Notes

%% 实验2 闭环控制：PID控制算法（P、PI、PID对比），图中包含稳定值
clear; clc; close all;

%% 参数设置
Ts = 0.001; % 采样时间(s)
T_end = 0.2; % 仿真时间(s)
t = 0:Ts:T_end;
N = length(t);

% 被控对象: G(s)=1/(0.02s+1) 离散化 (一阶保持器)
T_obj = 0.02;
a = exp(-Ts/T_obj); % y(k)=a*y(k-1)+b*u(k-1)
b = 1 - a;

% 设定值: 阶跃信号 (0.02s后从0跳变到1)
r = zeros(1,N);
r(round(0.02/Ts):end) = 1;
steady_value = 1; % 稳定值

%% PID参数
% 组1: 纯比例 P
Kp1 = 1; Ki1 = 0; Kd1 = 0;
% 组2: 比例积分 PI
Kp2 = 1; Ki2 = 20; Kd2 = 0;
% 组3: 比例积分微分 PID
Kp3 = 1; Ki3 = 20; Kd3 = 0.002;

%% 存储变量
y1 = zeros(1,N); u1 = zeros(1,N);
y2 = zeros(1,N); u2 = zeros(1,N);
y3 = zeros(1,N); u3 = zeros(1,N);

%% 递推变量初始化 (各组独立)
% 组1
integ1 = 0; e_prev1 = 0; y_prev1 = 0;
% 组2
integ2 = 0; e_prev2 = 0; y_prev2 = 0;
% 组3
integ3 = 0; e_prev3 = 0; y_prev3 = 0;

%% 主循环 (位置式PID)
for k = 1:N
% ----- 组1: P控制 -----
e1 = r(k) - y_prev1;
integ1 = integ1 + e1 * Ts;
der1 = (e1 - e_prev1) / Ts;
u1(k) = Kp1 * e1 + Ki1 * integ1 + Kd1 * der1;
y1(k) = a * y_prev1 + b * u1(k);
e_prev1 = e1;
y_prev1 = y1(k);

% ----- 组2: PI控制 -----
e2 = r(k) - y_prev2;
integ2 = integ2 + e2 * Ts;
der2 = (e2 - e_prev2) / Ts;
u2(k) = Kp2 * e2 + Ki2 * integ2 + Kd2 * der2;
y2(k) = a * y_prev2 + b * u2(k);
e_prev2 = e2;
y_prev2 = y2(k);

% ----- 组3: PID控制 -----
e3 = r(k) - y_prev3;
integ3 = integ3 + e3 * Ts;
der3 = (e3 - e_prev3) / Ts;
u3(k) = Kp3 * e3 + Ki3 * integ3 + Kd3 * der3;
y3(k) = a * y_prev3 + b * u3(k);
e_prev3 = e3;
y_prev3 = y3(k);
end

%% 绘图: 被控量响应，包含稳定值水平线
figure('Name','闭环控制响应');
plot(t, r, 'k--', 'LineWidth',1.2); hold on;
plot(t, y1, 'b-', 'LineWidth',1);
plot(t, y2, 'g-', 'LineWidth',1);
plot(t, y3, 'r-', 'LineWidth',1);
% 添加稳定值水平线
yline(steady_value, 'k:', 'LineWidth',1.2);
xlabel('时间 (s)'); ylabel('输出 y(t)');
title('不同PID参数下的闭环阶跃响应（稳定值 = 1）');
legend('给定值 r(t)','P (Kp=1)','PI (Kp=1, Ki=20)','PID (Kp=1, Ki=20, Kd=0.002)','稳定值','Location','best');
grid on;

%% 绘图: 控制器输出
figure('Name','控制器输出');
plot(t, u1, 'b-', t, u2, 'g-', t, u3, 'r-', 'LineWidth',1);
xlabel('时间 (s)'); ylabel('控制量 u(t)');
title('控制器输出信号');
legend('P','PI','PID');
grid on;

disp('闭环仿真完成，图中已标注稳定值。');