System identification using fractional models: State of the art

Rachid R. Malti (1) , Stéphane Victor (1) , Olivier Nicolas (1) , Alain Oustaloup (1)

1 IMS - Laboratoire de l'intégration, du matériau au système

This paper presents a state of the art of actual achievements in time-domain system identification using fractional models. It starts with some general aspects on time and frequency-domain representations, time-domain simulation, and stability of fractional models. Then, an overview on system identification methods using fractional models is presented. Both equation-error and output-error-based models are detailed. In the former models, prior knowledge is generally used to fix differentiation orders; model coefficients are estimated using least squares. The latter models allow simultaneous estimation of model's coefficients and differentiation orders, using non linear programming. A real thermal example is identified using a fractional model and compared to a rational one.

Mots clés: Fractional differentiation; fractional integration; identification; simulation; output error models; equation error models; state variable filter

Domaines: Automatique / Robotique

Rachid R. Malti, Stéphane Victor, Olivier Nicolas, Alain Oustaloup. System identification using fractional models: State of the art. ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2007), Sep 2007, Las Vegas, Nevada, United States. pp.DETC2007-35332. ⟨hal-00182374⟩