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Review Article

Initialization of Identification of Fractional Model by Output-Error Technique

[+] Author and Article Information
Abir Khadhraoui

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

Khaled Jelassi

Laboratoire des systèmes Electriques (LSE),
Ecole Nationale d'Ingenieurs de Tunis,
Tunis, Tunisia
e-mail: jelassi_2000@yahoo.com

Jean-Claude Trigeassou

Laboratoire Intégration du Matériau au Système
(IMS-APS),
Université Bordeaux 1,
Bordeaux 33000, France
e-mail: jeanclaude.trigeassou@yahoo.fr

Pierre Melchior

Laboratoire Intégration du Matériau au Système
(IMS-APS),
Université Bordeaux 1,
Bordeaux 33000, France
e-mail: pierre.melchior@laps.ims-bordeaux.fr

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 27, 2015; final manuscript received May 4, 2015; published online August 26, 2015. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 11(2), 020801 (Aug 26, 2015) (12 pages) Paper No: CND-15-1025; doi: 10.1115/1.4030541 History: Received January 27, 2015

A bad initialization of output-error (OE) technique can lead to an inappropriate identification results. In this paper, we introduce a solution to this problem; the basic idea is to estimate the parameters and the fractional order of the noninteger system by a new approach of least-squares (LS) method based on repeated fractional integration to initialize OE technique. It will be shown that LS method offers a good initialization to OE algorithm and leads to acceptable identification results. The performance of the proposed method is shown through numerical simulation examples.

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References

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

OE identification technique

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Fig. 8

Evolution of the estimated orders and parameters of Hn model in no-noise condition

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Fig. 9

Evolution of the estimated orders and parameters of Hn1,n2 model without noise

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Fig. 6

Estimated and exact response of Hn model in no-noise condition

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Fig. 12

Exact and estimated response in noisy context: Hn1,n2 model

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Fig. 15

Exact and estimated response in noisy context: Hn1,n2,n3 model

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Fig. 11

Exact and estimated response in noisy context: Hn model

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Fig. 10

Evolution of the estimated orders and parameters of Hn1,n2,n3 model without noise

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