step模型设置在8以下基本上没问题。
以下是MATLAB Fcn函数，参考李献的那本书。
function u= BP_PID(t,rin,yout)
persistent x u_1 u_2 u_3 u_4 u_5 y_1 y_2 y_3
persistent xite alfa IN H Out wi wi_1 wi_2 wi_3 wo wo_1 wo_2 wo_3
persistent Oh error_2 error_1
persistent k
if t==0
xite=0.25;
alfa=0.05;
IN=4;H=5;Out=3; %NN Structure
wi=0.50*rands(H,IN);
wi_1=wi;wi_2=wi;wi_3=wi;
wo=0.50*rands(Out,H);
wo_1=wo;wo_2=wo;wo_3=wo;
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;
k=2;
end
%Unlinear model
%a = 1.2*(1-0.8*exp(-0.1*k));
%yout = a*y_1/(1+y_1^2)+u_1;
error = rin-yout;
xi=[rin,yout,error,1];
x(1)=error-error_1;
x(2)=error;
x(3)=error-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)=1/(1+exp(-K(l))); %Getting kp,ki,kd
end
kp=K(1)*20;ki=K(2)*3;kd=K(3);
Kpid=[kp,ki,kd];
du=Kpid*epid;
u=u_1+du;
if u>=80 % Restricting the output of controller
u=80;
end
if u<=-80
u=-80;
end
dyu=sign((yout-y_1)/(u-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*dyu*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;
y_2=y_1;y_1=yout;
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;
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