怎么通过MATLAB使用遗传算法实现pid参数整定

我的毕设只用把PID和模糊PID相比较

常规PID，用Matlab里的Simulink模块仿真，建立你要做的动力学模型的传函或者状态空间。PID参数调节可用临界比度法。

模糊PID就麻烦了，打开Matlab中FIS模块，一般都用二阶模糊？输入E,EC的隶属函数，一般为高斯，和输出模糊Kp,Ki,Kd，一般为三角。还要整定模糊规则，再加载到Simulink里。调节模糊因子Gu，Ge，Gec，设置模糊PID的参数。

总之，你这个问题在白度知道里很难说清楚。

这个问题也困扰了我好久，终于解决了。给你个gam程序，新建m文件复制进去，再运行程序试试。

%gam

function [x,endPop,bPop,traceInfo] = ga(bounds,evalFN,evalOps,startPop,opts,

termFN,termOps,selectFN,selectOps,xOverFNs,xOverOps,mutFNs,mutOps)

% GA run a genetic algorithm

% function [x,endPop,bPop,traceInfo]=ga(bounds,evalFN,evalOps,startPop,opts,

% termFN,termOps,selectFN,selectOps,

% xOverFNs,xOverOps,mutFNs,mutOps)

%

% Output Arguments:

% x - the best solution found during the course of the run

% endPop - the final population

% bPop - a trace of the best population

% traceInfo - a matrix of best and means of the ga for each generation

%

% Input Arguments:

% bounds - a matrix of upper and lower bounds on the variables

% evalFN - the name of the evaluation m function

% evalOps - options to pass to the evaluation function ([NULL])

% startPop - a matrix of solutions that can be initialized

% from initializem

% opts - [epsilon prob_ops display] change required to consider two

% solutions different, prob_ops 0 if you want to apply the

% genetic operators probabilisticly to each solution, 1 if

% you are supplying a deterministic number of operator

% applications and display is 1 to output progress 0 for

% quiet ([1e-6 1 0])

% termFN - name of the m termination function (['maxGenTerm'])

% termOps - options string to be passed to the termination function

% ([100])

% selectFN - name of the m selection function (['normGeomSelect'])

% selectOpts - options string to be passed to select after

% select(pop,#,opts) ([008])

% xOverFNS - a string containing blank seperated names of Xoverm

% files (['arithXover heuristicXover simpleXover'])

% xOverOps - A matrix of options to pass to Xoverm files with the

% first column being the number of that xOver to perform

% similiarly for mutation ([2 0;2 3;2 0])

% mutFNs - a string containing blank seperated names of mutationm

% files (['boundaryMutation multiNonUnifMutation

% nonUnifMutation unifMutation'])

% mutOps - A matrix of options to pass to Xoverm files with the

% first column being the number of that xOver to perform

% similiarly for mutation ([4 0 0;6 100 3;4 100 3;4 0 0])

% Binary and Real-Valued Simulation Evolution for Matlab

% Copyright (C) 1996 CR Houck, JA Joines, MG Kay

%

% CR Houck, JJoines, and MKay A genetic algorithm for function

% optimization: A Matlab implementation ACM Transactions on Mathmatical

% Software, Submitted 1996

%

% This program is free software; you can redistribute it and/or modify

% it under the terms of the GNU General Public License as published by

% the Free Software Foundation; either version 1, or (at your option)

% any later version

%

% This program is distributed in the hope that it will be useful,

% but WITHOUT ANY WARRANTY; without even the implied warranty of

% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the

% GNU General Public License for more details A copy of the GNU

% General Public License can be obtained from the

% Free Software Foundation, Inc, 675 Mass Ave, Cambridge, MA 02139, USA

%%$Log: gam,v $

%Revision 110 1996/02/02 15:03:00 jjoine

% Fixed the ordering of imput arguments in the comments to match

% the actual order in the ga function

%

%Revision 19 1995/08/28 20:01:07 chouck

% Updated initialization parameters, updated mutation parameters to reflect

% b being the third option to the nonuniform mutations

%

%Revision 18 1995/08/10 12:59:49 jjoine

%Started Logfile to keep track of revisions

%

n=nargin;

if n<2 | n==6 | n==10 | n==12

disp('Insufficient arguements')

end

if n<3 %Default evalation opts

evalOps=[];

end

if n<5

opts = [1e-6 1 0];

end

if isempty(opts)

opts = [1e-6 1 0];

end

if any(evalFN<48) %Not using a m file

if opts(2)==1 %Float ga

e1str=['x=c1; c1(xZomeLength)=', evalFN ';'];

e2str=['x=c2; c2(xZomeLength)=', evalFN ';'];

else %Binary ga

e1str=['x=b2f(endPop(j,:),bounds,bits); endPop(j,xZomeLength)=',

evalFN ';'];

end

else %Are using a m file

if opts(2)==1 %Float ga

e1str=['[c1 c1(xZomeLength)]=' evalFN '(c1,[gen evalOps]);'];

e2str=['[c2 c2(xZomeLength)]=' evalFN '(c2,[gen evalOps]);'];

else %Binary ga

e1str=['x=b2f(endPop(j,:),bounds,bits);[x v]=' evalFN

'(x,[gen evalOps]); endPop(j,:)=[f2b(x,bounds,bits) v];'];

end

end

if n<6 %Default termination information

termOps=[100];

termFN='maxGenTerm';

end

if n<12 %Default muatation information

if opts(2)==1 %Float GA

mutFNs=['boundaryMutation multiNonUnifMutation nonUnifMutation unifMutation'];

mutOps=[4 0 0;6 termOps(1) 3;4 termOps(1) 3;4 0 0];

else %Binary GA

mutFNs=['binaryMutation'];

mutOps=[005];

end

end

if n<10 %Default crossover information

if opts(2)==1 %Float GA

xOverFNs=['arithXover heuristicXover simpleXover'];

xOverOps=[2 0;2 3;2 0];

else %Binary GA

xOverFNs=['simpleXover'];

xOverOps=[06];

end

end

if n<9 %Default select opts only ie roullete wheel

selectOps=[];

end

if n<8 %Default select info

selectFN=['normGeomSelect'];

selectOps=[008];

end

if n<6 %Default termination information

termOps=[100];

termFN='maxGenTerm';

end

if n<4 %No starting population passed given

startPop=[];

end

if isempty(startPop) %Generate a population at random

%startPop=zeros(80,size(bounds,1)+1);

startPop=initializega(80,bounds,evalFN,evalOps,opts(1:2));

end

if opts(2)==0 %binary

bits=calcbits(bounds,opts(1));

end

xOverFNs=parse(xOverFNs);

mutFNs=parse(mutFNs);

xZomeLength = size(startPop,2); %Length of the xzome=numVars+fittness

numVar = xZomeLength-1; %Number of variables

popSize = size(startPop,1); %Number of individuals in the pop

endPop = zeros(popSize,xZomeLength); %A secondary population matrix

c1 = zeros(1,xZomeLength); %An individual

c2 = zeros(1,xZomeLength); %An individual

numXOvers = size(xOverFNs,1); %Number of Crossover operators

numMuts = size(mutFNs,1); %Number of Mutation operators

epsilon = opts(1); %Threshold for two fittness to differ

oval = max(startPop(:,xZomeLength)); %Best value in start pop

bFoundIn = 1; %Number of times best has changed

done = 0; %Done with simulated evolution

gen = 1; %Current Generation Number

collectTrace = (nargout>3); %Should we collect info every gen

floatGA = opts(2)==1; %Probabilistic application of ops

display = opts(3); %Display progress

while(~done)

%Elitist Model

[bval,bindx] = max(startPop(:,xZomeLength)); %Best of current pop

best = startPop(bindx,:);

if collectTrace

traceInfo(gen,1)=gen; %current generation

traceInfo(gen,2)=startPop(bindx,xZomeLength); %Best fittness

traceInfo(gen,3)=mean(startPop(:,xZomeLength)); %Avg fittness

traceInfo(gen,4)=std(startPop(:,xZomeLength));

end

if ( (abs(bval - oval)>epsilon) | (gen==1)) %If we have a new best sol

if display

fprintf(1,'\n%d %f\n',gen,bval); %Update the display

end

if floatGA

bPop(bFoundIn,:)=[gen startPop(bindx,:)]; %Update bPop Matrix

else

bPop(bFoundIn,:)=[gen b2f(startPop(bindx,1:numVar),bounds,bits)

startPop(bindx,xZomeLength)];

end

bFoundIn=bFoundIn+1; %Update number of changes

oval=bval; %Update the best val

else

if display

fprintf(1,'%d ',gen); %Otherwise just update num gen

end

end

endPop = feval(selectFN,startPop,[gen selectOps]); %Select

if floatGA %Running with the model where the parameters are numbers of ops

for i=1:numXOvers,

for j=1:xOverOps(i,1),

a = round(rand(popSize-1)+1); %Pick a parent

b = round(rand(popSize-1)+1); %Pick another parent

xN=deblank(xOverFNs(i,:)); %Get the name of crossover function

[c1 c2] = feval(xN,endPop(a,:),endPop(b,:),bounds,[gen xOverOps(i,:)]);

if c1(1:numVar)==endPop(a,(1:numVar)) %Make sure we created a new

c1(xZomeLength)=endPop(a,xZomeLength); %solution before evaluating

elseif c1(1:numVar)==endPop(b,(1:numVar))

c1(xZomeLength)=endPop(b,xZomeLength);

else

%[c1(xZomeLength) c1] = feval(evalFN,c1,[gen evalOps]);

eval(e1str);

end

if c2(1:numVar)==endPop(a,(1:numVar))

c2(xZomeLength)=endPop(a,xZomeLength);

elseif c2(1:numVar)==endPop(b,(1:numVar))

c2(xZomeLength)=endPop(b,xZomeLength);

else

%[c2(xZomeLength) c2] = feval(evalFN,c2,[gen evalOps]);

eval(e2str);

end

endPop(a,:)=c1;

endPop(b,:)=c2;

end

end

for i=1:numMuts,

for j=1:mutOps(i,1),

a = round(rand(popSize-1)+1);

c1 = feval(deblank(mutFNs(i,:)),endPop(a,:),bounds,[gen mutOps(i,:)]);

if c1(1:numVar)==endPop(a,(1:numVar))

c1(xZomeLength)=endPop(a,xZomeLength);

else

%[c1(xZomeLength) c1] = feval(evalFN,c1,[gen evalOps]);

eval(e1str);

end

endPop(a,:)=c1;

end

end

else %We are running a probabilistic model of genetic operators

for i=1:numXOvers,

xN=deblank(xOverFNs(i,:)); %Get the name of crossover function

cp=find(rand(popSize,1)<xOverOps(i,1)==1);

if rem(size(cp,1),2) cp=cp(1:(size(cp,1)-1)); end

cp=reshape(cp,size(cp,1)/2,2);

for j=1:size(cp,1)

a=cp(j,1); b=cp(j,2);

[endPop(a,:) endPop(b,:)] = feval(xN,endPop(a,:),endPop(b,:),

bounds,[gen xOverOps(i,:)]);

end

end

for i=1:numMuts

mN=deblank(mutFNs(i,:));

for j=1:popSize

endPop(j,:) = feval(mN,endPop(j,:),bounds,[gen mutOps(i,:)]);

eval(e1str);

end

end

end

gen=gen+1;

done=feval(termFN,[gen termOps],bPop,endPop); %See if the ga is done

startPop=endPop; %Swap the populations

[bval,bindx] = min(startPop(:,xZomeLength)); %Keep the best solution

startPop(bindx,:) = best; %replace it with the worst

end

[bval,bindx] = max(startPop(:,xZomeLength));

if display

fprintf(1,'\n%d %f\n',gen,bval);

end

x=startPop(bindx,:);

if opts(2)==0 %binary

x=b2f(x,bounds,bits);

bPop(bFoundIn,:)=[gen b2f(startPop(bindx,1:numVar),bounds,bits)

startPop(bindx,xZomeLength)];

else

bPop(bFoundIn,:)=[gen startPop(bindx,:)];

end

if collectTrace

traceInfo(gen,1)=gen; %current generation

traceInfo(gen,2)=startPop(bindx,xZomeLength); %Best fittness

traceInfo(gen,3)=mean(startPop(:,xZomeLength)); %Avg fittness

end

（1）关于fitness value，你要自己定义一个函数，如你所说从25个x变量经过一系列运算得到y值 可以其作为fitness value

（2）由于x的取值是离散的 染色体不一定要是二进制 最简单的做法是一个5进制的长为25的串。

% 主程序

%遗传算法主程序

%Name:genmainm

%author：杨幂

clear

clf

%%初始化

popsize=50; %群体大小

chromlength=30; %字符串长度（个体长度）

pc=06; %交叉概率

pm=01; %变异概率

pop=initpop(popsize,chromlength); %随机产生初始群体

%%开始迭代

for i=1:20 %20为迭代次数

[objvalue]=calobjvalue(pop); %计算目标函数

fitvalue=calfitvalue(objvalue); %计算群体中每个个体的适应度

[newpop]=selection(pop,fitvalue); %复制

[newpop]=crossover(pop,pc); %交叉

[newpop]=mutation(pop,pm); %变异

[bestindividual,bestfit]=best(pop,fitvalue); %求出群体中适应值最大的个体及其适应值

y(i)=max(bestfit);%储存最优个体适应值

n(i)=i;

pop5=bestindividual;%储存最优个体

%解码

x1(i)=decodechrom(pop5,1,chromlength/2)2/32767;

x2(i)=10+decodechrom(pop5,chromlength/2+1,chromlength/2)10/32767;

pop=newpop;%将新产生的种群作为当前种群

end

%%绘图

figure(1)%最优点变化趋势图

i=1:20;

plot(y(i),'-r')

xlabel('迭代次数');

ylabel('最优个体适应值');

title('最优点变化趋势');

legend('最优点');

grid on

figure(2)%最优点分布图

[X1,X2]=meshgrid(0:01:2,10:01:20);

Z=X1^2+X2^2;

mesh(X1,X2,Z);

xlabel('自变量x1'),ylabel('自变量x2'),zlabel('函数值f(x1,x2)');

hold on

plot3(x1,x2,y,'ro','MarkerEdgeColor','r','MarkerFaceColor','r','MarkerSize',5)

title('最优点分布');

legend('最优点');

hold off

[z index]=max(y); %计算最大值及其位置

x5=[x1(index),x2(index)]%计算最大值对应的x值

z

把下面的（1）-（7）依次存成相应的m文件，在（7）的m文件下运行就可以了

（1） 适应度函数fitm

function fitness=fit(len,m,maxlen,minlen)

fitness=len;

for i=1:length(len)

fitness(i,1)=(1-(len(i,1)-minlen)/(maxlen-minlen+00001))^m;

end

(2)个体距离计算函数 mylengthm

function len=myLength(D,p)

[N,NN]=size(D);

len=D(p(1,N),p(1,1));

for i=1:(N-1)

len=len+D(p(1,i),p(1,i+1));

end

end

(3)交叉 *** 作函数 crossm

function [A,B]=cross(A,B)

L=length(A);

if L<10

W=L;

elseif ((L/10)-floor(L/10))>=rand&&L>10

W=ceil(L/10)+8;

else

W=floor(L/10)+8;

end

p=unidrnd(L-W+1);

fprintf('p=%d ',p);

for i=1:W

x=find(A==B(1,p+i-1));

y=find(B==A(1,p+i-1));

[A(1,p+i-1),B(1,p+i-1)]=exchange(A(1,p+i-1),B(1,p+i-1));

[A(1,x),B(1,y)]=exchange(A(1,x),B(1,y));

end

end

(4)对调函数 exchangem

function [x,y]=exchange(x,y)

temp=x;

x=y;

y=temp;

end

(5)变异函数 Mutationm

function a=Mutation(A)

index1=0;index2=0;

nnper=randperm(size(A,2));

index1=nnper(1);

index2=nnper(2);

%fprintf('index1=%d ',index1);

%fprintf('index2=%d ',index2);

temp=0;

temp=A(index1);

A(index1)=A(index2);

A(index2)=temp;

a=A;

end

(6)连点画图函数 plot_routem

function plot_route(a,R)

scatter(a(:,1),a(:,2),'rx');

hold on;

plot([a(R(1),1),a(R(length(R)),1)],[a(R(1),2),a(R(length(R)),2)]);

hold on;

for i=2:length(R)

x0=a(R(i-1),1);

y0=a(R(i-1),2);

x1=a(R(i),1);

y1=a(R(i),2);

xx=[x0,x1];

yy=[y0,y1];

plot(xx,yy);

hold on;

end

end

(7)主函数

clear;

clc;

%%%%%%%%%%%%%%%输入参数%%%%%%%%

N=50; %%城市的个数

M=100; %%种群的个数

C=100; %%迭代次数

C_old=C;

m=2; %%适应值归一化淘汰加速指数

Pc=04; %%交叉概率

Pmutation=02; %%变异概率

%%生成城市的坐标

pos=randn(N,2);

%%生成城市之间距离矩阵

D=zeros(N,N);

for i=1:N

for j=i+1:N

dis=(pos(i,1)-pos(j,1))^2+(pos(i,2)-pos(j,2))^2;

D(i,j)=dis^(05);

D(j,i)=D(i,j);

end

end

%%如果城市之间的距离矩阵已知，可以在下面赋值给D，否则就随机生成

%%生成初始群体

popm=zeros(M,N);

for i=1:M

popm(i,:)=randperm(N);

end

%%随机选择一个种群

R=popm(1,:);

figure(1);

scatter(pos(:,1),pos(:,2),'rx');

axis([-3 3 -3 3]);

figure(2);

plot_route(pos,R); %%画出种群各城市之间的连线

axis([-3 3 -3 3]);

%%初始化种群及其适应函数

fitness=zeros(M,1);

len=zeros(M,1);

for i=1:M

len(i,1)=myLength(D,popm(i,:));

end

maxlen=max(len);

minlen=min(len);

fitness=fit(len,m,maxlen,minlen);

rr=find(len==minlen);

R=popm(rr(1,1),:);

for i=1:N

fprintf('%d ',R(i));

end

fprintf('\n');

fitness=fitness/sum(fitness);

distance_min=zeros(C+1,1); %%各次迭代的最小的种群的距离

while C>=0

fprintf('迭代第%d次\n',C);

%%选择 *** 作

nn=0;

for i=1:size(popm,1)

len_1(i,1)=myLength(D,popm(i,:));

jc=rand03;

for j=1:size(popm,1)

if fitness(j,1)>=jc

nn=nn+1;

popm_sel(nn,:)=popm(j,:);

break;

end

end

end

%%每次选择都保存最优的种群

popm_sel=popm_sel(1:nn,:);

[len_m len_index]=min(len_1);

popm_sel=[popm_sel;popm(len_index,:)];

%%交叉 *** 作

nnper=randperm(nn);

A=popm_sel(nnper(1),:);

B=popm_sel(nnper(2),:);

for i=1:nnPc

[A,B]=cross(A,B);

popm_sel(nnper(1),:)=A;

popm_sel(nnper(2),:)=B;

end

%%变异 *** 作

for i=1:nn

pick=rand;

while pick==0

pick=rand;

end

if pick<=Pmutation

popm_sel(i,:)=Mutation(popm_sel(i,:));

end

end

%%求适应度函数

NN=size(popm_sel,1);

len=zeros(NN,1);

for i=1:NN

len(i,1)=myLength(D,popm_sel(i,:));

end

maxlen=max(len);

minlen=min(len);

distance_min(C+1,1)=minlen;

fitness=fit(len,m,maxlen,minlen);

rr=find(len==minlen);

fprintf('minlen=%d\n',minlen);

R=popm_sel(rr(1,1),:);

for i=1:N

fprintf('%d ',R(i));

end

fprintf('\n');

popm=[];

popm=popm_sel;

C=C-1;

%pause(1);

end

figure(3)

plot_route(pos,R);

axis([-3 3 -3 3]);

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