%PID Controler with intergration sturation
clear all;
close all;

ts=0.001;
sys=tf(5.235e005,[1,87.35,1.047e004,0]);
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;

um=6;
kp=0.85;ki=9.0;kd=0.0;   
rin=30;           %Step Signal

for k=1:1:800
time(k)=k*ts;
   
u(k)=kp*x(1)+kd*x(2)+ki*x(3);   % PID Controller

if u(k)>=um
   u(k)=um;
end
if u(k)<=-um
   u(k)=-um;
end

%Linear model
yout(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;

error(k)=rin-yout(k);

M=2;
if M==1  %Using intergration sturation
if u(k)>=um
   if error(k)>0
      alpha=0;
   else 
      alpha=1;
   end
elseif u(k)<=-um
   if error(k)>0
      alpha=1;
   else 
      alpha=0;
   end
else
   alpha=1;
end

elseif M==2  %Not using intergration sturation
	alpha=1;   
end

%Return of PID parameters
u_3=u_2;u_2=u_1;u_1=u(k);   
y_3=y_2;y_2=y_1;y_1=yout(k);
error_1=error(k);
   
x(1)=error(k);                % Calculating P
x(2)=(error(k)-error_1)/ts;   % Calculating D
x(3)=x(3)+alpha*error(k)*ts;  % Calculating I

xi(k)=x(3);
end
figure(1);
subplot(311);
plot(time,rin,'b',time,yout,'r');
xlabel('time(s)');ylabel('Position tracking');
subplot(312);
plot(time,u,'r');
xlabel('time(s)');ylabel('Controller output');
subplot(313);
plot(time,xi,'r');
xlabel('time(s)');ylabel('Integration');