!控制系统计算机辅助设计课后题部分答案

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=[1 10 32 32];num=[6 4 2 2];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=[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))/q^5/(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=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/(q-1);H=1/(0.5*q-1);feedb ack(Go*Gc,H)

>> G1=ss(G)

>> G2=zpk(G)

7.3 syms Km J B Kr Lq Rq Kv s

>> 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=[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,'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=[g11 g12;g21 g22]; Gc=[-10 77.5;0 50]; 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

clear all

syms G1 G2 G3 G4 G5 G6 H1 H2 H3 H4

G23=feedback(G2*G3,H2);

G45=feedback(G4*G5,H3);

G7=feedback(G23*G45,H4/G2/G5);

G=feedback(G1*G7*G6,H1)

14

clear all

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 -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];

>> 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

4011

clear all

num=[1];den=[1 2 1 2];G=tf(num,den);

pzmap(G)