%Increment PID Controller
clear all;
close all;

ts=0.001;
sys=tf(400,[1,50,0]);
dsys=c2d(sys,ts,'z');
[num,den]=tfdata(dsys,'v');

u_1=0.0;u_2=0.0;u_3=0.0;
y_1=0;y_2=0;y_3=0;

x=[0,0,0]';

error_1=0;
error_2=0;
for k=1:1:1000
   time(k)=k*ts;
   
   rin(k)=1.0;
   kp=8;
   ki=0.10;
   kd=10;
   
   du(k)=kp*x(1)+kd*x(2)+ki*x(3); 
   u(k)=u_1+du(k);

   if u(k)>=10
      u(k)=10;
   end
   if u(k)<=-10
      u(k)=-10;
   end   
   yout(k)=-den(2)*y_1-den(3)*y_2+num(2)*u_1+num(3)*u_2;
   
   error=rin(k)-yout(k);
   u_3=u_2;u_2=u_1;u_1=u(k);
   y_3=y_2;y_2=y_1;y_1=yout(k);
   
   x(1)=error-error_1;             %Calculating P
   x(2)=error-2*error_1+error_2;   %Calculating D
   x(3)=error;                     %Calculating I
   
   error_2=error_1;
   error_1=error;
end
plot(time,rin,'b',time,yout,'r');
xlabel('time(s)');ylabel('rin,yout');