how to DESIGN ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM (ANFIS)

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great do 2022-8-14

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评论： Sam Chak 2024-1-8

if my state space representation is given by:

%State-space representation of the system

A= [-23.5 120 32];

B= [18 0; 0 500; ];

C=[0 0 1 0 0 0];

D=[0 0;0 0];

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Sam Chak 2024-1-8

在 MATLAB Online 中打开

It appears that there may have been an accident. I think the subsequent statement represents the initial description of the question provided by @welesh beyene:

------------------------------------------

if my state space representation is given by:

%State-space representation of the system 
A= [-300 0 0 0 0 0; 0 -300 0 0 0 0; 0 0 0 0 1 0; 0 0 0 0 0 1; 10.7206 -9.5648 10.7206 -9.5648 0 0; -9.5648 10.7206 -9.5648 10.7206 0 0];
B= [300 0; 0 300; 0 0; 0 0; 0 0; 0 0];              
C=[0 0 1 0 0 0;0 0 0 1 0 0]; 
D=[0 0;0 0]; 
%states={'iA' 'iB' 'XA' 'XB' 'XdotA' 'XdotB'}; 
%inputs={'UA' 'UB'}; 
%outputs = {'YA' 'YB'}; 
sys=ss(A,B,C,D)
%Open-Loop Step Response 
step(sys)
title('Open-Loop Step Response') 
figure(1)
% check the controllability of the system 
Ct=ctrb(A,B);  
rank(Ct) 
if rank(Ct)<rank(A); 
    disp('the system is not controllable') 
else  
    disp('the system is controllable') 
end 
% check the observability of the system  
Ob=obsv(A,C);    
rank(Ob) 
if rank(Ob)<rank(A); 
    disp('the system is not observable') 
else  
    disp('the system is observable') 
end 

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Answer 1

Sam Chak 2022-8-14

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1779030-how-to-design-adaptive-neuro-fuzzy-inference-system-anfis#answer_1026205

在 MATLAB Online 中打开

Hi @welesh beyene

Have already recommended you to use ode45() function. Links and Examples were given previously.

https://www.mathworks.com/matlabcentral/answers/1776845-how-to-extract-data-from-sys-ss-a-b-c-d-that-is-inputs-and-outputs?s_tid=prof_contriblnk

This should generate the inputs–outputs that you need to train the ANFIS:

[t, x] = ode45(@system, [0 10], [0; 0; 0; 0; 0; 0]);

figure(1)

subplot(211), plot(t, x(:,3)), grid on, xlabel('t'), ylabel('y_3')

subplot(212), plot(t, x(:,4)), grid on, xlabel('t'), ylabel('y_4')

A = [-300 0 0 0 0 0; 0 -300 0 0 0 0; 0 0 0 0 1 0; 0 0 0 0 0 1; 10.7206 -9.5648 10.7206 -9.5648 0 0; -9.5648 10.7206 -9.5648 10.7206 0 0];

B = [300 0; 0 300; 0 0; 0 0; 0 0; 0 0];

Q = diag([0.1, 0.1, 0.1, 0.1, 1, 1]);

R = diag([10, 10]);

K = lqr(A, B, Q, R);

u1 = - K(1,:)*x' + 1;

u2 = - K(2,:)*x' + 1;

data1 = [x u1']; % Data Set 1

data2 = [x u2']; % Data Set 2

figure(2)

subplot(211), plot(t, u1), grid on, xlabel('t'), ylabel('u_1')

subplot(212), plot(t, u2), grid on, xlabel('t'), ylabel('u_2')

% 6th-order system

function dxdt = system(t, x)

A = [-300 0 0 0 0 0; 0 -300 0 0 0 0; 0 0 0 0 1 0; 0 0 0 0 0 1; 10.7206 -9.5648 10.7206 -9.5648 0 0; -9.5648 10.7206 -9.5648 10.7206 0 0];

B = [300 0; 0 300; 0 0; 0 0; 0 0; 0 0];

Q = diag([0.1, 0.1, 0.1, 0.1, 1, 1]);

R = diag([10, 10]);

K = lqr(A, B, Q, R);

r = [1; 1];

u = - K*x + r;

dxdt = A*x + B*u;

end

Because the following code for ANFIS training takes more 55 seconds, it won't work in the forum.

% setting up the ANFIS
genOpt = genfisOptions('GridPartition');
genOpt.NumMembershipFunctions = 3;
genOpt.InputMembershipFunctionType = 'gaussmf';
inFIS1 = genfis(data1(:,1:6), data1(:,7), genOpt);
opt1   = anfisOptions('InitialFIS', inFIS1, 'EpochNumber', 60);
fis1   = anfis(data1, opt1);
inFIS2 = genfis(data2(:,1:6), data2(:,7), genOpt);
opt2   = anfisOptions('InitialFIS', inFIS2, 'EpochNumber', 60);
fis2   = anfis(data2, opt2);

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great do 2022-8-16

编辑：great do 2022-8-16

let me tell you shortly , my target is ,to compare LQR and ANFIS result for my system but still now i didnt get satsfied answer with training of ANFIS.

when i run the code what you said above that is, the code below. it says

function dxdt = system(t, x)

↑

Error: Function definition not supported in this context. Create functions in code file.

so please, write all approprate codes for training of ANFIS for my system with its graphs.

function dxdt = system(t, x)

A = [-300 0 0 0 0 0; 0 -300 0 0 0 0; 0 0 0 0 1 0; 0 0 0 0 0 1; 10.7206 -9.5648 10.7206 -9.5648 0 0; -9.5648 10.7206 -9.5648 10.7206 0 0];

B = [300 0; 0 300; 0 0; 0 0; 0 0; 0 0];

Q = diag([0.1, 0.1, 0.1, 0.1, 1, 1]);

R = diag([10, 10]);

K = lqr(A, B, Q, R);

r = [1; 1];

u = - K*x + r;

dxdt = A*x + B*u;

end

% setting up the ANFIS

genOpt = genfisOptions('GridPartition');

genOpt.NumMembershipFunctions = 3;

genOpt.InputMembershipFunctionType = 'gaussmf';

inFIS1 = genfis(data1(:,1:6), data1(:,7), genOpt);

opt1 = anfisOptions('InitialFIS', inFIS1, 'EpochNumber', 60);

fis1 = anfis(data1, opt1);

inFIS2 = genfis(data2(:,1:6), data2(:,7), genOpt);

opt2 = anfisOptions('InitialFIS', inFIS2, 'EpochNumber', 60);

fis2 = anfis(data2, opt2);

great do 2022-8-18

ya you are correct, i simply copied and pasted it. so please tell how to generate data for that state space representation because if input and output data is obtain, then by saving in work space or in a file it is easy for training.i understand already the process but difficult in data generating for my system.