控制系统计算机辅助设计课后题部分答案word.docx
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控制系统计算机辅助设计课后题部分答案word.docx
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控制系统计算机辅助设计课后题部分答案word
第三章
1.1>>s=tf('s');G=(s^2+5*s+6)/(((s+1)^2+1)*(s+2)*(s+4))或者G=(s^2+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=[1103232];num=[6422];G=tf(num,den)
>>zpk(G)
3.A=[-1,1,0;0,-1,-3;-1,-5,-3];B=[0,0;1,0;0,1];
C=[0,-1,0];D=[1,-5];G=ss(A,B,C,D)
>>G1=tf(G)
4.den=[110.16];num=[12];H=tf(num,den,'Ts',1,'ioDelay',2)
5.>>z=[-1+j,-1-j];p=[00-5-6-jj];
>>G=zpk(z,p,8)
5.2z=tf('z',0.05);q=z^-1;H=((q+3.2)*(q+2.6))/q^5/(q-8.2);zpk(H)
6.>>A=[123;456;780];B=[4;3;2];
C=[123];D=zeros(1,1);G=ss(A,B,C,D);
>>G1=tf(G)
>>zpk(G1)
7.1s=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)
7.2z=tf('z',1);q=z^-1;Go=(35786.7*q+108444)/(q+4)/(q+20)/(q+74);Gc=1/(q-1);H=1/(0.5*q-1);feedback(Go*Gc,H)
>>G1=ss(G)
>>G2=zpk(G)
7.3symsKmJBKrLqRqKvs
>>G=Km*J/(J*s^2+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*s^2+B*s+Kr))+1))
8.
s=tf('s');G=10/(s+1)^3;Gpid=0.48*(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=[46;24;22;02];C=[0001;0202];D=zeros(2,2);
>>G1=ss(A,B,C,D)
G2=tf(G1)
G3=c2d(G2,0.1,'tustin')
>>G4=ss(G3)
G5=d2c(G4)不能够变回去
10.s=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=[g11g12;g21g22];Gc=[-1077.5;050];I=eye(2,2);G1=feedback(Gc*G,I)
11>>s=tf('s');c1=(1/(s+1))*(s/(s^2+2));c2=(4*s+2)/(s+1)^2;c3=(s^2+2)/(s^3+14);c4=feedback(i/s^2,50);c5=feedback(c1,c2);G=3*feedback(c4*c5,c3)
13
clearall
symsG1G2G3G4G5G6H1H2H3H4
G23=feedback(G2*G3,H2);
G45=feedback(G4*G5,H3);
G7=feedback(G23*G45,H4/G2/G5);
G=feedback(G1*G7*G6,H1)
14
clearall
s=tf('s');
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*G2
15.不能直接实现延迟系统可用PADE近似
16.G=(s+1)^2*(s^2+2*s+400)/(s+5)^2/(s^2+3*s+100)/(s^2+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=[-9-26-240;1000;0100;011-1];b=[1;0;0;0];c=[0112];d=[0];
>>G=ss(a,b,c,d)
minreal(G)
2statesremoved.不是最小实现
17.2den=[110355024];num=[21816];G=tf(den,num)
minreal(G)
第四章
4011
clearall
num=[1];den=[1212];G=tf(num,den);
pzmap(G)
eig(G)%不稳定
4012
clearall
num=[1];den=[63211];G=tf(num,den);
pzmap(G)
eig(G)%不稳
4013
clearall
num=[1];den=[11-3-12];G=tf(num,den);
pzmap(G)
eig(G)%不稳
4014
clearall
num=[31];den=[3006005031];G=tf(num,den);
pzmap(G)
eig(G)%不稳
4015
clearall
s=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
4021
clearall
num=[-32];
den=[1-0.2-0.250.05];
H=tf(num,den,'Ts',1);
pzmap(H)
abs(eig(H)')%稳定
ans=
0.50000.50000.2000
4022
clearall
num=[3-0.39-0.09];
den=[1-1.71.040.2680.024];
H=tf(num,den,'Ts',1);
pzmap(H)
abs(eig(H)')
ans=
1.19391.19390.12980.1298%不稳
4023
clearall
num=[13-0.13];
den=[11.3520.44810.0153-0.01109-0.001043];
H=tf(num,den,'Ts',1);
pzmap(H)
abs(eig(H)')%稳定
ans=
0.87430.15200.27230.23440.1230
4024
clearall
num=[2.1211.7615.91];
den=[1-7.368-20.15102.480.39-340];
z=tf('z');
q=z^-1;
H=tf(num,den,'Ts',1,'Variable','q');
pzmap(H)
abs(eig(H)')%不稳
4031
clearall
A=[-0.20.5000;0-0.51.600;00-14.385.80;000-33.3100;0000-10];
B=[0;0;0;0;30];
C=[00001];D=[0];
G=ss(A,B,C,D)
eig(A)'%稳定
4032
clearall
A=[1724.541815;23.54571416;4613.752022.5889;10.86891.290019.099...
21.8963;1118.0898252.3569];
B=[1;2;3;4;5];
C=[00001];D=[0];
G=ss(A,B,C,D)
abs(eig(A)'%不稳
404
A=[-3121;0-4-2-1;12-11;-1-11-2];
B=[10;02;03;11];
C=[122-1;21-12];
D=zeros(2,2);
G=ss(A,B,C,D);
G1=tf(G)
pzmap(G1)
tzero(G1)
405
s=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')
4061
A=[0111;0001;0100;0011];
B=[10;00;01;10];
C=[1000;0100];
D=zeros(2,2);
Tc=ctrb(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*T
B=inv(T)*B
norm(G)
norm(G,inf)
4062
A=[0200;01-20;0031;1000];
B=[20;12;01;00];
C=[0100;0010];
D=zeros(2,2);
Tc=ctrb(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*T
%B=inv(T)*B
norm(G)
norm(G,inf)
407
A=[0-300;1-400;0000;001-2];
B=[32;12;11;11];
C=[0100;0001];
D=zeros(2,2);
G=ss(A,B,C,D);
G1=minreal(G)
408
f=@(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=[1200];
[t,x]=ode45(f,[0,t_final],x0);
plot(t,x)
409
clearall
num=[1851459823638012266422208818576040320];
den=[1365464536224496728411812410958440320];
[r,p,k]=residue(num,den);
[rp]
[nd]=rat(r);
第五章
502
503
504
505
506
507
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
509
510
512封装
第六章
601
clearall
G=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);
%unsteady
G1=G*Gc;
%G2=leadlagc(G,20,30,1000,3)
%[a2,b2,c2,d2]=margin(G2)
step(G,'-b',G*Gc,'-r')
602
s=tf('s');
G1=zpk([],[0-1-2-8],16);
G2=2*(s+1)/s/(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,'-r',Gc2,'-b')
clearall
G=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);
%unsteady
G1=G*Gc;
%G2=leadlagc(G,20,30,1000,3)
%[a2,b2,c2,d2]=margin(G2)
step(G,'-b',G*Gc,'-r')
603
A=[0100;0010;-3123;2100];B=[10;21;32;43];
Q=diag([1,2,3,4]);R=eye(2,2);
[KP]=lqr(A,B,Q,R);
eig(A-B*K)
I=eye(4,4);D=[00;00;00;00];
G=ss(A,B,I,D)
G1=ss(A-B*K,B,I-D*K,D);
%G1=tf(G);
step(G)
figure;
step(G1)%stablity
604
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=[46;24;22;02];C=[0001;0202];D=[00;00];
Q=diag([1,2,10,4]);R=eye(2,2);
[KP]=lqr(A,B,Q,R);
eig(A-B*K)
I=eye(4,4);D1=[00;00;00;00];
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)%stablity
605
clear
A=[-0.20.5000;0-0.51.600;...
00-14.385.80;000-33.3100;0000-10];
B=[0;0;0;0;30];C=[10000];
D=[0];
P=[-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));
606
clearall
A=[2100;0200;00-10;000-1];
B=[0;1;1;1];
C=[1010];
P=[-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
608
s=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);G1
[K2,L2,T2,G2]=getfolpd(2,Ga);G2
[K3,L3,T3,G3]=getfolpd(3,Ga);G3
[K4,L4,T4,G4]=getfolpd(4,Ga);G4
a=K1*L1/T1;
Kp=1.2/a;Ti=2*L1;Td=0.5*L1;
G11=Kp*(1+tf(1,[Ti,0])+tf([Td0],[Td/N1]));
figure
(1);step(G1,G2,G3,G4,G11)
[K2,L2,T2,G2]=getfolpd(1,Gb);G2;
a=K2*L2/T2;
Kp=1.2/a;Ti=2*L2;Td=0.5*L2;
G21=Kp*(1+tf(1,[Ti,0])+tf([Td0],[Td/N1]));
figure
(2);step(G2,G21)
[K3,L3,T3,G3]=getfolpd(1,Gc);G3;
a=K3*L3/T3;
Kp=1.2/a;Ti=2*L3;Td=0.5*L3;
G32=Kp*(1+tf(1,[Ti,0])+tf([Td0],[Td/N1]));
figure(3);step(G3,G32)
612
614
616
第七章
701
A=[0010;0001;-1.251.2500;1.25-1.2500];
B=[0;0;1;0];C=[2134];D=[0];
G=ss(A,B,C,D);
XI=1.25e-3;theta=2.26e-5;
[Gk,Kf,P]=kalman(G,XI,theta)
704
clearall
s=tf('s');
G=1/((0.01*s+1)^2);w1=10/(s^3+2*s^2+2*s+1);w2=1e-5;w3=(10*s+1)/(20*(0.01*s+1));
stss=augtf(G,w1,w2,w3);
[ab1b2c1c2d11d12d21d22]=branch(stss)
[g1G1]=h2lqg(stss);[abcd]=branch(G1);G1=zpk(ss(a,b,c,d));
%[g,Gc,sca]=hinfopt(stss);
[r,g,G2]=hinfopt(stss);[abcd]=branch(G2);G2=zpk(ss(a,b,c,d));
figure
(1);step(G1,'-r',G2,':
b')
figure
(2);nichols(G1,G2);
figure(3);step(stss)
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