RBF神经网络的PID控制

%Adaptive PID control based on RBF Identification clear all; close all; clc; clear; xite=0.5; alfa=0.05; beta=0.01; x=[0,0,0]'; ci=zeros(3,6); bi=10*ones(6,1); w=0.10*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; kp0=0.01;ki0=0.01;kd0=0.01; kp_1=kp0; kd_1=kd0; ki_1=ki0; xitekp=0.15; xitekd=0.15; xiteki=0.15; ts=0.001; for k=1:1:1000 time(k)=k*ts; yd(k)=1.0; y(k)=(-0.1*y_1+u_1)/(1+y_1^2); %Nonlinear plant for j=1:1:6 h(j)=exp(-norm(x-ci(:,j))^2/(2*bi(j)*bi(j))); end ym(k)=w'*h; d_w=0*w; for j=1:1:6 d_w(j)=xite*(y(k)-ym(k))*h(j); end w=w_1+d_w+alfa*(w_1-w_2); d_bi=0*bi; for j=1:1:6 d_bi(j)=xite*(y(k)-ym(k))*w(j)*h(j)*(bi(j)^-3)*norm(x-ci(:,j))^2; end bi=bi_1+ d_bi+alfa*(bi_1-bi_2); for j=1:1:6 for i=1:1:3 d_ci(i,j)=xite*(y(k)-ym(k))*w(j)*h(j)*(x(i)-ci(i,j))*(bi(j)^-2); end end ci=ci_1+d_ci+alfa*(ci_1-ci_2); %%%%%%%%%%%%%%%%%%%%%%Jacobian%%%%%%%%%%%%%%%%%%%%%%% yu=0; for j=1:1:6 yu=yu+w(j)*h(j)*(-x(1)+ci(1,j))/bi(j)^2; end dyu(k)=yu; %%%%%%%%%%%%%%%%%%%%%%Start of Control system%%%%%%%%%%%%%%%%%% error(k)=yd(k)-y(k); kp(k)=kp_1+xitekp*error(k)*dyu(k)*xc(1); kd(k)=kd_1+xitekd*error(k)*dyu(k)*xc(2); ki(k)=ki_1+xiteki*error(k)*dyu(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; switch M case 1 case 2 %Only PID Control kp(k)=kp0; ki(k)=ki0; kd(k)=kd0; end du(k)=kp(k)*xc(1)+kd(k)*xc(2)+ki(k)*xc(3); u(k)=u_1+du(k); %Return of parameters x(1)=du(k); x(2)=y(k); x(3)=y_1; u_1=u(k); y_1=y(k); ci_3=ci_2; ci_2=ci_1; ci_1=ci; bi_3=bi_2; bi_2=bi_1; bi_1=bi; 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 if M==1 figure(1); plot(time,yd,'r',time,y,'k:','linewidth',2); xlabel('time(s)');ylabel('yd,y'); legend('ideal position','position tracking'); figure(2); plot(time,y,'r',time,ym,'b','linewidth',2); xlabel('time(s)');ylabel('y,ym'); figure(3); plot(time,dyu,'r','linewidth',2); xlabel('time(s)');ylabel('Jacobian value'); figure(4); subplot(311); plot(time,kp,'r','linewidth',2); xlabel('time(s)');ylabel('kp'); subplot(312); plot(time,ki,'r','linewidth',2); xlabel('time(s)');ylabel('ki'); subplot(313); plot(time,kd,'r','linewidth',2); xlabel('time(s)');ylabel('kd'); elseif M==2 figure(5); plot(time,yd,'r',time,y,'k:','linewidth',2); xlabel('time(s)');ylabel('yd,y'); legend('ideal position','position tracking'); end