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arXiv · 1311.3805

Flatness For Linear Fractional Systems With Application to a Thermal System

Stéphane Victor·Pierre Melchior·Jean Lévine·Alain Oustaloup
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Abstract

This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs and a simple algorithm to compute them. We also obtain a characterization of the so-called fractionnally $0$-flat outputs. We then present an application to a two dimensional heated metallic sheet, whose dynamics may be approximated by a fractional model of order 1/2. The trajectory planning of the temperature at a given point of the metallic sheet is obtained thanks to the fractional flatness property, without integrating the system equations. The pertinence of this approach is discussed on simulations.

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Stéphane Victor, Pierre Melchior, Jean Lévine, Alain Oustaloup. 2015-09-09. Flatness For Linear Fractional Systems With Application to a Thermal System. https://doi.org/10.1016/j.automatica.2015.04.021

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