%PID Controller
%挖掘機動臂控制系統的數字PID設計
clear all;
close all;
ts=0.001;
sys=tf(1,[6.312e-011 3.729e-008 1.948e-005 0.003495 1 0]);
dsys=c2d(sys,ts,'z');
[num,den]=tfdata(dsys,'v');
u_1=0.0;u_2=0.0;u_3=0.0;u_4=0;u_5=0;
y_1=0.0;y_2=0.0;y_3=0.0;y_4=0;y_5=0;
x=[0,0,0]';
error_1=0;
for k=1:1:1000
time(k)=k*ts;
S=1;
if S==1
    kp=15;ki=0.15;kd=0;          
    rin(k)=1;                       %Step Signal
elseif S==2
    kp=60;ki=0.1;kd=0;          
    rin(k)=sign(sin(2*2*pi*k*ts));  %Square Wave Signal
elseif S==3
    kp=70;ki=0.35;kd=0;          %Sine Signal
    rin(k)=0.5*sin(2*2*pi*k*ts);           
end
u(k)=kp*x(1)+kd*x(2)+ki*x(3);   %PID Controller
%Restricting the output of controller
if u(k)>=10       
   u(k)=10;
end
if u(k)<=-10
   u(k)=-10;
end
%Linear model
yout(k)=-den(2)*y_1-den(3)*y_2-den(4)*y_3-den(5)*y_4-den(6)*y_5+num(2)*u_1+num(3)*u_2+num(4)*u_3+num(5)*u_4+num(6)*u_5;
error(k)=rin(k)-yout(k);
%Return of parameters
u_5=u_4;u_4=u_3;u_3=u_2;u_2=u_1;u_1=u(k);
y_5=y_4;y_4=y_3;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
error_1=error(k);
end
if S==1
figure(1);
plot(time,rin,'b',time,yout,'r');
xlabel('time(s)'),ylabel('rin,yout');
title('單位階躍響應曲線')
grid on
elseif S==2
figure(2);
plot(time,rin,'b',time,yout,'r');
xlabel('time(s)'),ylabel('rin,yout');
title('正弦跟蹤曲線')
grid on   
elseif S==3
figure(3);
plot(time,rin,'b',time,yout,'r');
xlabel('time(s)'),ylabel('rin,yout');
title('正弦跟蹤曲線')
grid on 
end