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Review Article

Identification of Fractional Model by Least-Squares Method and Instrumental Variable

[+] Author and Article Information
Abir Khadhraoui

Laboratoire des systèmes Electriques (LSE),
Ecole Nationale d’Ingenieurs de Tunis,
Le Belvedere 1002
Tunis, Tunisia
e-mail: abbir_k2007@yahoo.fr

Khaled Jelassi

Laboratoire des systèmes Electriques (LSE),
Ecole Nationale d’Ingenieurs de Tunis,
Le Belvedere 1002
Tunis, Tunisia
e-mail: jelassi_2000@yahoo.fr

Jean-Claude Trigeassou

Laboratoire Intégration du Matériau
au Système (IMS-APS),
Université Bordeaux 1,
Bordeaus, France
e-mail: jean.claude.trigeassou@ims-bordeaux.fr

Pierre Melchior

Laboratoire Intégration du Matériau
au Système (IMS-APS),
Université Bordeaux 1,
Bordeaux, France
e-mail: pierre.melchior@laps.ims-bordeaux.fr

1Corresponding author.

Manuscript received November 27, 2014; final manuscript received February 20, 2015; published online April 8, 2015. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 10(5), 050801 (Sep 01, 2015) (10 pages) Paper No: CND-14-1301; doi: 10.1115/1.4029904 History: Received November 27, 2014; Revised February 20, 2015; Online April 08, 2015

This paper deals with fractional model identification using least-squares (LS) method and instrumental variable (IV) in a noisy output context. A new identification method, which extends LS techniques to fractional system to identify not only the parameters but also the unknown order, is presented. In order to eliminate the bias of identification results, IV method is chosen which permits unbiased parameter estimation. Monte Carlo simulation analyses are used to demonstrate the validity and the performance of the proposed fractional order system identification method.

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Khadrahoui, A., Jelassi, K., and Trigeassou, J. C., 2013, “Identification of a Fractional Order Model by a Least Squares Technique: Hn Model,” Prog. Comput. Appl., 2(2), pp. 91–101.
Khadrhoui, A., Jelassi, K., and Trigeassou, J. C., 2013, “Identification of a Fractional Order Model by a Least Squares Technique: Hn1,n2 Model,” Proceedings of the 2013 14th International Conference Sciences and Techniques of Automatic Control and Computer Engineering (STA), Sousse, Tunisia, Dec. 20–22, pp. 461–467.
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Figures

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Fig. 1

Frequency discretization of μ(w)

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Fig. 2

The modal representation (infinite state representation) of fractional integrator

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Fig. 3

Simulation of a one derivate FDE

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Fig. 4

Simulation of the two derivate DFE

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Fig. 5

Estimated and true response of Hn model

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Fig. 6

Quadratic criterion variation: Hn model

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Fig. 7

Error variation: Hn model

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Fig. 8

Output data of Hn model, and estimated response: SNR = 1

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Fig. 9

Output data of Hn1,n2 model, and estimated response: SNR = 15

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