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Research Papers: Control

Advances in System Identification Using Fractional Models

[+] Author and Article Information
Rachid Malti

IMS, UMR 5218 CNRS, Université Bordeaux 1, 351 Cours de la Libération, F 33405 Talence Cedex, Francerachid.malti@ims-bordeaux.fr

Stephane Victor

IMS, UMR 5218 CNRS, Université Bordeaux 1, 351 Cours de la Libération, F 33405 Talence Cedex, Francestephane.victor@ims-bordeaux.fr

Alain Oustaloup

IMS, UMR 5218 CNRS, Université Bordeaux 1, 351 Cours de la Libération, F 33405 Talence Cedex, Francealain.oustaloup@ims-bordeaux.fr

J. Comput. Nonlinear Dynam 3(2), 021401 (Jan 28, 2008) (7 pages) doi:10.1115/1.2833910 History: Received June 08, 2007; Revised November 12, 2007; Published January 28, 2008

This paper presents an up to date advances in time-domain system identification using fractional models. 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 coefficients and differentiation orders using nonlinear programing. As an example, a thermal system is identified using a fractional model and is compared to a rational one.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 2

Bode diagrams of a fractional integrator and the asymptotic behavior of its rational approximation (Eq. 9 with N=5)

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Figure 1

Approximation of a fractional integrator using a rational model

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Figure 4

Modal decomposition

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Figure 5

Insulated long aluminium rod heated by a resistor

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