控制系统计算机辅助设计课后题部分答案

1、第三章1.1>>s=tf('s'); G=(s2+5*s+6)/(s+1)2+1)*(s+2)*(s+4)或者G=(s2+5*s+6)/(s+1)2+1)/(s+2)/(s+4)1.2 >> z=tf('z',0.1);H=5*(z-0.2)2/(z*(z-0.4)*(z-1)*(z-0.9)+0.6)2>> den=1 10 32 32;num=6 4 2 2;G=tf(num,den)>> zpk(G)3A=-1,1,0; 0,-1,-3; -1,-5,-3;B=0,0; 1,0; 0,1;C=0,-1,0;D

2、=1,-5;G=ss(A,B,C,D)>> G1=tf(G)4den=1 1 0.16;num=1 2 ;H=tf(num,den,'Ts',1,'ioDelay',2)5>> z=-1+j,-1-j;p=0 0 -5 -6 -j j;>> G=zpk(z,p,8)5.2 z=tf('z',0.05);q=z-1;H=(q+3.2)*(q+2.6)/q5/(q-8.2);zpk(H)6>> A=1 2 3; 4 5 6; 7 8 0;B=4; 3; 2;C=1 2 3;D=zeros(1,1);G=

3、ss(A,B,C,D);>> G1=tf(G)>> zpk(G1)7.1 s=tf('s');Go=(211.87*s+317.64)/(s+20)/(s+94.34)/(s+0.17);>> Gc=(169.6*s+400)/s/(s+4);H=1/(0.01*s+1);>> G=feedback(Go*Gc,H) >> G1=ss(G)>> zpk(G)7.2 z=tf('z',1);q=z-1;Go=(35786.7*q+108444)/(q+4)/(q+20)/(q+74);Gc=1

4、/(q-1);H=1/(0.5*q-1);feedback(Go*Gc,H)>> G1=ss(G)>> G2=zpk(G)7.3 syms Km J B Kr Lq Rq Kv s>> G=Km*J/(J*s2+B*s+Kr);Gc=Lq/(Lq*s+Rq),H=Kv*s;Gc =Lq/(Rq + Lq*s)feedback(G*Gc,H)ans =1/(Kv*s) - 1/(Kv*s*(J*Km*Kv*Lq*s)/(Rq + Lq*s)*(J*s2 + B*s + Kr) + 1)8s=tf('s');G=10/(s+1)3;Gpid=0.

5、48*(1+1/(1.814*s)+0.4353*s/(1+0.04353*s);>> G0=feedback(Gpid*G,1)ss(G0)G2=minreal(G1)zpk(G0)9>> A=2.25 -5 -1.25 -0.5;2.25 -4.25 -1.25 -0.25;0.25 -0.5 -1.25 -1; 1.25 -1.75 -0.25 -0.75;>> B=4 6 ;2 4; 2 2;0 2;C=0 0 0 1;0 2 0 2;D=zeros(2,2);>> G1=ss(A,B,C,D)G2=tf(G1)G3=c2d(G2,0.1

6、,'tustin')>> G4=ss(G3)G5=d2c(G4) 不能够变回去10s=tf('s');g11=-0.252/(1+3.3*s)3/(1+1800*s);g12=0.43/(1+12*s)/(1+1800*s);>>g21=-0.0435/(1+25.3*s)3/(1+360*s);g22=0.097/(1+12*s)/(1+360*s);>> G=g11 g12;g21 g22; Gc=-10 77.5;0 50; I=eye(2,2); G1=feedback(Gc*G,I)11>> s=tf(&

7、#39;s');c1=(1/(s+1)*(s/(s2+2);c2=(4*s+2)/(s+1)2;c3=(s2+2)/(s3+14);c4=feedback(i/s2,50);c5=feedback(c1,c2);G=3*feedback(c4*c5,c3)13clear allsyms G1 G2 G3 G4 G5 G6 H1 H2 H3 H4G23=feedback(G2*G3,H2);G45=feedback(G4*G5,H3);G7=feedback(G23*G45,H4/G2/G5);G=feedback(G1*G7*G6,H1)14clear alls=tf('s&#

8、39;);g1=1/(1+0.01*s);g2=(1+0.17*s)/(0.085*s);g3=(1+0.15*s)/(0.051*s);g4=70/(1+0.0067*s);g5=0.21/(1+0.15*s);g6=130/s;h1=0.212;h2=0.1/(0.01*s+1);h3=0.0044/(1+0.01*s);G0=feedback(g5*g6,h1);G1=feedback(g4*g5*G0,h2/g6);G2=feedback(g2*g3*G1,h3);G=g1*G215不能直接实现延迟系统 可用PADE近似16G=(s+1)2*(s2+2*s+400)/(s+5)2/(s

9、2+3*s+100)/(s2+3*s+2500)zpk(G)；H1=c2d(G,0.01);H2=c2d(G,0.1);H3=c2d(G,1);>> step(G,'-',H1,'*r',H2,'o',H3,'-')>> step(G,'-k',H1,'-r',H2,'-y',H3,'-b')17 >> a=-9 -26 -24 0;1 0 0 0;0 1 0 0;0 1 1 -1;b=1;0 ;0 ;0;c=0 1 1 2;d=0

10、;>> G=ss(a,b,c,d)minreal(G)2 states removed. 不是最小实现17.2 den=1 10 35 50 24;num=2 18 16;G=tf(den,num)minreal(G)第四章4011clear allnum=1;den=1 2 1 2;G=tf(num,den);pzmap(G)eig(G)%不稳定4012clear allnum=1;den=6 3 2 1 1;G=tf(num,den);pzmap(G)eig(G)%不稳4013clear allnum=1;den=1 1 -3 -1 2;G=tf(num,den);pzmap(

11、G)eig(G)%不稳4014clear allnum=3 1;den=300 600 50 3 1;G=tf(num,den);pzmap(G)eig(G)%不稳4015clear alls=tf('s');G=0.2*(s+2)/(s*(s+0.5)*(s+0.8)*(s+3)+0.2*(s+2);pzmap(G)eig(G) %稳定4021clear allnum=-3 2;den=1 -0.2 -0.25 0.05;H=tf(num,den,'Ts',1);pzmap(H)abs(eig(H)')% 稳定ans =0.5000 0.5000 0.

12、2000 4022clear allnum=3 -0.39 -0.09;den=1 -1.7 1.04 0.268 0.024;H=tf(num,den,'Ts',1);pzmap(H)abs(eig(H)')ans =1.1939 1.1939 0.1298 0.1298 %不稳4023clear allnum=1 3 -0.13;den=1 1.352 0.4481 0.0153 -0.01109 -0.001043;H=tf(num,den,'Ts',1);pzmap(H)abs(eig(H)') %稳定ans =0.8743 0.1520

13、 0.2723 0.2344 0.12304024clear allnum=2.12 11.76 15.91;den=1 -7.368 -20.15 102.4 80.39 -340;z=tf('z');q=z-1;H=tf(num,den,'Ts',1,'Variable','q')；pzmap(H)abs(eig(H)')%不稳4031clear allA=-0.2 0.5 0 0 0;0 -0.5 1.6 0 0;0 0 -14.3 85.8 0;0 0 0 -33.3 100;0 0 0 0 -10;B=0;0;0

14、;0;30;C=0 0 0 0 1;D=0;G=ss(A,B,C,D)eig(A)'%稳定4032clear allA=17 24.54 1 8 15;23.54 5 7 14 16;4 6 13.75 20 22.5889;10.8689 1.2900 19.099 .21.896 3;11 18.0898 25 2.356 9;B=1;2;3;4;5;C=0 0 0 0 1;D=0;G=ss(A,B,C,D)abs(eig(A)' %不稳404A=-3 1 2 1;0 -4 -2 -1;1 2 -1 1;-1 -1 1 -2;B=1 0;0 2;0 3;1 1;C=1 2

15、2 -1;2 1 -1 2;D=zeros(2,2);G=ss(A,B,C,D);G1=tf(G)pzmap(G1)tzero(G1)405s=tf('s');G=0.2*(s+2)/(s*(s+0.5)*(s+0.8)*(s+0.3)+0.2*(s+2);G1=ss(G);Gs=sscanform(G1,'obsv')Gs1=sscanform(G1,'ctrl')4061A=0 1 1 1;0 0 0 1;0 1 0 0;0 0 1 1;B=1 0;0 0;0 1;1 0;C=1 0 0 0;0 1 0 0;D=zeros(2,2);Tc=c

16、trb(A,B);r1=rank(Tc)Tc1=obsv(A,C);r2=rank(Tc1)G=ss(A,B,C,D);Gs=canon(G,'model')T=luenberger(A,B);A1=inv(T)*A*TB=inv(T)*Bnorm(G)norm(G,inf)4062A=0 2 0 0;0 1 -2 0 ;0 0 3 1;1 0 0 0;B=2 0;1 2;0 1;0 0;C=0 1 0 0;0 0 1 0;D=zeros(2,2);Tc=ctrb(A,B);r1=rank(Tc)Tc1=obsv(A,C);r2=rank(Tc1)G=ss(A,B,C,D);G

17、s=canon(G,'model')%T=luenberger(A,B);%A1=inv(T)*A*T%B=inv(T)*Bnorm(G)norm(G,inf)407A=0 -3 0 0;1 -4 0 0;0 0 0 0;0 0 1 -2;B=3 2;1 2; 1 1;1 1;C=0 1 0 0;0 0 0 1;D=zeros(2,2);G=ss(A,B,C,D);G1=minreal(G)408f=(t,x)-5*x(1)+2*x(2);-4*x(2);-3*x(1)+2*x(2)-4*x(3)-x(4);-3*x(1)+2*x(2)-4*x(4);t_final=10;x0

18、=1 2 0 0;t,x=ode45(f,0,t_final,x0);plot(t,x)409clear allnum=18 514 5982 36380 122664 222088 185760 40320;den=1 36 546 4536 22449 67284 118124 109584 40320;r,p,k=residue(num,den);r pn d=rat(r);第五章502503504505506507用LTI模块，在工作空间中写出G的表达式。s=tf(s);G=1/(1+4*s) 0.7/(1+5*s) 0.3/(1+5*s) 0.2/(1+5*s);508没有做出来50

19、9510512 封装第六章601clear allG=zpk(-1.5,-1.75 -16 -1.5-3 -1.5+3,210); Gc=zpk(-1.5,-14.86,52.5);a,b,c,d=margin(G);a1,b1,c1,d1=margin(G*Gc); % unsteadyG1=G*Gc;%G2=leadlagc(G,20,30,1000,3)%a2,b2,c2,d2=margin(G2)step(G,'-b',G*Gc,'-r')602s=tf('s');G1=zpk(,0 -1 -2 -8,16);G2=2*(s+1)/s/(

20、47.5*s+1)/(0.0625*s+1)2;wc1=1;gam1=55;wc2=25;gam2=45;Gc1=leadlagc(G1,wc1,gam1,1000,3);Gc2=leadlagc(G2,wc2,gam2,1000,3);figure(1);step(G1,'-r',Gc1,'-b'),figure(2);step(G2,'-r',Gc2,'-b')>> figure(1);step(G1,'-r',Gc1,'-b'),>> figure(2);step(G2

21、,'-r',Gc2,'-b')clear allG=zpk(-1.5,-1.75 -16 -1.5-3 -1.5+3,210); Gc=zpk(-1.5,-14.86,52.5);a,b,c,d=margin(G);a1,b1,c1,d1=margin(G*Gc); % unsteadyG1=G*Gc;%G2=leadlagc(G,20,30,1000,3)%a2,b2,c2,d2=margin(G2)step(G,'-b',G*Gc,'-r')603A=0 1 0 0;0 0 1 0;-3 1 2 3;2 1 0 0;B=1 0

22、;2 1;3 2;4 3;Q=diag(1,2,3,4);R=eye(2,2);K P=lqr(A,B,Q,R);eig(A-B*K)I=eye(4,4);D=0 0;0 0;0 0;0 0;G=ss(A,B,I,D)G1=ss(A-B*K,B,I-D*K,D);%G1=tf(G);step(G)figure;step(G1) %stablity604A=2.25 -5 -1.25 -0.5;2.25 -4.25 -1.25 -0.25;0.25 -0.5 -1.25 -1;1.25 -1.75 -0.25 -0.75;B=4 6;2 4;2 2;0 2;C=0 0 0 1;0 2 0 2;D

23、=0 0;0 0;Q=diag(1,2,10,4);R=eye(2,2);K P=lqr(A,B,Q,R);eig(A-B*K)I=eye(4,4);D1=0 0;0 0;0 0;0 0;G=ss(A-B*K,B,C-D*K,D)G1=ss(A-B*K,B,I-D1*K,D1);%G1=tf(G);step(G)figure;step(G1) %stablity605clearA=-0.2 0.5 0 0 0;0 -0.5 1.6 0 0;. 0 0 -14.3 85.8 0;0 0 0 -33.3 100;0 0 0 0 -10;B=0;0;0;0;30;C=1 0 0 0 0;D=0;P=

24、-1 -2 -3 -4 -5;K=place(A,B,P);eig(A-B*K)'G=ss(A-B*K,B,C-D*K,D);figure(1);step(G);L=acker(A',C',P)'xh,x,t=simobsv(ss(A,B,C,D),L);figure(2); plot(t,x,t,xh,':')Gc,H=obsvsf(G,K,L);figure(3);step(ss(A-B*K,B,C,D);606clear allA=2 1 0 0;0 2 0 0;0 0 -1 0;0 0 0 -1;B=0;1;1;1;C=1 0 1 0;P

25、=-2 -2 -1 -1;m=rank(ctrb(A,B)不完全可控不能用几点配置607不完全可控不能用几点配置608s=tf('s');N=10;Ga=1/(s+1)3;Gb=1/(s+1)5;Gc=(-1.5*s+1)/(s+1)3;K1,L1,T1,G1=getfolpd(1,Ga);G1K2,L2,T2,G2=getfolpd(2,Ga);G2K3,L3,T3,G3=getfolpd(3,Ga);G3K4,L4,T4,G4=getfolpd(4,Ga);G4a=K1*L1/T1;Kp=1.2/a;Ti=2*L1;Td=0.5*L1;G11=Kp*(1+tf(1,Ti,0)+tf(Td 0,Td/N 1);figure