Approximation and identification of diffusive interfaces by fractional models

Authors:
A. Benchellal;T. Poinot;J.-C. Trigeassou
Affiliations:
Laboratoire d'Automatique et d'Informatique Industrielle, Ecole Supérieure d'Ingénieurs de Poitiers, Poitiers Cedex, France;Laboratoire d'Automatique et d'Informatique Industrielle, Ecole Supérieure d'Ingénieurs de Poitiers, Poitiers Cedex, France;Laboratoire d'Automatique et d'Informatique Industrielle, Ecole Supérieure d'Ingénieurs de Poitiers, Poitiers Cedex, France
Venue:
Signal Processing - Fractional calculus applications in signals and systems
Year:
2006

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Abstract

Heat transfer problems obey to diffusion phenomenon. In this paper we show that they can be modelled with the help of fractional systems. The simulation is based on a fractional integrator operator where the non-integer behaviour acts only over a limited spectral band. Starting with frequency considerations derived from the analysis of a diffusion problem, a more general approximation of the fractional system is proposed. A state-space model is presented that gives an accurate simulation for transients, and with which it is possible to carry out an output-error technique to estimate the model parameters. Numerical simulations of the heat transfer problem are used to illustrate the improvements of the proposed model.