控制系统仿真与CAD-实验报告

(a) >> s=tf('s');G=(s+6)*(s-6)/(s*(s+3)*(s+4-4j)*(s+4+4j));rlocus(G),grid

不存在K使得系统稳定。

(b) >> G=tf([1,2,2],[1 1 14 8 0]);rlocus(G),grid

放大根轨迹图像，可以看到，根轨迹与虚轴交点处，K值为5.53，因此，0

时，系统稳定。 15.

pade_app.m

function Gr=pade_app(c,r,k)

w=-c(r+2:r+k+1)';vv=[c(r+1:-1:1)';zeros(k-1-r,1)];

W=rot90(hankel(c(r+k:-1:r+1),vv));V=rot90(hankel(c(r:-1:1))); x=[1 (W\\w)'];dred=x(k+1:-1:1)/x(k+1);

y=[c(1) x(2:r+1)*V'+c(2:r+1)];nred=y(r+1:-1:1)/x(k+1); Gr=tf(nred,dred); paderm.m

function [n,d]=paderm(tau,r,k)

c(1)=1;for i=2:r+k+1,c(i)=-c(i-1)*tau/(i-1);end

Gr=pade_app(c,r,k);n=Gr.num{1}(k-r+1:end);d=Gr.den{1};

>> tau=2;[n,d]=paderm(tau,1,3);s=tf('s');G=tf(n,d)*(s-1)/(s+1)^5,rlocus(G)

G =

-1.5 s^2 + 4.5 s - 3

---------------------------------------------------------------------------

s^8 + 8 s^7 + 29.5 s^6 + 65.5 s^5 + 95 s^4 + 91 s^3 + 55.5 s^2 + 19.5 s + 3 Continuous-time transfer function.

由图得0

(a)>>s=tf('s');G=8*(s+1)/(s^2*(s+15)*(s^2+6*s+10));bode(G),figure,nyquist(G),figure,nichols(G),[Gm,y,wcg,wcp]=margin(G),figure,step(feedback(G,1))

Gm =

30.4686 y =

4.2340 wcg =

1.5811 wcp =

0.2336

系统稳定。

(b)>>z=tf('z');G=0.45*(z+1.31)*(z+0.054)*(z-0.957)/(z*(z-1)*(z-0.368)*(z-0.99));bode(G),figure,nyquist(G),figure,nichols(G),[Gm,y,wcg,wcp]=margin(G),figure,step(feedback(G,1))

Warning: The closed-loop system is unstable. > In warning at 26

In DynamicSystem.margin at 63 Gm =

0.9578 y =

-1.7660 wcg =

1.0464 wcp =

1.0734