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

Ritu Raj; Murali Mohan Bosukonda

doi:10.26599/FIE.2023.9270004

Fuzzy Information and Engineering 2023, 15(1): 36-54 https://doi.org/10.26599/FIE.2023.9270004

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Open Access | Issue | Published: 24 March 2023

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

Show Author's Information Hide Author's Information Ritu Raj^¹(

), Murali Mohan Bosukonda^²

1Department of Electronics and Communication Engineering, Indian Institute of Information Technology Kota, MNIT Campus, Jaipur 302017, India

2Department of Electrical Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India

Keywords:

mathematical model, fuzzy control, Takagi−Sugeno controller, TITO controller, variable gain controller

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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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.

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

Show Author's information Hide Author's Information Ritu Raj^¹(

), Murali Mohan Bosukonda^²

1Department of Electronics and Communication Engineering, Indian Institute of Information Technology Kota, MNIT Campus, Jaipur 302017, India

2Department of Electrical Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India

Abstract

Keywords: mathematical model, fuzzy control, Takagi−Sugeno controller, TITO controller, variable gain controller

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Received: 23 January 2019

Revised: 06 September 2022

Accepted: 15 January 2023

Published: 24 March 2023

Issue date: March 2023

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