how to write fuzzy rules for pd controller

Respected Sir, please tell me how to write fuzzy rules for proportional-derivative controller and proportional integral controller. BY the way to get same response in simulink as these conventional controller(PI & PD)replacing with FL controller.

Answer 1

[Sam Chak]

To design a fuzzy controller that achieves the same performance as a conventional PI or PD controller, we can use a 9-rule Sugeno fuzzy system for clarity (although similar performance can be 100% obtained with only 4 rules [see Hao Ying’s early 90's papers]). Specifically, we design a linear fuzzy system with a mathematical structure of the form z = x + y. For example, x is the proportional-gained error () and y is the derivative-gained change in error (). If necessary, the fuzzy output can then be externally scaled to match the desired magnitude.

For more details, please refer to the "Construct Type-1 FIS" section in the following article:

https://www.mathworks.com/help/fuzzy/fuzzy-pid-control-with-type-2-fis.html

fis1 = sugfis;

% define the universe of discourse for inputs
fis1 = addInput(fis1, [-1  1], Name="E");   % Input 1: Error
fis1 = addInput(fis1, [-1  1], Name="CE");  % Input 2: Change in Error

% Input 1 fuzzy sets
fis1 = addMF(fis1,  "E", "trimf", [-2 -1  0], Name="N");    % Negative
fis1 = addMF(fis1,  "E", "trimf", [-1  0  1], Name="Z");    % Zero
fis1 = addMF(fis1,  "E", "trimf", [ 0  1  2], Name="P");    % Positive

% Input 2 fuzzy sets
fis1 = addMF(fis1, "CE", "trimf", [-2 -1  0], Name="N");    % Negative
fis1 = addMF(fis1, "CE", "trimf", [-1  0  1], Name="Z");    % Zero
fis1 = addMF(fis1, "CE", "trimf", [ 0  1  2], Name="P");    % Positive

figure
subplot(2,1,1)
plotmf(fis1, "input", 1, 2001), grid on
title("MFs for Input 1: Error")
subplot(2,1,2)
plotmf(fis1, "input", 2, 2001), grid on
title("MFs for Input 2: Change in Error")

% define the universe of discourse for the output
fis1 = addOutput(fis1, [-2  2], Name="U");  % Fuzzy Control Output, U

% These are actually Singleton MFs
fis1 = addMF(fis1, "U", "constant", -2.0, Name="NB");   % Negative Big
fis1 = addMF(fis1, "U", "constant", -1.0, Name="NM");   % Negative Medium
fis1 = addMF(fis1, "U", "constant",  0.0, Name="ZO");   % Zero
fis1 = addMF(fis1, "U", "constant",  1.0, Name="PM");   % Positive Medium
fis1 = addMF(fis1, "U", "constant",  2.0, Name="PB");   % Positive Big

% Fuzzy Rules
rules = [...
    "if E is N and CE is N then U is NB (1)";   % rule 1
    "if E is Z and CE is N then U is NM (1)";   % rule 2
    "if E is P and CE is N then U is ZO (1)";   % rule 3
    "if E is N and CE is Z then U is NM (1)";   % rule 4
    "if E is Z and CE is Z then U is ZO (1)";   % rule 5
    "if E is P and CE is Z then U is PM (1)";   % rule 6
    "if E is N and CE is P then U is ZO (1)";   % rule 7
    "if E is Z and CE is P then U is PM (1)";   % rule 8
    "if E is P and CE is P then U is PB (1)";   % rule 9
    ];
fis1 = addRule(fis1, rules);

figure
opt = gensurfOptions('NumGridPoints', 51);
gensurf(fis1, opt)
title("Control surface of a Linear Fuzzy PD Controller")