Title: The simplest fuzzy two-term controllers: mathematical models and stability analysis

Authors: B.M. Mohan, Arpita Sinha

Addresses: Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, India. ' Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, India

Abstract: This paper reveals mathematical models for some simplest fuzzy two-term (PI/PD) controllers which employ two symmetric fuzzy sets for each of the two input variables and three symmetric fuzzy sets for the output variable. The basic constituents of these models are Γ-function type and L-function type membership functions for the input variables and triangular membership functions for the output variable, minimum triangular norm, algebraic sum triangular conorm, different inference methods and Centre of Sums (COS) defuzzification method. The properties of these models are studied to examine their suitability for control application. Using the well-known small-gain theorem, sufficient condition for Bounded-Input Bounded-Output (BIBO) stability of a feedback system, containing any fuzzy controller as a subsystem, is established. Finally, some numerical examples along with their simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI/PD controllers.

Keywords: mathematical models; two-term controllers; minimum triangular norm; algebraic sum triangular conorm; BIBO stability; fuzzy control.

DOI: 10.1504/IJAAC.2008.020426

International Journal of Automation and Control, 2008 Vol.2 No.1, pp.5 - 21

Published online: 24 Sep 2008 *

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