Analytical structures and analysis of the simplest fuzzy PD controllers

This paper deals with simplest fuzzy PD controllers which employ only two fuzzy sets on the universe of discourse of each input variable, and three fuzzy sets on the universe of discourse of output variable. First, analytical structures of the simplest fuzzy PD controllers are derived via triangular...

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Published inIEEE transactions on systems, man and cybernetics. Part B, Cybernetics Vol. 32; no. 2; pp. 239 - 248
Main Authors Mohan, B.M., Patel, A.V.
Format Journal Article
LanguageEnglish
Published United States IEEE 01.04.2002
Subjects
Boilers
Control systems
Controllers
Cybernetics
Fuzzy
Fuzzy control
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Fuzzy systems
Input variables
Mathematical analysis
PD control
Stability analysis
Steam engines
Sufficient conditions
Universe
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Summary:This paper deals with simplest fuzzy PD controllers which employ only two fuzzy sets on the universe of discourse of each input variable, and three fuzzy sets on the universe of discourse of output variable. First, analytical structures of the simplest fuzzy PD controllers are derived via triangular membership functions for fuzzification, intersection T-norm, Lukasiewicz OR and Zadeh (1965) OR T-conorms, Mamdani's minimum, Larsen's product and drastic product inference methods, and center of area method for defuzzification. Properties of such fuzzy PD controllers are investigated. Based on these properties a comparative study is made on fuzzy controllers derived, and also on the fuzzy controllers and their counterpart-conventional linear PD controller. Finally, sufficient conditions for bounded-input bounded-output stability of fuzzy PD control systems are established using the well known small gain theorem.
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ISSN:1083-4419
1941-0492
DOI:10.1109/3477.990881