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Interval Type-2 Fuzzy PID Controllers

  • Chapter
Springer Handbook of Computational Intelligence

Part of the book series: Springer Handbooks ((SHB))

Abstract

The aim of this chapter is to present a general overview about interval type-2 fuzzy GlossaryTerm

PID

(proportional-integral-derivative) controller structures. We will focus on the standard double input direct action type fuzzy GlossaryTerm

PID

controller structures and their present design methods. It has been shown in various works that the type-1 fuzzy GlossaryTerm

PID

controllers, using crisp type-1 fuzzy sets, might not be able to fully handle the high levels of uncertainties associated with control applications while the type-2 fuzzy GlossaryTerm

PID

controller using type-2 fuzzy sets might be able to handle such uncertainties to produce a better control performance. Thus, we will classify and examine the handled fuzzy GlossaryTerm

PID

controllers within two groups with respect to the fuzzy sets they employ, namely type-1 and interval type-2 fuzzy sets. We will present and examine the controller structures of the direct action type-1 fuzzy GlossaryTerm

PID

and interval type-2 fuzzy GlossaryTerm

PID

controllers on a generic, a symmetrical 3 × 3 rule base. We will present general information about the type-1 fuzzy GlossaryTerm

PID

and interval type-2 fuzzy GlossaryTerm

PID

controllers tuning parameters and design strategies. Finally, we will present a simulation study to evaluate the control performance of the type-1 fuzzy GlossaryTerm

PID

and interval type-2 fuzzy GlossaryTerm

PID

on a first-order plus time-delay benchmark process.

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Abbreviations

FLC:

fuzzy logic controller

FOU:

footprint of uncertainty

FPID:

fuzzy PID

FS:

fuzzy set

IT2:

interval type-2

ITAE:

integral time absolute error

KM:

Karnik–Mendel

MF:

membership function

OS:

overshoot

PID:

proportional-integral-derivative

RAM:

random access memory

SF:

scaling factor

T1:

type-1

T2:

type-2

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Author information

Authors and Affiliations

  1. Control Engineering Dep., Istanbul Technical University, 34469, Maslak, Istanbul, Turkey

    Tufan Kumbasar

  2. The Computational Intelligence Centre, University of Essex, Wivenhoe Park, CO4 3SQ, Colchester, UK

    Hani Hagras

Authors
  1. Tufan Kumbasar
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  2. Hani Hagras
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Corresponding author

Correspondence to Tufan Kumbasar .

Editor information

Editors and Affiliations

  1. Systems Research Inst., Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Dep. Electrical and Computer Engineering, University of Alberta, 116 Street 9107, T6J 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

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Kumbasar, T., Hagras, H. (2015). Interval Type-2 Fuzzy PID Controllers. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_18

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  • DOI: https://doi.org/10.1007/978-3-662-43505-2_18

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  • Print ISBN: 978-3-662-43504-5

  • Online ISBN: 978-3-662-43505-2

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