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Article | Open Access

Mathematical Modelling and Analysis of the Simplest Fuzzy Two-Input Two-Output Two-Term Controller of Takagi−Sugeno Type

Ritu Raj1( ), Murali Mohan Bosukonda2
Department of Electronics and Communication Engineering, Indian Institute of Information Technology Kota, MNIT Campus, Jaipur 302017, India
Department of Electrical Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India
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Abstract

Mathematical modelling of the simplest Takagi−Sugeno fuzzy Two-Input Two-Output (TITO) Proportional-Integral/Proportional-Derivative (PI/PD) controller is presented in this paper. Mathematical model of fuzzy PI/PD controller is proposed using Algebraic Product (AP) t-norm, Bounded Sum (BS) t-co-norm and Center of Gravity (CoG) defuzzifier. The inputs are fuzzified by fuzzy sets having L and Γ type membership functions. The rule base consists of five rules with different linear models in the consequent parts. Both static and dynamic couplings are taken into account while deriving the models. The model of the fuzzy PI/PD controller reveals that it is a variable gain/structure controller. Also, each output of the TITO fuzzy controller is the sum of two nonlinear PI or PD controllers with variable gains. The properties and the gain variations of the controllers are investigated.

Keywords

fuzzy controlmathematical modelTakagi−Sugeno controllerTITO controllervariable gain controller

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Fuzzy Information and Engineering
Volume 15 Issue 1,
March 2023
Pages 36-54
DOI: 10.26599/FIE.2023.9270004
Cite this article:
Raj R, Mohan Bosukonda M. Mathematical Modelling and Analysis of the Simplest Fuzzy Two-Input Two-Output Two-Term Controller of Takagi−Sugeno Type. Fuzzy Information and Engineering, 2023, 15(1): 36-54. https://doi.org/10.26599/FIE.2023.9270004

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Received: 23 January 2019
Revised: 06 September 2022
Accepted: 15 January 2023
Published: 24 March 2023
© The Author(s) 2023. Published by Tsinghua University Press.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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