Flatness For Linear Fractional Systems With Application to a Thermal System
Computational Physics
2015-09-10 v3
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 -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.
Cite
@article{arxiv.1311.3805,
title = {Flatness For Linear Fractional Systems With Application to a Thermal System},
author = {Stéphane Victor and Pierre Melchior and Jean Lévine and Alain Oustaloup},
journal= {arXiv preprint arXiv:1311.3805},
year = {2015}
}