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%Adaptive PID control based on RBF Identification 
clear all; 
close all; 
 
xite=0.25; 
alfa=0.05; 
belte=0.01; 
x=[0,0,0]'; 
 
ci=30*ones(3,6); 
bi=40*ones(6,1); 
w=10*ones(6,1);  
 
h=[0,0,0,0,0,0]'; 
     
ci_1=ci;ci_3=ci_1;ci_2=ci_1; 
bi_1=bi;bi_2=bi_1;bi_3=bi_2; 
w_1=w;w_2=w_1;w_3=w_1; 
 
u_1=0;y_1=0; 
xc=[0,0,0]'; 
error_1=0;error_2=0;error=0; 
 
%kp=rand(1);         
%ki=rand(1);      
%kd=rand(1); 
kp=0.03;         
ki=0.01;      
kd=0.03; 
 
kp_1=kp; 
kd_1=kd; 
ki_1=ki;   
 
xitekp=0.20; 
xitekd=0.20; 
xiteki=0.20; 
 
ts=0.001; 
for k=1:1:2000 
   time(k)=k*ts; 
   rin(k)=1.0*sign(sin(2*pi*k*ts)); 
   yout(k)=(-0.1*y_1+u_1)/(1+y_1^2);  %Nonlinear plant 
 
   for j=1:1:6 
      h(j)=exp(-norm(x-ci_1(:,j))^2/(2*bi_1(j)*bi_1(j))); 
   end 
 
   ymout(k)=w_1'*h;          
 
   d_w=0*w;      % Defining matrix number of d_w equal to that of w 
   for j=1:1:6 
      d_w(j)=xite*(yout(k)-ymout(k))*h(j); 
   end 
   w=w_1+d_w+alfa*(w_1-w_2)+belte*(w_2-w_3); 
    
   d_bi=0*bi; 
   for j=1:1:6 
      d_bi(j)=xite*(yout(k)-ymout(k))*w_1(j)*h(j)*(bi_1(j)^-3)*norm(x-ci_1(:,j))^2; 
   end 
   bi=bi_1+ d_bi+alfa*(bi_1-bi_2)+belte*(bi_2-bi_3); 
   for j=1:1:6 
     for i=1:1:3 
      d_ci(i,j)=xite*(yout(k)-ymout(k))*w_1(j)*h(j)*(x(i)-ci_1(i,j))*(bi_1(j)^-2); 
     end 
   end 
   ci=ci_1+d_ci+alfa*(ci_1-ci_2)+belte*(ci_2-ci_3); 
   
%%%%%%%%%%%%%%%%%%%%%%Jacobian%%%%%%%%%%%%%%%%%%%%%%% 
  yu=0; 
  for  j=1:1:6 
      yu=yu+w(j)*h(j)*(-x(1)+ci(1,j))/bi(j)^2;  
  end 
  dyout(k)=yu; 
%%%%%%%%%%%%%%%%%%%%%%Start of Control system%%%%%%%%%%%%%%%%%% 
   error(k)=rin(k)-yout(k); 
   kp(k)=kp_1+xitekp*error(k)*dyout(k)*xc(1); 
   kd(k)=kd_1+xitekd*error(k)*dyout(k)*xc(2); 
   ki(k)=ki_1+xiteki*error(k)*dyout(k)*xc(3);   
   if kp(k)<0 
      kp(k)=0; 
   end 
   if kd(k)<0 
      kd(k)=0; 
   end 
   if ki(k)<0 
      ki(k)=0; 
   end 
    
   M=1; 
   if M==2  %Only PID Control 
		kp(k)=0.03;         
		ki(k)=0.01;      
		kd(k)=0.03; 
	end 
   u(k)=u_1+kp(k)*xc(1)+kd(k)*xc(2)+ki(k)*xc(3);  
 
   if u(k)>=10 
      u(k)=10; 
   end 
   if u(k)<=-10 
      u(k)=-10; 
   end    
%Return of parameters 
   x(1)=u(k); 
   x(2)=yout(k); 
   x(3)=y_1; 
    
   u_1=u(k); 
   y_1=yout(k); 
    
   w_3=w_2; 
   w_2=w_1; 
   w_1=w; 
    
   xc(1)=error(k)-error_1;             %Calculating P 
   xc(2)=error(k)-2*error_1+error_2;   %Calculating D 
   xc(3)=error(k);                     %Calculating I 
    
   error_2=error_1; 
   error_1=error(k); 
    
   kp_1=kp(k); 
   kd_1=kd(k); 
   ki_1=ki(k);   
end 
figure(1); 
plot(time,rin,'b',time,yout,'r'); 
xlabel('time(s)');ylabel('rin,yout'); 
figure(2); 
plot(time,yout,'r',time,ymout,'b'); 
xlabel('time(s)');ylabel('yout,ymout'); 
figure(3); 
plot(time,dyout); 
xlabel('time(s)');ylabel('Jacobian value'); 
figure(4); 
subplot(311); 
plot(time,kp,'r'); 
xlabel('time(s)');ylabel('kp'); 
subplot(312); 
plot(time,ki,'r'); 
xlabel('time(s)');ylabel('ki'); 
subplot(313); 
plot(time,kd,'r'); 
xlabel('time(s)');ylabel('kd');