Title: Mathematical modelling of the simplest fuzzy two-input two-output proportional integral or proportional derivative controller via Larsen product inference

Authors: N.K. Arun; B.M. Mohan

Addresses: Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, 721 302, India ' Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, 721 302, India

Abstract: In this paper, a mathematical model of the simplest Mamdani type fuzzy two-input two-output (TITO) proportional integral (PI) or proportional derivative (PD) controller using Larsen product inference is presented. Components of the fuzzy controller include two fuzzy sets on each input variable, five fuzzy sets on each output variable, five linear control rules, algebraic product AND operator, bounded sum OR operator, Larsen product inference, and Centre of Sums (CoS) defuzzification. Each output of the fuzzy controller is shown to be the sum of two nonlinear PI (or PD) controllers with variable gains that change continuously with TITO process outputs.

Keywords: fuzzy control; TITO control; PI control; PD control; variable gain control; nonlinear control; variable structure control; VSC; mathematical modelling; Mamdani type controller; Larsen product inference; fuzzy sets.

DOI: 10.1504/IJAAC.2016.075139

International Journal of Automation and Control, 2016 Vol.10 No.1, pp.34 - 51

Available online: 04 Mar 2016 *

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