控制系统计算机辅助设计控制系统计算机辅助设计第一部分1functiondx=lorenzeq(t,x)dx=[-x(2)-x(3);x(1)+0.2*x(2);0.2+(x(1)-5.7)*x(3);]>>x0=[0;0;0];>>[t,y]=ode45('lorenzeq',[0,100],x0);>>plot(t,y)>>figure;plot3(y(:,1),y(:,2),y(:,3)),grid,1控制系统计算机辅助设计2function[y,yeq]=f2a(x)yeq=[];y=4*x(1)^2+x(2)^2-4;>>Aeq=[];Beq=[];A=[];B=[];>>xm=[0;0];xM=[];x0=[0;0];>>f1=inline('x(1)^2-2*x(1)+x(2)');>>[x,f]=fmincon(f1,x0,A,B,Aeq,Beq,xm,xM,'f2a');x',fans=1.00000f=-13（a）>>s=tf('s');G=(s^3+4*s+2)/s^3/(s^2+2)/[(s^2+1)^3+2*s+5]Transferfunction:s^3+4s+2------------------------------------------------------s^11+5s^9+9s^7+2s^6+12s^5+4s^4+12s^3（b）>>z=tf('z',0.1);>>H=(z^2+0.568)/(z-1)/(z^2-0.2*z+0.99)Transferfunction:z^2+0.568-----------------------------z^3-1.2z^2+1.19z-0.99Samplingtime:0.142控制系统计算机辅助设计>>A=[010;001;-5-4-13];>>B=[0;0;2];>>C=[100;000;000];>>D=[0];>>G=ss(A,B,C,D);>>Ga=x1x2x3x1010x2001x3-5-4-13b=u1x10x20x32c=x1x2x3y1100y2000y3000d=u1y10y20y30Continuous-timemodel.>>G=tf(G)Transferfunctionfrominputtooutput...2#1:----------------------s^3+13s^2+4s+5#2:0#3:0>>GG=zpk(G)Zero/pole/gainfrominputtooutput...2#1:----------------------------------(s+12.72)(s^2+0.2836s+0.3932)#2:0#3:0根据微分方程也可以直接写出传递函数模型：>>num=[2];>>den=[1,13,4,5];3控制系统计算机辅助设计>>G=tf(num,den);>>GTransferfunction:2----------------------s^3+13s^2+4s+5>>GG=zpk(G)Zero/pole/gain:2----------------------------------(s+12.72)(s^2+0.2836s+0.3932)5>>num=[1,2];>>den=[1,1,0.16];>>H=tf(num,den,'Ts',1);>>HTransferfunction:z+2--------------z^2+z+0.16Samplingtime:16functionH=feedback(G1,G2,key)ifnargin==2;key=-1;end,H=G1/(sym(1)-key*G1*G2);H=simple(H);>>symsJKpKis;>>gc=(Kp*s+Ki)/s;>>g=(s+1)/(J*s^2+2*s+5);>>gg=feedback(g*gc,1)>>gg=feedback(g*gc,1)gg=((Ki+Kp*s)*(s+1))/(J*s^3+(Kp+2)*s^2+(Ki+Kp+5)*s+Ki)7（a）>>s=tf('s');>>G=(211.87*s+317.64)/(s+20)/(s+94.34)/(s+0.1684);>>Gc=(169.6*s+400)/s/(s+4);>>Hs=1/(0.01*s+1);>>GG=feedback(G*Gc,Hs)4控制系统计算机辅助设计Transferfunction:359.3s^3+3.732e004s^2+1.399e005s+127056-----------------------------------------------------------------0.01s^6+2.185s^5+142.1s^4+2444s^3+4.389e004s^2+1.399e005s+127056>>zpk(GG)Zero/pole/gain:35933.152(s+100)(s+2.358)(s+1.499)--------------------------------------------------------------------------(s^2+3.667s+3.501)(s^2+11.73s+339.1)(s^2+203.1s+1.07e004)（b）>>z=tf('z');>>G=(35786.7*z^-1+108444)/[(z^-1+4)*(z^-1+20)*(z^-1+74.04)];>>Gc=1/(z^-1-1);>>H=1/(0.5*z^-1-1);>>GG=feedback(G*Gc,H)Transferfunction:-108444z^6+1.844e004z^5+1.789e004z^4------------------------------------------------------------------1.144e005z^6+2.876e004z^5+274.2z^4+782.4z^3+47.52z^2+0.5zSamplingtime:unspecified>>zpk(GG)Zero/pole/gain:-0.94821z^4(z-0.5)(z+0.33)-------------------------------------------------------------z(z+0.3035)(z+0.04438)(z+0.01355)(z^2-0.11z+0.02396)Samplingtime:unspecified8>>s=tf('s');c1=feedback(1/(s+1)*s/(s^2+2),(4*s+2)/(s+1)^2);c2=feedback(1/s^2,50);G=feedback(c1*c2,(s^2+2)/(s^3+14))Transferfunction:s^6+2s^5+s^4+14s^3+28s^2+14s---------------------------------------------------------------------------------s^10+3s^9+55s^8+175s^7+300s^6+1323s^5+2656s^4+3715s^3+7732s^2+5602s+140095控制系统计算机辅助设计>>s=tf('s');>>G=(s+1)^2*(s^2+2*s+400)/(s+5)^2/(s^2+3*s+100)/(s^2+3*s+2500);>>G1=c2d(G,0.01)Transferfunction:4.716e-005z^5-0.0001396z^4+9.59...
