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%PID Controller with changing integration rate 
clear all; 
close all; 
 
%Big time delay Plant 
ts=20; 
sys=tf([1],[60,1],'inputdelay',80); 
dsys=c2d(sys,ts,'zoh'); 
[num,den]=tfdata(dsys,'v'); 
 
u_1=0;u_2=0;u_3=0;u_4=0;u_5=0; 
y_1=0;y_2=0;y_3=0; 
error_1=0;error_2=0; 
ei=0; 
 
for k=1:1:200 
time(k)=k*ts; 
 
rin(k)=1.0;  %Step Signal 
 
%Linear model 
yout(k)=-den(2)*y_1+num(2)*u_5; 
error(k)=rin(k)-yout(k); 
 
kp=0.45;kd=12;ki=0.0048; 
A=0.4;B=0.6; 
 
%T type integration 
ei=ei+(error(k)+error_1)/2*ts;  
 
M=1; 
if M==1     %Changing integration rate 
if abs(error(k))<=B 
   f(k)=1; 
elseif abs(error(k))>B&abs(error(k))<=A+B 
   f(k)=(A-abs(error(k))+B)/A; 
else 
   f(k)=0; 
end 
 
elseif M==2  %Not changing integration rate 
	f(k)=1; 
end 
 
u(k)=kp*error(k)+kd*(error(k)-error_1)/ts+ki*f(k)*ei; 
 
if u(k)>=10 
   u(k)=10; 
end 
if u(k)<=-10 
   u(k)=-10; 
end 
%Return of PID parameters 
u_5=u_4;u_4=u_3;u_3=u_2;u_2=u_1;u_1=u(k);    
y_3=y_2;y_2=y_1;y_1=yout(k); 
    
error_2=error_1; 
error_1=error(k); 
end 
figure(1); 
plot(time,rin,'b',time,yout,'r'); 
xlabel('time(s)');ylabel('rin,yout'); 
figure(2); 
plot(time,f,'r'); 
xlabel('time(s)');ylabel('Integration rate f');