%基于BP神經網絡的PID控制
clear all; 
close all; 
xite=0.25; 
alfa=0.05; 
S=2; %信號類型
IN=4;H=5;Out=3;  %神經網絡結構
if S==1  %階躍信號
   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  %正弦信號
   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);    %神經網絡中間層輸出 
I=Oh;             %神經網絡中間層輸入
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 
   %非線性模型
   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))); %中間層
   end 
   K=wo*Oh;             %輸出層 
   for l=1:1:Out 
       K(l)=exp(K(l))/(exp(K(l))+exp(-K(l)));        %求kp,ti,td 
   end 
   kp(k)=K(1);ti(k)=K(2);td(k)=K(3); 
   Kpid=[kp(k),ti(k),td(k)]; 
    du(k)=Kpid*epid; 
   u(k)=u_1+du(k); 
   if u(k)>=10       % 限制控制器輸出
       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)); 
   %輸出層
   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); 
   %隱含層 
   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); 
    %參數更新
   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('時間（秒）');ylabel('系統輸入、輸出'); 
figure(2); 
plot(time,error,'r'); 
xlabel('時間（秒）');ylabel('誤差'); 
figure(3); 
subplot(311);
plot(time,kp,'r'); 
xlabel('時間（秒）');ylabel('參數kp'); 
subplot(312); 
plot(time,ti,'g'); 
xlabel('時間（秒）');ylabel('參數ti'); 
subplot(313); 
plot(time,td,'b'); 
xlabel('時間（秒）');ylabel('參數td');