%PID Controller with Partial differential
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;u_2=0;u_3=0;u_4=0;u_5=0;
y_1=0;y_2=0;y_3=0;

kp=0.12;ki=0.015;
x=[0,0];
for k=1:1:3000
time(k)=k*ts;
rin(k)=20;  %Step Signal

%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;
     
D(k)=0.50*rands(1);  %Disturbance signal
yyout(k)=yout(k)+D(k);

M=1;
if M==1             %No filter
   filty(k)=yyout(k);
elseif M==2         %Using filter with tracker and differentiation
r=2000;
h=0.02;
T=ts;

delta=r*h; 
delta0=delta*h; 
y=x(1)-yyout(k)+h*x(2);
a0=sqrt(delta*delta+8*r*abs(y));
if abs(y)<=delta0
    a=x(2)+y/h;
else
    a=x(2)+0.5*(a0-delta)*sign(y);
end
if abs(a)<=delta
   fst2=-r*a/delta;
else
   fst2=-r*sign(a);
end
     
x(1)=x(1)+T*x(2);
x(2)=x(2)+T*fst2;
filty(k)=x(1);
end

error(k)=rin(k)-filty(k);
%I separation
if abs(error(k))<=0.8
   ei=ei+error(k)*ts;
else
   ei=0;
end
   u(k)=kp*error(k)+ki*ei;

if u(k)>=10       % Restricting the output of controller
   u(k)=10;
end
if u(k)<=-10
   u(k)=-10;
end
%----------Return of PID parameters------------
rin_1=rin(k);
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);
end
figure(1);
subplot(211);
plot(time,rin,'b',time,filty,'r');
xlabel('time(s)');ylabel('rin,yout');
subplot(212);
plot(time,u,'r');
xlabel('time(s)');ylabel('u');

figure(2);
plot(time,D,'r');
xlabel('time(s)');ylabel('Disturbance signal');

figure(3);
plot(time,yyout,'r',time,filty,'b');
xlabel('time(s)');ylabel('ideal signal,practical signal');