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%Integration Separation PID Controller 
clear all; 
close all; 
 
ts=20; 
%Delay plant 
sys=tf([1],[60,1],'inputdelay',80); 
dsys=c2d(sys,ts,'zoh'); 
[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; 
error_1=0;error_2=0; 
ei=0; 
for k=1:1:200 
time(k)=k*ts; 
 
%Delay plant 
yout(k)=-den(2)*y_1+num(2)*u_5; 
 
%I separation 
rin(k)=40; 
error(k)=rin(k)-yout(k); 
ei=ei+error(k)*ts; 
 
M=1; 
if M==1            %Using integration separation 
   if abs(error(k))>=30&abs(error(k))<=40 
      beta=0.3; 
   elseif abs(error(k))>=20&abs(error(k))<=30 
      beta=0.6; 
   elseif abs(error(k))>=10&abs(error(k))<=20 
      beta=0.9; 
   else 
      beta=1.0; 
   end 
elseif M==2 
       beta=1.0;   %Not using integration separation 
end 
 
kp=0.80; 
ki=0.005; 
kd=3.0; 
u(k)=kp*error(k)+kd*(error(k)-error_1)/ts+beta*ki*ei; 
 
if u(k)>=110       % Restricting the output of controller 
   u(k)=110; 
end 
if u(k)<=-110 
   u(k)=-110; 
end 
 
u_5=u_4;u_4=u_3;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_2=error_1; 
error_1=error(k); 
end 
figure(1); 
plot(time,rin,'b',time,yout,'r'); 
xlabel('time(s)');ylabel('rin,yout'); 
figure(2); 
plot(time,u,'r'); 
xlabel('time(s)');ylabel('u');