Flatness for linear fractional systems with application to a thermal system

Stephane Victor (1) , Pierre Melchior (1) , Jean Lévine (2) , Alain Oustaloup (1)

1 IMS - Laboratoire de l'intégration, du matériau au système
2 CAS - Centre Automatique et Systèmes

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.

Mots clés: Differential flatness; Fractional systems; Polynomial matrices; Thermal system; Trajectory planning

Domaines: Automatique / Robotique

Stephane Victor, Pierre Melchior, Jean Lévine, Alain Oustaloup. Flatness for linear fractional systems with application to a thermal system. Automatica, 2015, 57, pp.213-221. ⟨10.1016/j.automatica.2015.04.021⟩. ⟨hal-01319169⟩