An Introduction to Fractional Control

Cloth: 978 1 84919 545 4 / $121.00
Published: March 2013  

Publisher: The Institution of Engineering and Technology
200 pp., 6 1/8" x 9 1/4"
Fractional control techniques provide an effective way to control dynamic behaviors, 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 pseudostatespace 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 H8 control, fractional predictive control, trajectory planning and fractional timevarying 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. This is an essential guide for researchers and advanced students of control engineering in academia and industry.

Table of Contents:
1 Preliminaries
Part I Fractional derivatives with real orders
2 Fractional calculus: real orders
3 Fractional transfer functions
4 Approximations of fractional transfer functions
5 Fractional identification
6 First and second-generation Crne control
7 Fractional PIDs
8 Fractional reset control
9 Fractional H2 and H1 control
10 Pseudo-state-space representations
11 Fractional sliding mode control
12 Trajectory planning
Part II Fractional derivatives with complex orders
13 Fractional calculus: complex orders
14 Complex order transfer functions
15 Third generation Crone control
Part III Fractional derivatives with variable orders
16 Fractional calculus: variable orders
17 Fractional time-varying control
18 General considerations
Appendix A

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