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Erschienen in:
Fractional Order Models Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

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

verfasst von : P. Melchior, S. Victor

Erschienen in: Fractional Order Differentiation and Robust Control Design

Verlag: Springer Netherlands

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Abstract

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 activating the windmill sails in order to reduce the velocity. During the industrial revolution, Watt adapted a ball regulator for steam engines: the greater the ball velocity, the wider the opening of a valve that released the steam. By lowering the boiler pressure, the velocity could be reduced. The main problem was to maintain a constant speed despite load variations. In 1868, the physicist Maxwell published the first mathematical analysis explaining some of the behaviors observed on the regulators employed at that time. That was the beginning of several studies on stability to which the mathematicians Hurwitz and Routh were the main contributors. After theoretical and technological developments, it became possible to handle linear and nonlinear multivariable systems thanks to the important contributions of Bellman in dynamical programming (Brassard and Bratley 1996), Kalman (1960) in filtering and linear quadratic control and Pontryagin et al. (1962) in optimal control. Their contributions still feed research in control theory today.

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Vorheriges Kapitel H ∞ Control of Commensurate Fractional Order Models
Fußnoten
1
A noetherian ring is a ring dotted with the addition and multiplication compatible with the addition in the distributivity sense
 
2
For an n-tuple \( \tau =1 \sec \), t 0
 
3
By taking t 2, we come back to a physical case where two masses are coupled with a spring, the whole being piloted by a force u
 
4
\( GL_m (\mathrm{R} \lfloor\text{D}^{v}\rfloor) \) is the group of unimodular square \( \text{D}^{v} \)-polynomial matrices, i.e. the set of invertible square \( \text{D}^{v} \)-polynomial matrices whose inverse is also a \( \text{D}^{v} \)-polynomial matrix.
 
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Metadaten
Titel
Fractional Approaches in Path Tracking Design (or Motion Control): Prefiltering, Shaping, and Flatness
verfasst von
P. Melchior
S. Victor
Copyright-Jahr
2015
Verlag
Springer Netherlands
Buch
Fractional Order Differentiation and Robust Control Design

Print ISBN: 978-94-017-9806-8

Electronic ISBN: 978-94-017-9807-5

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-94-017-9807-5_5

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