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Modelling and Simulation in Engineering
Volume 2011, Article ID 573715, 7 pages
Research Article

Mathematical Models of the Simplest Fuzzy Two-Term (PI/PD) Controllers Using Algebraic Product Inference

Department of Electrical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

Received 31 March 2011; Accepted 5 September 2011

Academic Editor: Agostino Bruzzone

Copyright © 2011 Murali Bosukonda and Naresh Kelothu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper reveals mathematical models of the simplest Mamdani PI/PD controllers which employ two fuzzy sets (N: negative and P: positive) on the universe of discourse (UoD) of each of two input variables (displacement and velocity) and three fuzzy sets (N: negative, Z: zero, and P: positive) on the UoD of output variable (control output in the case of PD, and incremental control output in the case of PI). The basic constituents of these models are algebraic product/minimum AND, bounded sum/algebraic sum/maximum OR, algebraic product inference, three linear fuzzy control rules, and Center of Sums (CoS) defuzzification. Properties of all these models are investigated. It is shown that all these controllers are different nonlinear PI/PD controllers with their proportional and derivative gains changing with the inputs. The proposed models are significant and useful to control community as they are completely new and qualitatively different from those reported in the literature.