基于遗传算法的PID整定原理及matlab仿真程序

主程序：chap5_2.m

%GA(Generic Algorithm) Program to optimize PID Parameters clear all; close all;

global rin yout timef

Size=30; CodeL=3;

MinX(1)=zeros(1); MaxX(1)=20*ones(1); MinX(2)=zeros(1); MaxX(2)=1.0*ones(1); MinX(3)=zeros(1); MaxX(3)=1.0*ones(1);

Kpid(:,1)=MinX(1)+(MaxX(1)-MinX(1))*rand(Size,1); Kpid(:,2)=MinX(2)+(MaxX(2)-MinX(2))*rand(Size,1); Kpid(:,3)=MinX(3)+(MaxX(3)-MinX(3))*rand(Size,1);

G=100; BsJ=0;

%*************** Start Running *************** for kg=1:1:G

time(kg)=kg;

%****** Step 1 : Evaluate BestJ ****** for i=1:1:Size Kpidi=Kpid(i,:);

[Kpidi,BsJ]=chap5_2f(Kpidi,BsJ);

BsJi(i)=BsJ; end

[OderJi,IndexJi]=sort(BsJi); BestJ(kg)=OderJi(1); BJ=BestJ(kg);

Ji=BsJi+1e-10; %Avoiding deviding zero

fi=1./Ji;

% Cm=max(Ji);

% fi=Cm-Ji;

[Oderfi,Indexfi]=sort(fi); %Arranging fi small to bigger Bestfi=Oderfi(Size); %Let Bestfi=max(fi)

BestS=Kpid(Indexfi(Size),:); %Let BestS=E(m), m is the Indexfi belong to max(fi)

kg BJ BestS

%****** Step 2 : Select and Reproduct Operation****** fi_sum=sum(fi);

fi_Size=(Oderfi/fi_sum)*Size;

fi_S=floor(fi_Size); % Selecting Bigger fi value r=Size-sum(fi_S);

Rest=fi_Size-fi_S;

[RestValue,Index]=sort(Rest);

for i=Size:-1:Size-r+1

fi_S(Index(i))=fi_S(Index(i))+1; % Adding rest to equal Size end

k=1;

for i=Size:-1:1 % Select the Sizeth and Reproduce firstly for j=1:1:fi_S(i)

TempE(k,:)=Kpid(Indexfi(i),:); % Select and Reproduce

k=k+1; % k is used to reproduce end end

%************ Step 3 : Crossover Operation ************

Pc=0.90;

for i=1:2:(Size-1) temp=rand;

if Pc>temp %Crossover Condition alfa=rand;

TempE(i,:)=alfa*Kpid(i+1,:)+(1-alfa)*Kpid(i,:); TempE(i+1,:)=alfa*Kpid(i,:)+(1-alfa)*Kpid(i+1,:); end end

TempE(Size,:)=BestS; Kpid=TempE;

%************ Step 4: Mutation Operation ************** Pm=0.10-[1:1:Size]*(0.01)/Size; %Bigger fi,smaller Pm Pm_rand=rand(Size,CodeL); Mean=(MaxX + MinX)/2; Dif=(MaxX-MinX);

for i=1:1:Size

for j=1:1:CodeL

if Pm(i)>Pm_rand(i,j) %Mutation Condition TempE(i,j)=Mean(j)+Dif(j)*(rand-0.5); end end end

%Guarantee TempE(Size,:) belong to the best individual TempE(Size,:)=BestS; Kpid=TempE; end Bestfi BestS

Best_J=BestJ(G) figure(1);

plot(time,BestJ);

xlabel(’Times’);ylabel(’Best J’); figure(2);

plot(timef,rin,’r’,timef,yout,’b’); xlabel(’Time(s)’);ylabel(’rin,yout’);

子程序：chap5_2f.m

function [Kpidi,BsJ]=pid_gaf(Kpidi,BsJ) global rin yout timef

ts=0.001;

sys=tf(400,[1,50,0]); dsys=c2d(sys,ts,’z’);

[num,den]=tfdata(dsys,’v’);

rin=1.0;

u_1=0.0;u_2=0.0;

y_1=0.0;y_2=0.0; x=[0,0,0]’; B=0;

error_1=0; tu=1; s=0; P=100;

for k=1:1:P

timef(k)=k*ts; r(k)=rin;

u(k)=Kpidi(1)*x(1)+Kpidi(2)*x(2)+Kpidi(3)*x(3);

if u(k)>=10 u(k)=10; end

if u(k)<=-10 u(k)=-10; end

yout(k)=-den(2)*y_1-den(3)*y_2+num(2)*u_1+num(3)*u_2; error(k)=r(k)-yout(k);

%------------ Return of PID parameters ------------- u_2=u_1;u_1=u(k); y_2=y_1;y_1=yout(k);

x(1)=error(k); % Calculating P x(2)=(error(k)-error_1)/ts; % Calculating D x(3)=x(3)+error(k)*ts; % Calculating I

error_2=error_1; error_1=error(k); if s==0

if yout(k)>0.95&yout(k)<1.05 tu=timef(k); s=1; end end end

for i=1:1:P

Ji(i)=0.999*abs(error(i))+0.01*u(i)^2*0.1; B=B+Ji(i); if i>1

erry(i)=yout(i)-yout(i-1); if erry(i)<0

B=B+100*abs(erry(i)); end end end

BsJ=B+0.2*tu*10;

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