%Expert PID Controller
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;y_2=0;y_3=0;

x=[0,0,0]';
x2_1=0;

kp=0.6;
ki=0.03;     
kd=0.01;

error_1=0;
for k=1:1:500
time(k)=k*ts;
   
rin(k)=1.0;                   %Tracing Jieyue Signal

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

%Expert control rule
if abs(x(1))>0.8      %Rule1:Unclosed control firstly
   u(k)=0.45;
elseif abs(x(1))>0.40        
   u(k)=0.40;
elseif abs(x(1))>0.20    
   u(k)=0.12; 
elseif abs(x(1))>0.01 
   u(k)=0.10;   
end   

if x(1)*x(2)>0|(x(2)==0)       %Rule2
   if abs(x(1))>=0.05
      u(k)=u_1+2*kp*x(1);
   else
      u(k)=u_1+0.4*kp*x(1);
   end
end
                                                                                                                                                                                                                                                                                                                                                                                                              
if (x(1)*x(2)<0&x(2)*x2_1>0)|(x(1)==0)   %Rule3
    u(k)=u(k);
end

if x(1)*x(2)<0&x(2)*x2_1<0   %Rule4
   if abs(x(1))>=0.05
      u(k)=u_1+2*kp*error_1;
   else
      u(k)=u_1+0.6*kp*error_1;
   end
end

if abs(x(1))<=0.001   %Rule5:Integration separation PI control
   u(k)=0.5*x(1)+0.010*x(3);
end

%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+num(1)*u(k)+num(2)*u_1+num(3)*u_2+num(4)*u_3;
error(k)=rin(k)-yout(k);

%----------Return of PID 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
x2_1=x(2);
x(2)=(error(k)-error_1)/ts;   % Calculating D
x(3)=x(3)+error(k)*ts;        % Calculating I

error_1=error(k);
end
figure(1);
plot(time,rin,'b',time,yout,'r');
xlabel('time(s)');ylabel('rin,yout');
figure(2);
plot(time,rin-yout,'r');
xlabel('time(s)');ylabel('error');