%chap10_1.m
%PID Controler
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=0.0;y_2=0.0;y_3=0.0;
x=[0,0,0]';
error_1=0;

for k=1:1:500
time(k)=k*ts;
   
rin(k)=1;                       %Tracing Step Signal
kp=0.50;ki=0.001;kd=0.001;          

u(k)=kp*x(1)+kd*x(2)+ki*x(3);   %PID Controller

%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(k)-yout(k);

%Return of 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);
   
x(1)=error(k);                        %Calculating P
x(2)=(error(k)-error_1)/ts;           %Calculating D
x(3)=x(3)+error(k)*ts;                %Calculating I
xi(k)=x(3);

error_1=error(k);
end
figure(1);
plot(time,rin,'b',time,yout,'r');
xlabel('time(s)');ylabel('rin,yout');