How to generate 2-D Lookup Table data for a 3-Output Fuzzy Logic System

I want design a look up table for fuzzy logic which has 2 inputs and 3 outputs. I referred to help on mathworks however its for 2 inputs and 1 output. Please refer to attached image.

https://www.mathworks.com/help//releases/R2021a/fuzzy/implement-fuzzy-pid-controller-in-simulink-using-lookup-table.html#d123e17778

Please suggest a way to create look up table for fuzzy logic using 2 inputs and 3 outputs.

[Venkateshkumar Mohan]

you can do this. first open fuzzy tool box and select edit and go to add variable ( input and output )

Answer 1

[Sam Chak]

Hi @Aditya Gandhi

The code in your image is flawed, as it should have used 'LookUpTableData(j,i)' instead of 'LookUpTableData(i,j)'. This mistake went unnoticed for many years because the ranges of the Error (E) and the Change in Error (CE) are identical, and the design of the control surface is linear and symmetrical.

The solution from a similar question also uses the evalfis() function to generate the 2-D lookup table data for a 2-input, 1-output Fuzzy PID controller using a for-loop indexing approach. For users who are unfamiliar with looping and indexing, the following solution can directly generate the 2-D lookup table data for a 2-input, 3-output fuzzy system using the gensurf() function. The desired output and the number of grid points for the 2-D table can be selected via the 'OutputIndex' and 'NumGridPoints' options in the gensurfOptions() function.

%% World's simplest Fuzzy PID Gain Scheduler (not a Controller yet!)
fis = sugfis;

% Fuzzy Input E
fis = addInput(fis,  [-1 +1], 'Name', 'E');
fis = addMF(fis, 'E',  'trapmf', [-2 -2 +2 +2], 'Name', 'All-Encompassing');

% Fuzzy Input CE
fis = addInput(fis,  [-1 +1], 'Name', 'CE');
fis = addMF(fis, 'CE', 'trapmf', [-2 -2 +2 +2], 'Name', 'All-Encompassing');

% Fuzzy Output 1 Kp
fis = addOutput(fis, [0 2], 'Name', 'Kp');
kp  = 1;    % proportional gain
fis = addMF(fis, 'Kp', 'constant', kp, 'Name', 'kp_gain');

% Fuzzy Output 2 Ki
fis = addOutput(fis, [2 4], 'Name', 'Ki');
ki  = 2;    % integral gain
fis = addMF(fis, 'Ki', 'constant', ki, 'Name', 'ki_gain');

% Fuzzy Output 3 Kd
fis = addOutput(fis, [1 3], 'Name', 'Kd');
kd  = 3;    % derivative gain
fis = addMF(fis, 'Kd', 'constant', kd, 'Name', 'kd_gain');

% Fuzzy Rule
fis = addRule(fis, "If E is All-Encompassing and CE is All-Encompassing then Kp is kp_gain, Ki is ki_gain, Kd is kd_gain");

%% Testing evalfis outputs
e   = (-1:0.5:1)';
ce  = e;
K   = evalfis(fis, [e ce])

K = 5×3

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

%% PLot results
figure
subplot(211)
plotmf(fis, 'input', 1), grid on, ylim([-0.2, 1.2]), 
xlabel('Error'), title('Only one membership function of E')

subplot(212)
plotmf(fis, 'input', 2), grid on, ylim([-0.2, 1.2]), 
xlabel('Change in Error'), title('Only one membership function of CE')

%% Generate the 2-D lookup table data using gensurf
opt1 = gensurfOptions('OutputIndex', 1, 'NumGridPoints', 51);
[E, CE, Kp] = gensurf(fis, opt1);   % <-- generate 2-D Lookup Table data for Kp

figure
surf(E, CE, Kp);
xlabel('Error'), ylabel('Change in Error'), zlabel('Kp')
title ('Fuzzy Kp Gain Surface')

opt2 = gensurfOptions('OutputIndex', 2, 'NumGridPoints', 51);
[E, CE, Ki] = gensurf(fis, opt2);   % <-- generate 2-D Lookup Table data for Ki

figure
surf(E, CE, Ki);
xlabel('Error'), ylabel('Change in Error'), zlabel('Ki')
title ('Fuzzy Ki Gain Surface')

opt3 = gensurfOptions('OutputIndex', 3, 'NumGridPoints', 51);
[E, CE, Kd] = gensurf(fis, opt3);   % <-- generate 2-D Lookup Table data for Kd

figure
surf(E, CE, Kd);
xlabel('Error'), ylabel('Change in Error'), zlabel('Kd')
title ('Fuzzy Kd Gain Surface')