带死区的PID控制算法及仿真

1.基本概念

在计算机控制系统重，某些系统为了避免控制作用过于频繁，消除由于频繁动作所引起的振荡，可采用带死区的PID控制算法：

err(k) 为位置跟踪偏差，err0为可调参数，其具体数值可根据实际控制对象由实验确定。若err0太小，会使动作更新过于频繁，达不到稳定被控对象的目的；若err0值太大，则系统则会产生较大滞后。

带死区的PID控制实际上是一个非线性系统，在死区范围内，控制器输出为零；在死区外，控制器有输出。

2.仿真程序

clear all;
close all;

ts = 0.01;
sys = tf(5.235e005,[1, 87.35, 1.047e4, 0]);
dsys = c2d(sys, ts, 'z');
[num, den] = tfdata(dsys, 'v');

u_1 = 0;
u_2 = 0;
u_3 = 0;
u_4 = 0;
u_5 = 0;

y_1 = 0;
y_2 = 0;
y_3 = 0;
yn_1 = 0;

error_1 = 0;
errpr_2 = 0;
ei = 0;

sys1 = tf(1, [0.04, 1]); %low freq signal  filter
dsys1 = c2d(sys1, ts, 'tusion');
[num1, den1] = tfdata(dsys1, 'v');
f_1 = 0;


for k = 1:2000
    time(k) = k*ts;

    yd(k) = 1; % step signal

    %linear model
    y(k) = -den(2)*y_1 - den(3)*y_2 - den(4)*y_3 + num(2)*u_1 + num(3)*u_2 + num(4)*u_3;

    n(k) = 0.5*rands(1); % noisy signal
    yn(k) = y(k) + n(k);

    % low freq filter
    filty(k) = -den1(2)*f_1 + num1(1)*(yn(k) + yn_1);
    error(k) = yd(k) - filty(k);
    
    if abs(error(k)) <= 0.2
        ei = ei + error(k)*ts;
    else
        ei = 0;
    end

    kp = 0.5;
    ki = 0.1;
    kd = 0.02;

    u(k) = kp*error(k) + ki*ei + kd*(error(k) - error_1)/ts;

    if abs(error(k)) <= 0.0
        u(k) = 0;
    end

    if u(k) >= 10
        u(k) = 10;
    elseif u(k) <= -10
        u(k) = -10;
    end

    yd_1 = yd(k);

    u_3 = u_2;
    u_2 = u_1;
    u_1 = u(k);

    y_3 = y_2;
    y_2 = y_1;
    y_1 = y(k);

    f_1 = filty(k);
    yn_1 = yn(k);

    error_2 = error_1;
    error_1 = error(k);
end

figure(1);
subplot(2,1,1);
plot(time, yd, 'r', time, y, 'k:', 'LineWidth', 2);
xlabel('time(s)');
ylabel('yd,y');
legend('ideal position signal', 'position tracking');
subplot(2,1,2);
plot(time, u, 'r', 'LineWidth', 2);
xlabel('time(s');
ylabel('control input');

figure(2);
plot(time, n, 'r', 'LineWidth', 2);
xlabel('time(s)');
ylabel('noisy signal');

如果取消死区，pid给定为：

给定死区范围0.2，输出波动明显减少：