ex4_25.m

华东理工大学自动化系《控制系统分析、设计和应用》教材配套程序实例,有关说明： 1. 安装MATLAB软件。安装时

% ex4_25
% 非线性系统的稳定性分析
figure('pos',[50,50,400,200],'color','w');
axes('pos',[0.12,0.14,0.35,0.75]);
num=[50];
den=conv([1  5  0],[1  1]);
G=tf(num,den);
k2=0.5;
k1=1;
h=2;
em=[2:0.3:200]; 
d=h./em;
n=k2+2*k2*(k1/k2-1)*(asin(d)+d.*sqrt(1-d.^2))/pi;
w=logspace(-3,1,500);
[ir,ii]=nyquist(inv(G),w);
ri(1,:)=ir(1,:);
mi(1,:)=ii(1,:);
plot(ri,mi);
axis([-1 0 -0.1 .1]);
hold on;
plot(-n,zeros(size(n))),
grid  
axes('pos',[0.62,0.14,0.35,0.75]);
a=compan(den);
b=zeros(length(a),1);
b(1,1)=1;
c=[zeros(1,length(a)-length(num)) num];
d=0;
ts=0.006;
[phi,del]=c2d(a,b,ts); 
tend=16; 
points=round(tend/ts)-1; 
yold=14;
ystor(1)=yold;
xold=[0  0  yold/50]';
t=zeros(size(ystor)); 
for i = 1:points+1
   t(i+1)=t(i)+ts;
   err=-yold; 
   u=err*k1*(abs(err)<=h)+sign(err)*(k1*h+k2*(abs(err)-h))*(abs(err)>h);
   xnew=phi*xold+del*u;yold=c*xnew+d*u;
   ystor(i+1)=yold;
   xold=xnew;
end
plot(t,ystor);
grid