RBF-PID

%Adaptive PID control based on RBF Identificationclear all;close all;xite=0.5;          %学习速率xitealfa=0.05;          %动量因子alfa% beta=0.01;          %x=[0,0,0]';         %输入向量xci=zeros(3,6);      %第i个节点的中心矢量Cbi=10*ones(6,1);    %第i个节点的基宽向量Bw=0.10*ones(6,1);   %权值向量Wh=[0,0,0,0,0,0]';   %径向基向量h    ci_1=ci;ci_3=ci_1;ci_2=ci_1;    %c(i-1),c(i-3),c(i-2)，迭代用bi_1=bi;bi_2=bi_1;bi_3=bi_2;    %b(i-1),b(i-2),b(i-3)w_1=w;w_2=w_1;w_3=w_1;          %w(i-1),w(i-2),w(i-3)u_1=0;y_1=0;                    %u(k-1),y(k-1)，迭代用xc=[0,0,0]';                    %增量式PID的输入error_1=0;error_2=0;            %error(k-1),error(k-1)，迭代用kp0=0.01;ki0=0.01;kd0=0.01;% kp0=0.003;ki0=0.34;kd0=0.01;pidu_1=0;pidy_1=0;pidxc=[0,0,0]';piderror_1=0;piderror_2=0;% pidkp=0.003;pidki=0.34;pidkd=0.01;pidkp=0.01;pidki=0.01;pidkd=0.01;kp_1=kp0;kd_1=kd0;ki_1=ki0;xitekp=0.15;xitekd=0.15;xiteki=0.15;% ts=0.001;ts=0.01for k=1:1:2000   time(k)=k*ts;%     yd(k)=1;%阶梯响应%    if mod(floor(k/100),3)==0%        yd(k)=1;%    elseif mod(floor(k/100),3)==1%        yd(k)=0;%    else %        yd(k)=-1;%    end   %单位正弦响应%    yd(k)=sin(time(k));              %预期输出yd%复合简弦响应yd(k)=sin(time(k))*cos(2*time(k));% yd(k)=3*sin(time(floor(k/10)+1))-2*cos(time(floor(k/10)+1));%    y(k)=(-0.1*y_1+u_1)/(1+y_1^2);   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)));  %计算径向基向量h   end   ym(k)=w'*h;                      %辨识器网络输出ym   d_w=0*w;   for j=1:1:6      d_w(j)=xite*(y(k)-ym(k))*h(j);%计算deta_w供迭代计算下次w   end   w=w_1+d_w+alfa*(w_1-w_2);        %权值向量w调整      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;%计算deta_b供迭代计算下次第i个节点的基宽向量   end   bi=bi_1+ d_bi+alfa*(bi_1-bi_2);  %基宽向量B调整   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);%计算deta_ci供迭代计算下次第i个节点的中心矢量ci     end   end   ci=ci_1+d_ci+alfa*(ci_1-ci_2);   %中心矢量调整%%%%%%%%%%%%%%%%%%%%%%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; %被控对象的Jacobian信息%%%%%%%%%%%%%%%%%%%%%%Start of Control system%%%%%%%%%%%%%%%%%%   error(k)=yd(k)-y(k);   %用梯度下降法调整P,I,D   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 Controlkp(k)=kp0;ki(k)=ki0;     kd(k)=kd0;   end   du(k)=kp(k)*xc(1)+kd(k)*xc(2)+ki(k)*xc(3);%PID输出的调整量deta_u   u(k)=u_1+du(k);%计算下次的输出   if k==300     % Adding disturbance(1.0v at time 0.3s)   u(k)=u(k)+0.5;   end%    if u(k)>=10%    u(k)=10;%    end%    if u(k)<=-10%    u(k)=-10;%    end  %Return of parameters   x(1)=du(k);   x(2)=y(k);   x(3)=y_1;%RBF网络的输入向量   %量的迭代   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);        %传统的Pid控制   pidy(k)=(-0.1*pidy_1+pidu_1)/(1+pidy_1^2);%传统PID控制的输出   piderror(k)=yd(k)-pidy(k);   piddu(k)=pidkp*pidxc(1)+pidkd*pidxc(2)+pidki*pidxc(3);%增量式PID计算   pidu(k)=pidu_1+piddu(k);%传统PID计算PID输出    if k==300     % Adding disturbance(1.0v at time 0.3s)       pidu(k)=pidu(k)+0.5;    end%     if pidu(k)>=10%        pidu(k)=10;%     end%     if pidu(k)<=-10%        pidu(k)=-10;%     end      pidu_1=pidu(k);   pidy_1=pidy(k);   pidxc(1)=piderror(k)-piderror_1;             %Calculating P   pidxc(2)=piderror(k)-2*piderror_1+piderror_2;   %Calculating D   pidxc(3)=piderror(k);                     %Calculating I      piderror_2=piderror_1;   piderror_1=piderror(k);endif M==1figure(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(1);% plot(time,yd,'r',time,y,'k:','linewidth',2);plot(time,yd,'r',time,y,'g',time,pidy,'b');xlabel('time(s)');ylabel('yd,y');legend('ideal position','RBF tracking','PID tracking');figure(2);plot(time,y,'r',time,ym,'b');xlabel('time(s)');ylabel('y,ym');figure(3);plot(time,dyu,'r');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');figure(5);subplot(211);plot(time,error,'r');xlabel('time(s)');ylabel('error');subplot(212);plot(time,piderror,'r');xlabel('time(s)');ylabel('piderror');elseif M==2figure(1);plot(time,yd,'r',time,y,'k:');xlabel('time(s)');ylabel('yd,y');legend('ideal position','position tracking');end