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%BP based PID Control 
clear all; 
close all; 
 
xite=0.25; 
alfa=0.05; 
 
S=1; %Signal type 
 
IN=4;H=5;Out=3;  %NN Structure 
if S==1  %Step Signal 
wi=[-0.6394   -0.2696   -0.3756   -0.7023; 
    -0.8603   -0.2013   -0.5024   -0.2596; 
    -1.0749    0.5543   -1.6820   -0.5437; 
    -0.3625   -0.0724   -0.6463   -0.2859; 
     0.1425    0.0279   -0.5406   -0.7660]; 
%wi=0.50*rands(H,IN); 
wi_1=wi;wi_2=wi;wi_3=wi; 
wo=[0.7576 0.2616 0.5820 -0.1416 -0.1325; 
   -0.1146 0.2949 0.8352  0.2205  0.4508; 
    0.7201 0.4566 0.7672  0.4962  0.3632]; 
%wo=0.50*rands(Out,H); 
wo_1=wo;wo_2=wo;wo_3=wo; 
end 
 
if S==2  %Sine Signal 
wi=[-0.2846    0.2193   -0.5097   -1.0668; 
    -0.7484   -0.1210   -0.4708    0.0988; 
    -0.7176    0.8297   -1.6000    0.2049; 
    -0.0858    0.1925   -0.6346    0.0347; 
     0.4358    0.2369   -0.4564   -0.1324]; 
%wi=0.50*rands(H,IN); 
wi_1=wi;wi_2=wi;wi_3=wi; 
wo=[1.0438    0.5478    0.8682    0.1446    0.1537; 
    0.1716    0.5811    1.1214    0.5067    0.7370; 
    1.0063    0.7428    1.0534    0.7824    0.6494]; 
%wo=0.50*rands(Out,H); 
wo_1=wo;wo_2=wo;wo_3=wo; 
end 
 
x=[0,0,0]; 
u_1=0;u_2=0;u_3=0;u_4=0;u_5=0; 
y_1=0;y_2=0;y_3=0; 
 
Oh=zeros(H,1);    %Output from NN middle layer 
I=Oh;             %Input to NN middle layer 
error_2=0; 
error_1=0; 
 
ts=0.001; 
for k=1:1:6000 
time(k)=k*ts; 
 
if S==1 
   rin(k)=1.0; 
elseif S==2 
   rin(k)=sin(1*2*pi*k*ts); 
end 
 
%Unlinear model 
a(k)=1.2*(1-0.8*exp(-0.1*k)); 
yout(k)=a(k)*y_1/(1+y_1^2)+u_1; 
 
error(k)=rin(k)-yout(k); 
 
xi=[rin(k),yout(k),error(k),1]; 
 
x(1)=error(k)-error_1; 
x(2)=error(k); 
x(3)=error(k)-2*error_1+error_2; 
 
epid=[x(1);x(2);x(3)]; 
I=xi*wi'; 
for j=1:1:H 
    Oh(j)=(exp(I(j))-exp(-I(j)))/(exp(I(j))+exp(-I(j))); %Middle Layer 
end 
K=wo*Oh;             %Output Layer 
for l=1:1:Out 
    K(l)=exp(K(l))/(exp(K(l))+exp(-K(l)));        %Getting kp,ki,kd 
end 
kp(k)=K(1);ki(k)=K(2);kd(k)=K(3); 
Kpid=[kp(k),ki(k),kd(k)]; 
 
du(k)=Kpid*epid; 
u(k)=u_1+du(k); 
if u(k)>=10       % Restricting the output of controller 
   u(k)=10; 
end 
if u(k)<=-10 
   u(k)=-10; 
end 
 
dyu(k)=sign((yout(k)-y_1)/(u(k)-u_1+0.0000001)); 
 
%Output layer 
for j=1:1:Out 
    dK(j)=2/(exp(K(j))+exp(-K(j)))^2; 
end 
for l=1:1:Out 
    delta3(l)=error(k)*dyu(k)*epid(l)*dK(l); 
end 
 
for l=1:1:Out 
   for i=1:1:H 
       d_wo=xite*delta3(l)*Oh(i)+alfa*(wo_1-wo_2); 
   end 
end 
    wo=wo_1+d_wo+alfa*(wo_1-wo_2); 
%Hidden layer 
for i=1:1:H 
    dO(i)=4/(exp(I(i))+exp(-I(i)))^2; 
end 
    segma=delta3*wo; 
for i=1:1:H 
   delta2(i)=dO(i)*segma(i); 
end 
 
d_wi=xite*delta2'*xi; 
wi=wi_1+d_wi+alfa*(wi_1-wi_2); 
 
%Parameters Update 
u_5=u_4;u_4=u_3;u_3=u_2;u_2=u_1;u_1=u(k);    
y_2=y_1;y_1=yout(k); 
    
wo_3=wo_2; 
wo_2=wo_1; 
wo_1=wo; 
    
wi_3=wi_2; 
wi_2=wi_1; 
wi_1=wi; 
 
error_2=error_1; 
error_1=error(k); 
end 
figure(1); 
plot(time,rin,'r',time,yout,'b'); 
xlabel('time(s)');ylabel('rin,yout'); 
figure(2); 
plot(time,error,'r'); 
xlabel('time(s)');ylabel('error'); 
figure(3); 
plot(time,u,'r'); 
xlabel('time(s)');ylabel('u'); 
figure(4); 
subplot(311); 
plot(time,kp,'r'); 
xlabel('time(s)');ylabel('kp'); 
subplot(312); 
plot(time,ki,'g'); 
xlabel('time(s)');ylabel('ki'); 
subplot(313); 
plot(time,kd,'b'); 
xlabel('time(s)');ylabel('kd');