基于BP神经网络整定的PID控制

博大广阔

%BP  based  PID
function BP_PID=BP_PID()
%本仿真程序是基于BP神经网络整定的PID控制。跟踪对象是正弦函数。采用的学习算法是带惯性项的ＢＰ算法。
%利用ＢＰ算法的自学习，调整ＰＩＤ的三个控制参数，ＢＰ的输入为四个，输出为ＰＩＤ参数
clc
clear all
close all

%%%%%%%%%%%%%%%%%%%%%%%%训练样本%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%P=-2:0.1:8; T=1+sin(P*pi/2);
%P=[1 2;-1 1;1 3];
%T=[1 1;1 1];
%%%%%%%%%%%%%%%%%%%%%%%BP算法参数%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Lr=0.28;        %学习效率
max_epoch=6000;  %最大迭代次数
goal=0.01;      %期望目标值
alfa=0.04;      %惯性系数
Layer_n=5;      %隐含层数目
output_n=3;       %输出层数目
input_n=4;        %输入层数目
%%%%%%%%%%%%%%%%%%%%%%权值初始值%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%[input_n,sample]=size(P);[output_n]=size(T,1);                         %初始化隐含层和输出层的权重系数
%weight1=0.5*rand(Layer_n,input_n)-1;weight2=rand(output_n,Layer_n);     %为防止等量调整，权重初始值为随机   
%bias1=rand(Layer_n,1);bias2=rand(size(output_n,1),1);
% 初始值的影响非常大，正常情况最好先实现离线学习初始值，或者预测好初始值的情况
weight1=[-0.2846    0.2193   -0.5097   -1.0668;
    -0.7484   -0.1210   -0.4708    0.0988;
    -0.7176    0.8297   -1.6000    0.2049;
    -0.0858    0.1925   -0.6346    0.0347;
     0.4358    0.2369   -0.4564   -0.1324];
weight2=[1.0438    0.5478    0.8682    0.1446    0.1537;
    0.1716    0.5811    1.1214    0.5067    0.7370;
    1.0063    0.7428    1.0534    0.7824    0.6494];
bias1=0.5*zeros(size(weight1,1),1);bias2=0.5*zeros(size(weight2,1),1);
%%%%%%%%%%%%%%%%%%%%%%循环预先值%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E0=0.5;ts=0.001;y_1=0;er_1=0 ;er_2=0;U_1=0;dU_1=0;
weight2_1=0;weight2_2=0;weight1_1=0 ;weight1_2=0;
%%%%%%%%%%%%%%%%%%%%%%%主仿真程序%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for k=1:1:max_epoch

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%控制模型%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
time=k*ts; rin=sin(2*pi*time);                         %跟踪信号
a=1.2*(1-0.8*exp(-0.1*k));  yout=a*y_1/(1+y_1^2)+U_1;  %模型

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%控制规律计算%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
er=rin-yout;                                            %误差
EPID=[er-er_1;er;er-2*er_1+er_2];                       %给增量式PID控制器的误差信号
input=[rin;yout;er;1];                                  %BP神经网络的输入 有点纳闷
[a1,da1]=fun1(weight1*input,bias1);                     %隐含层神经元计算
[a2,da2]=fun2(weight2*a1,bias2); KPID=a2.';             %输出层神经元计算
dU=KPID*EPID; U=U_1+dU;                                 %控制规律
%%%%%%%%%%%%%%%%%%%%%%%%%本控制规律的核心——学习算法ＢＰ带惯性%%%%%%%%%%%%%%%%%%%%%
dyu=sign((yout-y_1)/(dU-dU_1+0.0001));                 %模型近似部分————较ＢＰ算法是多得一项
Sout=da2.*(EPID*dyu*er);                               %输出层灵敏度
dweight2=alfa*(weight2_1-weight2_2)+Lr*Sout*a1.';      %输出层权值调整
weight2=weight2+dweight2+alfa*(weight2_1-weight2_2);

S1=a1.*(weight2.'*Sout);                              %隐含层灵敏度
dweight1=Lr*S1*input.';
weight1=weight1+dweight1+alfa*(weight1_1-weight1_2);
%for l=1:1:Out
%    delta3(l)=error(k)*dyu(k)*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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%循环程序参数更新%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
y_1=yout;er_1=er ;er_2=er_1;U_1=U;dU_1=dU;
weight2_2=weight2_1;weight2_1=weight2;
weight1_2=weight1_1;weight1_1=weight1_2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%性能记录%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
TT(k)=k; EE(k)=er; T(k)=time; RR(k)=rin; YY(k)=yout;

end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%性能比较%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%figure(1)
%plot(TT,EE,'r');grid on;
figure(2)
plot(T,RR,'x',T,YY,'r');grid on;
end

%%%%%%%%%%%%%%%%%%%%%%神经元传递函数%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [F,dF]=fun1(n,b)
%tansif 函数
if nargin<2;b=0;end            
if nargin==2;n=n+b(:,ones(1,size(n,2)));end %阀值等值的按列复制
%   F= 2 ./ (1 + exp(-2*n)) - 1;
%   df=@(X)4*exp(-2*X)./(exp(-2*X)+1).^2;
%   dF=df(n);
%对称的sigmoid函数
F=(exp(n)-exp(-n))./(exp(n)+exp(-n));
df=@(X)1./cosh(n).^2;
dF=df(n);
end
function [F,dF]=fun2(n,b)
%purelin
if nargin<2;b=0;end               %阀值等值的按列复制
if nargin==2;n=n+b(:,ones(1,size(n,2)));end
%F=n;
%df=@(X)ones(size(X));
%dF=df(n);
%非负的sigmoid 函数，因为PID的输出值为正
F=0.5*(1+tanh(n));
df=@(n)(2*exp(2.*n))./(exp(2.*n) + 1).^2;
dF=df(n);
end