How to design a Fuzzy Controller for the Plant 1/(s² + 2·s + 100) to track the Reference signal

How to make rules for above question?

Answer 1

[Sam Chak]

Hi @salman saeed

The plant has a low DC gain of and a relatively small damping coefficient of 2. If we apply a static gain of 100 (proportional control action) to achieve a DC gain of 1, the step response of the open-loop system will still exhibit oscillatory behavior. Therefore, we need to add damping to the system through derivative control action. For the derivative action, we can design only two If–Then rules for the fuzzy controller.

%% Fuzzy Controller
fis = mamfis;

% Fuzzy Input (Change in Error)
fis = addInput(fis, [-4 +4], 'Name', 'CE');
fis = addMF(fis, 'CE', 'linzmf', [-4 +4], 'Name', 'N');
fis = addMF(fis, 'CE', 'linsmf', [-4 +4], 'Name', 'P');

% Fuzzy Output (Derivative Control Action)
fis = addOutput(fis,  [-8 +8], 'Name', 'U');
fis = addMF(fis, 'U', 'trimf', [-4 -4 -4], 'Name', 'N');
fis = addMF(fis, 'U', 'trimf', [ 4  4  4], 'Name', 'P');

% Fuzzy Rules
rules = [
    "CE==N => U=N"    % Rule 1: If CE is Negative, then U is Negative.
    "CE==P => U=P"    % Rule 2: If CE is Positive, then U is Positive.
    ];
fis = addRule(fis, rules);

figure
subplot(211)
plotmf(fis, 'input',  1, 801),   grid on, title('Input fuzzy sets')
subplot(212)
plotmf(fis, 'output', 1, 16001), grid on, title('Output fuzzy sets')