Title: Fuzzy two-term controllers with multi-fuzzy sets: mathematical models and analysis

Authors: B.M. Mohan; Arpita Ghosh

Addresses: Department of Electrical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India. ' Material Science and Technology Division, National Metallurgical Laboratory, Jamshedpur 831007, India

Abstract: This paper first presents mathematical models for fuzzy two-term (PI/PD) controllers which employ N₁ (≥3) number of symmetric fuzzy sets for the input variable displacement, N₂ (≥3) number of symmetric fuzzy sets for the input variable velocity and N₁ + N₂ − 1 number of symmetric fuzzy sets for the output variable. These models are derived via triangular membership functions for fuzzification of the inputs and output variables, linear control rules, minimum/algebraic product triangular norm, different triangular conorms, different inference methods and centre of sums (COS) defuzzification method. Properties of such models are investigated. Using the well-known small-gain theorem bounded-input bounded-output (BIBO) stability analysis of feedback systems involving fuzzy PD controller as a subsystem is presented. Next, mathematical models with N₁ and N₂ number of asymmetric input fuzzy sets and N₁ + N₂ − 1 number of asymmetric output fuzzy sets (both triangular and trapezoidal) are also presented. Finally, some numerical examples along with their simulation results are included to demonstrate the effectiveness of the fuzzy two-term controllers.

Keywords: fuzzy control; PI control; PD control; mathematical modelling; BIBO stability; fuzzy logic; feedback systems; fuzzy sets; two-term controllers.

DOI: 10.1504/IJMIC.2012.045692

International Journal of Modelling, Identification and Control, 2012 Vol.15 No.3, pp.199 - 218

Published online: 29 Nov 2014 *

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