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%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');