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%Increment PID Controller 
clear all; 
close all; 
 
ts=0.001; 
sys=tf(400,[1,50,0]); 
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]'; 
 
error_1=0; 
error_2=0; 
for k=1:1:1000 
   time(k)=k*ts; 
    
   rin(k)=1.0; 
   kp=8; 
   ki=0.10; 
   kd=10; 
    
   du(k)=kp*x(1)+kd*x(2)+ki*x(3);  
   u(k)=u_1+du(k); 
 
   if u(k)>=10 
      u(k)=10; 
   end 
   if u(k)<=-10 
      u(k)=-10; 
   end    
   yout(k)=-den(2)*y_1-den(3)*y_2+num(2)*u_1+num(3)*u_2; 
    
   error=rin(k)-yout(k); 
   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-error_1;             %Calculating P 
   x(2)=error-2*error_1+error_2;   %Calculating D 
   x(3)=error;                     %Calculating I 
    
   error_2=error_1; 
   error_1=error; 
end 
plot(time,rin,'b',time,yout,'r'); 
xlabel('time(s)');ylabel('rin,yout');