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Introduction To Type-2 Fuzzy Logic Control:Theory and Applications

Cover Image Copyright Year: 2014
Author(s): Jerry Mendel; Hani Hagras; Woei-Wan Tan; William W. Melek; Hao Ying
Publisher: Wiley-IEEE Press
Content Type : Books & eBooks
Topics: Computing & Processing ;  General Topics for Engineers
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      FrontMatter

      Copyright Year: 2014

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      This chapter contains sections titled:
      Half-Title
      Series Page
      Title
      Copyright
      Dedication
      Contents
      Preface
      Contributors View full abstract»

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      Introduction

      Copyright Year: 2014

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      This is the introductory chapter of the book, which focuses on type-2 fuzzy logic control, and also provides background material about type-1 fuzzy logic control. It explains what type-1 fuzzy sets, type-1 fuzzy logic control, and type-2 fuzzy sets are. The author does this from a high-level perspective without touching on the mathematical aspects in order to give a feel for the nature of fuzzy sets and their applications. Nonlinear control involves a nonlinear relationship between the controller's inputs and outputs and is more complicated than linear control; however, it is able to achieve better performance than linear control for many real-world control applications. The chapter provides a brief overview of some of recent IT2 Mamdani fuzzy logic controllers (FLCs) for real-world control applications that are grouped into high-level application areas. View full abstract»

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      Introduction to Type-2 Fuzzy Sets

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      This chapter provides background materials about type-2 fuzzy sets (T2 FSs). To begun with, it reviews type-1 fuzzy sets (T1 FSs) because T2 FSs build upon T1 FSs. The chapter provides a lot of information about interval type-2 fuzzy sets (IT2 FSs). It then provides an introduction to the general type-2 fuzzy sets (GT2 FSs) because such sets are the wave of the future. The chapter shows how to derive formulas for the union and intersection of two IT2 FSs and also the formula for the complement of an IT2 FS because these operations are widely used in an IT2 FLC. Historically, the Karnik-Mendel (KM) algorithms were the first, and are still the most widely used, algorithms for computing the switch points. These algorithms are summarized in the chapter. View full abstract»

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      Interval Type-2 Fuzzy Logic Controllers

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      This chapter begins with short reviews of T1 Mamdani and TSK FLCs so as to set the stage for the complete descriptions of IT2 Mamdani and TSK FLCs. It focuses on the Wu-Mendel uncertainty bounds (WM UBs), which have let IT2 Mamdani FLCs run in real time. The chapter discusses about control performance for Interval Type-2 Fuzzy Logic Controllers (IT2 FLCs). It describes the two ways to determine FOU parameters of IT2 FLCs. The iterative nature of the EKM algorithms introduces time delays that may lead to unpredictability, reduced performance, or even system instability in a fuzzy logic control system. View full abstract»

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      Analytical Structure of Various Interval Type-2 Fuzzy PI and PD Controllers

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      This chapter stresses that the analytical structure of a fuzzy controller should be investigated in such a way that the structure is sensible in the context of control theory. It provides a brief review of the linear PID, PI, and PD controllers as most of the T2 fuzzy controllers. The chapter defines the common components of the T2 fuzzy controllers. It shows various techniques for deriving the explicit analytical structures of four different types of T2 Mamdani fuzzy controllers with two input variables and link the resulting structures to the PI and PD controllers. The chapter provides yet another derivation technique for a class of T2 TSK fuzzy controllers with two input variables and shows how the analytical structure obtained ties to the PI and PD controllers. It also establishes some design guidelines for the T2 Mamdani fuzzy controllers. View full abstract»

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      Analysis of Simplified Interval Type-2 Fuzzy PI and PD Controllers

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      This chapter focuses on the design, properties demonstration via simulations/experiments, and theoretical analysis of interval type-2 (IT2) fuzzy proportional plus integral (PI) or proportional plus derivative (PD) controllers. It presents the simplified IT2 fuzzy logic controllers (FLC). The chapter designs two type-1 FLCs and two type-2 FLCs with different degrees of Freedom, and their abilities to handle modeling uncertainties are compared using a coupled-tank liquid-level control system. It presents the methodology for deriving the analytical structure for a case of IT2 PI/PD FLCs, with the configuration. The algorithm delineated leverages on a property of the Karnik-Mendel (KM) type reducer that constrains the switch points to the location of the consequent sets to extend the analytical structure technique for T1 FLCs. The chapter also presents five examples that illustrate how the analytical structure framework may be applied. View full abstract»

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      On the Design of IT2 TSK FLCs

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      This chapter uses the TSK model structure for the design of IT2 FLCs. The approach is based on rigorous mathematical analyses for the design of IT2 FLCs, a development that plays a key role in this systematic design and analyses. TSK enables a mathematical formulation of FLCs that is very suitable for analytical design. The chapter begins by providing the preliminaries for IT2 TSK FLCs. Next, it presents a new inference engine for control design, and stability analyses for IT2 TSK FLCs. Then, the chapter describes a practical approach for the design of adaptive IT2 TSK FLCs for robot manipulators, and discusses the design of adaptive control with applications to robot manipulators. Finally, it presents robust control design. View full abstract»

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      Looking into the Future

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      This chapter focuses on where we feel T2 FL control should be heading. The authors of each section are identified and have an opportunity to express their viewpoints on where they feel T2 FL control should be heading. The book presents the foundations of IT2 FL control and provides several methodologies for modeling and control that utilize this advanced approach. The emphasis is on the simplest kind of T2 FL control, namely IT2 FL control that uses singleton fuzzification. Mamdani IT2 FLCs as discussed throughout most of this book are based on IT2 FSs. The book demonstrates that IT2 FL control is a diverse field of rich promise; however, a central challenge is to increase the number of applications and users in order to bring IT2 FL control into the mainstream of automation and control. View full abstract»

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      Appendix A T2 FLC Software: From Type-1 to zSlices-Based General Type-2 FLCs

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      References

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      Index

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      IEEE Press Series on Computational Intelligence

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