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%PID Controller for coupling plant 
clear all; 
close all; 
 
u1_1=0.0;u1_2=0.0;u1_3=0.0;u1_4=0.0; 
u2_1=0.0;u2_2=0.0;u2_3=0.0;u2_4=0.0; 
 
y1_1=0;y2_1=0; 
 
x1=[0;0];x2=[0;0];x3=[0;0]; 
 
kp=0.020; 
ki=0.050; 
kd=0.0001; 
 
error_1=[0;0]; 
ts=1; 
for k=1:1:1500 
time(k)=k*ts; 
 
%Step Signal 
R=[1;0]; 
%R=[0;1]; 
 
%PID Decouple Controller 
u1(k)=kp*x1(1)+kd*x2(1)+ki*x3(1);    
u2(k)=kp*x1(2)+kd*x2(2)+ki*x3(2);    
u=[u1(k),u2(k)]; 
 
if u1(k)>=10 
   u1(k)=10; 
end 
if u2(k)>=10 
   u2(k)=10; 
end 
if u1(k)<=-10 
   u1(k)=-10; 
end 
if u2(k)<=-10 
   u2(k)=-10; 
end 
 
%Coupling Plant 
yout1(k)=1.0/(1+y1_1)^2*(0.8*y1_1+u1_2+0.2*u2_3); 
yout2(k)=1.0/(1+y2_1)^2*(0.9*y2_1+0.3*u1_3+u2_2); 
 
error1(k)=R(1)-yout1(k); 
error2(k)=R(2)-yout2(k); 
error=[error1(k);error2(k)]; 
 
%-----------Return of PID parameters------------% 
u1_4=u1_3;u1_3=u1_2;u1_2=u1_1;u1_1=u(1); 
 
u2_4=u2_3;u2_3=u2_2;u2_2=u2_1;u2_1=u(2); 
 
y1_1=yout1(k);y2_1=yout2(k); 
 
x1=error;                %Calculating P 
x2=(error-error_1)/ts;   %Calculating D 
x3=x3+error*ts;          %Calculating I 
 
error_1=error; 
end 
hold on; 
plot(time,R(1),'b',time,yout1,'r'); 
plot(time,R(2),'r',time,yout2,'b'); 
xlabel('time(s)');ylabel('rin,yout');