P、PI、PD和PID控制器MATLAB实现及响应曲线

本文介绍P、PI、PD和PID控制器在MATLAB中的实现方法，并使用阶跃响应绘制了各控制器的控制曲线，方便理解不同控制器的特性。

1. P控制器程序

Kp = 1;

num = 1;
den = [1, 1.97, 2];
G = tf(num, den);

C = tf(Kp, 1);

T = feedback(C*G, 1);

t = 0:0.01:10;

u = ones(size(t));

[y, ~] = lsim(T, u, t);

figure;
plot(t, y);
title('P Control Response');
xlabel('Time');
ylabel('Output');

2. PI控制器程序

Kp = 1;
Ki = 1;

num = 1;
den = [1, 1.97, 2];
G = tf(num, den);

C = tf([Kp, Ki], [1, 0]);

T = feedback(C*G, 1);

t = 0:0.01:10;

u = ones(size(t));

[y, ~] = lsim(T, u, t);

figure;
plot(t, y);
title('PI Control Response');
xlabel('Time');
ylabel('Output');

3. PD控制器程序

Kp = 1;
Kd = 1;

num = 1;
den = [1, 1.97, 2];
G = tf(num, den);

C = tf([Kd, Kp], 1);

T = feedback(C*G, 1);

t = 0:0.01:10;

u = ones(size(t));

[y, ~] = lsim(T, u, t);

figure;
plot(t, y);
title('PD Control Response');
xlabel('Time');
ylabel('Output');

4. PID控制器程序

Kp = 1;
Ki = 1;
Kd = 1;

num = 1;
den = [1, 1.97, 2];
G = tf(num, den);

C = tf([Kd, Kp, Ki], [1, 0]);

T = feedback(C*G, 1);

t = 0:0.01:10;

u = ones(size(t));

[y, ~] = lsim(T, u, t);

figure;
plot(t, y);
title('PID Control Response');
xlabel('Time');
ylabel('Output');

通过运行以上程序，可以得到P、PI、PD和PID控制的控制曲线，并直观地比较它们之间的区别。