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%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');