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%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=1; 
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');