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Functional Fractional Calculus for System Identification and Controls

  • Book
  • © 2008

Overview

Authors:
  1. Shantanu Das

    1. Reactor Control Division, BARC

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  • Staringt point for research in applicatiosn of fractional calculus
  • The reader gets a feeling of the wide applicabilityof fractional calculus in the field of science and engineering
  • Written for a wide range of readers, who wish to learn the basic concepts of Fractional Calculus and its Applications
  • A starter can understand the concepts of this emerging field with a minimal effort and basic mathematics

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XVII
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  2. Introduction to Fractional Calculus

    • Shantanu Das
    Pages 1-18

  3. Functions Used in Fractional Calculus

    • Shantanu Das
    Pages 19-34

  4. Observation of Fractional Calculus in Physical System Description

    • Shantanu Das
    Pages 35-61

  5. Concept of Fractional Divergence and Fractional Curl

    • Shantanu Das
    Pages 63-79

  6. Fractional Differintegrations: Insight Concepts

    • Shantanu Das
    Pages 81-107

  7. Initialized Differintegrals and Generalized Calculus

    • Shantanu Das
    Pages 109-127

  8. Generalized Laplace Transform for Fractional Differintegrals

    • Shantanu Das
    Pages 129-156

  9. Application of Generalized Fractional Calculus in Electrical Circuit Analysis

    • Shantanu Das
    Pages 157-180

  10. Application of Generalized Fractional Calculus in Other Science and Engineering Fields

    • Shantanu Das
    Pages 181-204

  11. System Order Identification and Control

    • Shantanu Das
    Pages 205-232

  12. Back Matter

    Pages 233-240
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Keywords

About this book

This work is inspired by thought to have an overall fuel-ef?cient nuclear plant control system. I picked up the topic in 2002 while deriving the reactor control laws, which aimed at fuel ef?ciency. Controlling the nuclear reactor close to its natural behavior by concept of exponent shape governor, ratio control and use of logarithmic logic, aims at the fuel ef?ciency. The power-maneuvering trajectory is obtained by shaped-normalized-period function, and this de?nes the road map on which the reactor should be governed. The experience of this concept governing the Atomic Power Plant of Tarapur Atomic Power Station gives lesser overall gains compared to the older plants, where conventional proportional integral and deri- tive type (PID) scheme is employed. Therefore, this motivation led to design the scheme for control system than the conventional schemes to aim at overall plant ef?ciency. Thus, I felt the need to look beyondPID and obtained the answer in fr- tional order control system, requiring fractional calculus (a 300-year-old subject). This work is taken from a large number of studies on fractional calculus and here it is aimed at giving an application-orientedtreatment, to understandthis beautiful old new subject. The contribution in having fractional divergence concept to describe neutron ?ux pro?le in nuclear reactors and to make ef?cient controllers based on fractional calculus is a minor contribution in this vast (hidden) area of science.

Reviews

From the reviews:

"The book under review, entitled ‘Functional fractional calculus for system identification and controls’, which is organized into ten chapters, appears to be fairly inspiring for those who are engaged in varied applications of the fractional calculus. The chapters comprising the book are, according to the author’s intention, made as application oriented from various science and engineering fields." (P. K. Banerji, Zentralblatt MATH, Vol. 1154, 2009)

“This book introduces fractional calculus to researchers and practicing engineers by giving an applications-oriented treatment of the subject.” (IEEE Control Systems Magazine, Vol. 29, October, 2009)

Authors and Affiliations

  • Reactor Control Division, BARC

    Shantanu Das

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