度/N2/Hz)6、魔术公式xdata = 0 0.78 1.88 2.79 3.80 4.82 6.29 7.82 9.31 11.80;ydata = 0 7.99 16.05

27、20.65 23.82 26.00 27.78 28.87 29.65 30.09;zdata = 0 1.65 1.61 0.77 -0.21 -1.03 -1.90 -2.59 -2.61 -2.68;a0 = 11 1 0.8 1;b0 = 1 1 0.8 1;a = lsqcurvefit(fun1, a0, xdata, ydata);b = lsqcurvefit(fun2, b0, xdata, zdata);yy = fun1(a,xdata);zz = fun2(b,xdata);subplot(2,1,1)hold onscatter(xdata, ydata);grid

28、onplot(xdata, yy);set(gca,FontName,Helvetica,FontSize,10)title(MF公式拟合轮胎侧偏力-侧偏角曲线,FontSize,12);xlabel(侧偏角 /（）)ylabel(侧偏力 Fy/(N)subplot(2,1,2)hold on;scatter(xdata,zdata);grid onplot(xdata, zz);set(gca,FontName,Helvetica,FontSize,10)title(MF公式拟合轮胎回正力矩-侧偏角曲线,FontSize,12);xlabel(侧偏角 /（）)ylabel(回正力矩 Mz/(Nm)function y = fun1(a,xdata);y=a(1)*sin(a(2)*at