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Flatness for linear fractional systems with application to a thermal system

Authors: Stéphane Victor, Pierre Melchior, Jean Lévine, Alain Oustaloup, Automatica, Vol 57, pp. 213-221, July 2015. DOI: 10.1016/j.automatica.2015.04.021
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 fractionally 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.
author = {Pierre Melchior Stéphane Victor, Jean Lévine, Alain Oustaloup},
title = {Flatness for linear fractional systems with application to a thermal system},
journal = {Automatica},
volume = {57},
number = {},
pages = {213-221},
year = {2015},