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Journal of Vibration and Control
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Fractional Modelling and Identification of a Thermal Process

Amel Benchellal

Laboratoire d'automatique et d'Informatique Industrielle, Université de Poitiers, 40, Ave du Recteur Pineau 86022 Poitiers France, Amel.Benchellal{at}etu.univ-poitiers.fr

Thierry Poinot

Laboratoire d'automatique et d'Informatique Industrielle, Université de Poitiers, 40, Ave du Recteur Pineau 86022 Poitiers France

Jean-Claude Trigeassou

Laboratoire d'automatique et d'Informatique Industrielle, Université de Poitiers, 40, Ave du Recteur Pineau 86022 Poitiers France

Heat transfer problems are subject to diffusion phenomenon, and can be modelled with the help of fractional systems. The simulation of these particular systems is based on a fractional integrator, where the non-integer behaviour occurs only within a limited spectral band. A first model, based on the use of one fractional integrator, has been already defined and tested on a thermal pilot. Starting from frequency considerations derived from the analysis of a diffusion problem, a more general approximation of the fractional system is proposed here. The new model is based on the use of two fractional integrator operators. This makes it possible to define a state-space model for simulation of transients, and to use an output-error technique in order to estimate the parameters of the model. Experimental results obtained for a thermal process illustrate the improvements obtained using the proposed model.

Key Words: Fractional systems • non-integer systems • fractional operator • modelling • estimation • output-error identification • heat transfer • diffusive interfaces

Journal of Vibration and Control, Vol. 14, No. 9-10, 1403-1414 (2008)
DOI: 10.1177/1077546307087441
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