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Fractional Order Differentiation and Robust Control Design

Part of the Intelligent Systems, Control and Automation: Science and Engineering Book Series (volume 77)

DOI: 10.1007/978-94-017-9807-5

ISBN: 978-94-017-9806-8

Publisher: Springer Netherlands - Springer Journals

Feb 9, 2015

Available

Fractional Order Models

Sabatier, J.; Farges, C.; Oustaloup, A.

Pages: 1 –61

[In a letter to L’Hospital in 1695, Leibniz raised the possibility of generalizing the operation of differentiation to non-integer orders and L’Hospital asked what would be the result of half-differentiating a variable. Leibniz in an open letter dated September 30, 1695 replied “It leads to a...
Available

Fractional Order PID and First Generation CRONE Control System Design

Lanusse, P.; Sabatier, J.; Oustaloup, A.

Pages: 63 –105

[This chapter presents the design of controllers for Single Input/Single Output (SISO) systems, that is to say only one signal to control only one measured output. The fractional order controller is presented as a generalization of the common PID controller. Then, it is shown how the first...
Available

Second and Third Generation CRONE Control-System Design

Lanusse, P.; Sabatier, J.; Nelson Gruel, D.; Oustaloup, A.

Pages: 107 –192

[This chapter presents the second generation of the CRONE methodology that extends the field of application of the first generation one. By replacing the real fractional order by a complex order, the third generation of the CRONE methodology is defined for any perturbed SISO system and is finally...
Available

H∞ Control of Commensurate Fractional Order Models

Sabatier, J.; Farges, C.; Fadiga, L.

Pages: 193 –235

[A commensurate fractional order model can be represented by a pseudo state space representation similar to the state space representation of an integer order model as shown in Chap. 1. This similarity can be used to extend H∞ synthesis methods developed for integer order models represented by a...
Available

Fractional Approaches in Path Tracking Design (or Motion Control): Prefiltering, Shaping, and Flatness

Melchior, P.; Victor, S.

Pages: 237 –323

[Automatic control has a long history in engineering. At the end of the seventeenth century, Hooke introduced a system of balls rotating around an axis in which the velocity was proportional to the velocity of the windmill: the greater the ball velocity, the larger the gap from the axis...

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