matlab 中带迟延环节的开环传递函数来获得其闭环传递函数

采用PADE函数,有理函数来近似

%PID 带滞后的传递函数,not use feedback,but pade

%将迟延环节表示成一个多项式,有理函数来近似

% 传递函数为G（s）=2*e^(-0.5s)/(2s+1),

clc

clear all

close all

num=[0 2];

den=[2 1];

delay=0.5;

%T为延迟时间常数，n为要求拟合的阶数

[n2,d2]=pade(delay,2)

num2=conv(num,n2);

den2=conv(den,d2);

disp('object tranfer function')

G_obj=tf(num2,den2)%object transfer function

Kp=2;Ti=2;Td=0;%由对象模型求出理想PID

%PID tranfer function

disp('PID tranfer function')

G_PID=tf(Kp*[Ti*Td,Ti,1]/Ti,[1,0])

%Close tranfer function

G=feedback(G_PID*G_obj,1);

figure;

grid on;

hold on

step(G,'g')

xlabel('t');

ylabel('y');

%axis([0,12,0,1.3]);

grid on;

%error

hold off;

[y,t]=step(G);

error=1-y;

figure

plot(t,error)

xlabel('t');

ylabel('error');

grid on