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%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; 
r_1=rand; 
y_1=0;y_2=0;y_3=0; 
 
x=[0,0,0]'; 
error_1=0; 
 
for k=1:1:3000 
time(k)=k*ts; 
 
kp=1.0;ki=2.0;kd=0.01; 
    
S=3;    
if S==1   %Triangle Signal 
   if mod(time(k),2)<1      
	   rin(k)=mod(time(k),1); 
	else 
	   rin(k)=1-mod(time(k),1); 
	end 
	   rin(k)=rin(k)-0.5; 
end 
if S==2   %Sawtooth Signal 
   rin(k)=mod(time(k),1.0); 
end 
if S==3   %Random Signal 
	rin(k)=rand;   
	vr(k)=(rin(k)-r_1)/ts;  %Max speed is 5.0 
	while abs(vr(k))>=5.0 
   	rin(k)=rand;   
		vr(k)=abs((rin(k)-r_1)/ts); 
	end 
end 
 
u(k)=kp*x(1)+kd*x(2)+ki*x(3);   %PID Controller 
 
%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(2)*u_1+num(3)*u_2+num(4)*u_3; 
error(k)=rin(k)-yout(k); 
 
r_1=rin(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(k);                %Calculating P 
x(2)=(error(k)-error_1)/ts;   %Calculating D 
x(3)=x(3)+error(k)*ts;        %Calculating I 
xi(k)=x(3); 
 
error_1=error(k); 
D=0; 
if D==1  %Dynamic Simulation Display 
	plot(time,rin,'b',time,yout,'r'); 
	pause(0.00000000000000000); 
end 
end 
plot(time,rin,'r',time,yout,'b'); 
xlabel('time(s)');ylabel('rin,yout');