Example of Designing an Anti-Integral Saturation PID Controller Using MATLAB

First, fill in the transfer function of the device to be controlled, then determine the parameters for PID control, followed by setting the simulation time and sampling interval. Next, use the anti-integral saturation calculation method to determine the integral result of the PID, and then use the PID output to control the forward function, observing the output signal curve of the entire system’s closed-loop function.

G(s)=(s+3)/(s^3+7*s^2+8*s+1.2);
clear all;close all;clc;

% Parameter settings
 timeSample1=0.01;  % Sampling interval
 num1=200.0;
 den1=[1, 35, 160, 0];
 sys1=tf(num1,den1);

% Discrete system
 sysD1=c2d(sys1, timeSample1, 'z');

% Continuous system
 [num2,den2]=tfdata(sysD1,'v');
 inU1=0;  % Delay time 1
 inU2=0;  % Delay time 2
 inU3=0;  % Delay time 3
 outY1=0;  % Delay time 1
 outY2=0;  % Delay time 2
 outY3=0;  % Delay time 3
 x1=[0; 0; 0];
 err1=0;  % Delay time 1
 uMax=10;  % Maximum PID output
 Kp=8.2;  % PID parameter
 Ki=6.0;  % PID parameter
 Kd=0.1;  % PID parameter
 inUsr=36;
 Len=2000;
 time1=zeros(1, Len);
 pidU=zeros(1, Len);
 outVecY=zeros(1, Len);
 VecErr=zeros(1, Len);
 integ1=zeros(1, Len);

 for k1=1:1:Len
    time1(k1)=k1*timeSample1;
    pidU(k1)=Kp*x1(1)+Ki*x1(2)+Kd*x1(3);
    if pidU(k1) > uMax
        pidU(k1) = uMax;
    end
    if pidU(k1) < -uMax
        pidU(k1) = -uMax;
    end
    outVecY(k1)=-den2(2)*outY1-den2(3)*outY2-den2(4)*outY3+...
        num2(2)*inU1+num2(3)*inU2+num2(4)*inU3;
    VecErr(k1)=inUsr-outVecY(k1);
    if pidU(k1) >= uMax
        if VecErr(k1) > 0
            coef1=0;
        else
            coef1=1;
        end
    elseif pidU(k1) <= -uMax
        if VecErr(k1) > 0
            coef1=1;
        else
            coef1=0;
        end
    else
        coef1=1;
    end
    inU3=inU2;
    inU2=inU1;
    inU1=pidU(k1);
    outY3=outY2;
    outY2=outY1;
    outY1=outVecY(k1);
    x1(1)=VecErr(k1);
    x1(2)=x1(2)+coef1*VecErr(k1)*timeSample1;
    x1(3)=(VecErr(k1)-err1)/timeSample1;
    err1=VecErr(k1);
    integ1(k1)=x1(2);
 end

% Plotting results
 figure(1);plot(time1,inUsr*ones(1,Len),'b',time1,outVecY,'r');title('Input and Output');
 figure(2);plot(time1,pidU,'b');title('PID Output');
 figure(3);plot(time1,integ1,'b');title('PID Integral Output');
 disp('Calculation complete');