Analogue Realization of Fractional Order Controllers

Petras I., Podlubny I., O'Leary P., Dorcak L., Vinagre B.: Analogue Realization of Fractional Order Controllers. FBERG, Technical University of Kosice, Kosice, 2002, 84 pages, ISBN 8070996277.

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Table of Contents

• Preface
• 1 Introduction
• 2 Fundamentals of Fractional Calculus
  • 2.1 Introduction to fractional calculus
  • 2.2 Riemann-Liouville fractional integrals and derivatives
    • 2.2.1 Definitions
    • 2.2.2 Properties
  • 2.3 Laplace transform method
    • 2.3.1 Basic facts on the Laplace transform
    • 2.3.2 Laplace transform of fractional integrals
    • 2.3.3 Laplace transform of fractional derivatives
  • 2.4 Fourier transform method
    • 2.4.1 Basic facts on the Fourier transform
    • 2.4.2 Fourier transform of fractional integrals
    • 2.4.3 Fourier transform of fractional derivatives
  • 2.5 Fractional differential equations and transfer functions
• 3 Fractional-Order Controllers
  • 3.1 Definition of fractional PI^λD^μ controller
  • 3.2 Properties and characteristics of controller
    • 3.2.1 General considerations
    • 3.2.2 Bode ideal loop transfer function
    • 3.2.3 Illustrative example
  • 3.3 Design of controller parameters
• 4 Continued Fraction Expansion (CFE)
  • 4.1 CFE: General introduction
  • 4.2 CFE and approximations of functions
  • 4.3 CFE and stability of linear systems
  • 4.4 CFE and nested multiple-loop control systems
  • 4.5 CFE and rational and irrational numbers
• 5 Rational Approximation of Fractional Operators
  • 5.1 Preliminary considerations
  • 5.2 General CFE method
  • 5.3 Carlson's method
  • 5.4 Matsuda's method
  • 5.5 Oustaloup's method
  • 5.6 Charef's method
  • 5.7 Other approaches
    • 5.7.1 Roy's method
    • 5.7.2 Wan's method
    • 5.7.3 Jones' method
• 6 General Approach to Fractance Devices
  • 6.1 Introduction to fractance devices
    • 6.1.1 What is fractance?
    • 6.1.2 Negative impedance converters
  • 6.2 Domino ladder circuit
  • 6.3 Transmission lines circuit
  • 6.4 Tree structure circuit
• 7 Realization of Fractional-Order Controllers
  • 7.1 Introduction to analogue realization
  • 7.2 Realization of fractional I^λ controller
    • 7.2.1 Description of circuit
    • 7.2.2 Experimental results
  • 7.3 Realization of fractional PI^λ controller
    • 7.3.1 Description of circuit
    • 7.3.2 Experimental results
• 8 Conclusion
• Bibliography
• Index