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 = 1:2000time(k) = k*ts;yd(k) = 1; % step signal%linear modely(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 signalyn(k) = y(k) + n(k);% low freq filterfilty(k) = -den1(2)*f_1 + num1(1)*(yn(k) + yn_1);error(k) = yd(k) - filty(k);if abs(error(k)) <= 0.2ei = ei + error(k)*ts;elseei = 0;endkp = 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)) <= 0.0u(k) = 0;endif u(k) >= 10u(k) = 10;elseif u(k) <= -10u(k) = -10;endyd_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);
endfigure(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：
