Flatness for linear fractional systems with application to a thermal system

• Stéphane Victor ^[1] ; Pierre Melchior ^[1] ; Jean Lévine ^[2] ; Alain Oustaloup ^[1]
  1. [1] University of Bordeaux

     University of Bordeaux

     Arrondissement de Bordeaux, Francia

     
  2. [2] CAS-Mathématiques et Systèmes, MINES-ParisTechFontainebleau, France
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 57, 2015, págs. 213-221
• Idioma: inglés
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• Resumen

  • 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.