An Introduction to Fractional Control

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  • Author:

  • Year: 2012

  • Format: Hardback

  • Product Code: PBCE0910

  • ISBN: 978-1-84919-545-4

  • Pagination: 200 pp.

  • Stock Status: In stock

£60.45 Member price

£93.00 Full price


Fractional control techniques provide an effective way to control dynamic behaviours, using fractional differential equations. This can include the control of fractional plants, the control of a plant using a fractional controller, or the control of a plant so that the controlled system will have a fractional behaviour to achieve a performance that would otherwise be hard to come by.

An Introduction to Fractional Control outlines the theory, techniques and applications of fractional control. The theoretical background covers fractional calculus with real, complex and variable orders, fractional transfer functions, fractional identification and pseudo-state-space representations, while the control systems explored include:

  • Fractional lead control
  • Fractional lag control
  • First, second and third generation Crone control
  • Fractional PID, PI and PD control
  • Fractional sliding mode control
  • Logarithmic phase Crone control
  • Fractional reset control
  • Fractional H2 and H∞ control
  • Fractional predictive control
  • Trajectory planning
  • Fractional time-varying control

Each chapter contains solved examples, where the subject addressed is either expanded or applied to concrete cases, and references for further reading. Common definitions and proofs are included, along with a bibliography, and a discussion of how MATLAB can be used to assist in the design and implementation of fractional control.

Book review

The book is written by two prominent researchers in the field, and I would (and will) recommend the book to any young researcher interested in the field of applied “fractional" calculus, and in particular, anyone interested in the “fractional" perspective on systems theory.

Milan Rade Rapaic, Fakultet Tehničkih Nauka, Univerzitet u Novom Sadu, Serbia

Mathematical Reviews (October 2015)

Book readership

An essential guide for researchers and advanced students of control engineering in academia and industry.

Book contents

  • Fractional derivatives with real orders
  • Fractional calculus: real orders
  • Fractional transfer functions
  • Approximations of fractional transfer functions
  • Fractional identification
  • First and second generation Crone control
  • Fractional PIDs
  • Fractional reset control
  • Fractional H2 and H∞ control
  • Pseudo-state-space representations
  • Fractional sliding mode control
  • Trajectory planning
  • Fractional derivatives with complex orders
  • Fractional calculus: complex orders
  • Complex order transfer functions
  • Third-generation Crone control
  • Fractional derivatives with variable orders
  • Fractional calculus: variable orders
  • Fractional time-varying control
  • General considerations
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