NDLI: Analytical Structure and Characteristics of Symmetric Karnik–Mendel Type-Reduced Interval Type-2 Fuzzy PI and PD Controllers

Content Provider	IEEE Xplore Digital Library
Author	Maowen Nie Woei Wan Tan
Copyright Year	1993
Abstract	This paper presents the analytical structure of a class of interval type-2 (IT2) fuzzy proportional derivative (PD) and proportional integral (PI) controllers that have symmetrical rule base and symmetrical consequent sets. Two assumptions are made: 1) The Zadeh AND operator is employed as the t-norm operator; 2) type-reduction is performed by the Karnik-Mendel (KM) type-reduction method. The main contributions are the methodology that identifies the input conditions, where the KM algorithm uses a new switch point to compute the bounds of the type-reduced set, the closed-form expressions that relate the inputs and output of an IT2 fuzzy controller, and insights into the potential performance improvement because of the inclusion of the footprint of uncertainty (FOU). Compared with its T1 counterpart, two additional FOU parameters generate 31 extra local regions, each providing a unique relationship between the inputs and output signals. The generation of a relatively large number of local regions at the cost of two extra design parameters indicates that an IT2 fuzzy controller may be able to provide better performance. Furthermore, by comparing the analytical structure with the corresponding T1 counterpart, the potential advantages to use the IT2 over the T1 fuzzy controller are studied. Four interesting characteristics are identified, and they provide insights into why the IT2 fuzzy controller may better balance the conflicting aims of fast rise time and small overshoot.
Sponsorship	IEEE Computational Intelligence Society
Starting Page	416
Ending Page	430
Page Count	15
File Size	1454286
File Format	PDF
ISSN	10636706
Volume Number	20
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	PD control Frequency selective surfaces Switches Aerospace electronics Fuzzy logic Upper bound Uncertainty interval type-2 (IT2) fuzzy logic system Analytical structure fuzzy proportional derivative (PD) and proportional integral (PI) controllers
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Control and Systems Engineering Computational Theory and Mathematics

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