rbf.m

基于RBF的PID控制matlab程序

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;

kp0=0.03;
ki0=0.01;
kd0=0.03;

kp_1=kp0;
kd_1=kd0;
ki_1=ki0;

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);
    for j=1:1:6
        h(j)=exp(-norm(x-ci( : ,j))^2/(2*bi(j)*bi(j)));
    end
    ymout(k)=w'*h;
    
    d_w=0*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(j)*h(j)*(bi(j)^-3)*norm(x-ci( : ,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(j)*h(j)*(x(i)-ci(i,j))*(bi(j)^-2);
        end
    end
    ci=ci_1+d_ci+alfa*(ci_1-ci_2)+belte*(ci_2-ci_3);
    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;
    
    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;
    switch M
        case 1
        case 2
            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);
    
    x(1)=du(k);
    x(2)=yout(k);
    x(3)=y_1;
    
    u_1=u(k);
    y_1=yout(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;
    xc(2)=error(k)-2*error_1+error_2;
    xc(3)=error(k);
    
    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');