A method for modelling and simulation of fractional systems

Authors:
T. Poinot;J.-C. Trigeassou
Affiliations:
Laboratoire d'Automatique et d'Informatique Industrielle, Ecole Supérieure d'Ingénieurs de Poltiers, 40 Avenue du Recteur Pineau 86 022 Poitiers Cedex, France;Laboratoire d'Automatique et d'Informatique Industrielle, Ecole Supérieure d'Ingénieurs de Poltiers, 40 Avenue du Recteur Pineau 86 022 Poitiers Cedex, France
Venue:
Signal Processing - Special issue: Fractional signal processing and applications
Year:
2003

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Abstract

An original method for modelling and simulation of fractional systems is presented in this article. The basic idea is to model the fractional system by a state-space representation, where conventional integration is replaced by fractional one with the help of non-integer integrator. This operator is itself approximated by a N dimensional system composed of an integrator and of a phase-lead filter. This method is compared to other techniques like direct discretization of the fractional derivator and diffusive representation. Numerical simulations exhibit the general applicability and flexibility of this new approach to different types of fractional models and to non-conventional non-integer derivation with limited spectral range.