%BP based PID Control 
clear all;
close all;
xite=0.25;   %學習速率
alfa=0.05    %慣性系數;
S=1; %Signal type
IN=4;H=5;Out=3;  %NN Structure 定義網絡結構輸入層為4層，隱含層為5層，輸出層為3層
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');