Nonuniqueness of mathematical models of the simplest three-input Mamdani fuzzy proportional-integral-derivative controllers

Sadhna Malik and B. M. Mohan

International Journal of Systems Science, 2025, vol. 56, issue 16, 4157-4169

Abstract: Mathematical modelling of various fuzzy controllers has been extensively researched and well-documented. As a result, it is well-known that the model of a fuzzy controller depends on several factors, including AND operator, OR operator, inference method, aggregation operator, and defuzzification method. As it appears from the literature, Maximum (Max) aggregation operator has been often used in the modelling of fuzzy controllers. However, utilisation of Bounded Sum (BS) aggregation operator has been rarely seen. This paper aims to address three important issues: (i) studying the characteristics of three-input fuzzy Proportional-Integral-Derivative (PID) controllers developed via BS aggregation operator, (ii) studying the uniqueness of all 14 possible three-input fuzzy PID controllers, and (iii) studying the computational aspects of unique controllers. Surprisingly, it has been observed that the controllers developed using the BS aggregation operator are not unique. Moreover, out of 14 controllers, only nine have been identified as distinct and appropriate for control purposes, while one controller has been deemed unsuitable for control.

Date: 2025
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DOI: 10.1080/00207721.2025.2486158

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