A Comparative Study of Identification Techniques for Fractional Models

Abdelhamid Jalloul(1*), Khaled Jelassi(2), Jean-Claude Trigeassou(3)

(1) National Engineering School, Electrical Systems Laboratory (LSE), Tunis, Tunisia
(2) Laboratoire Intégration du Matériau au Système (IMS-LAPS), UMR 5218, Université Bordeaux, France
(3) Laboratoire Intégration du Matériau au Système (IMS-LAPS), UMR 5218, Université Bordeaux, France
(*) Corresponding author


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


A comparative study of methods for fractional system identification is presented in this paper. The fractional system is modeled by the help of a non integer integrator which is approximated by a J+1 dimensional modal system composed of an integrator and first order systems. This identification method is compared to other techniques available in the Matlab toolbox. The model parameters are estimated by an output-error technique using a non linear iterative optimization algorithm. Numerical simulations show the performance of the modal approach for modeling and identification.
Copyright © 2013 Praise Worthy Prize - All rights reserved.

Keywords


Fractional Systems; Fractional Integrator; Non Integer Identification; Output Error Identification

Full Text:

PDF


References


P.C. Young, Parameter estimation for continuous-time models, – a survey. Automatica, 17(1), 23-29, 1981.

H. Unbehauen, and G.P. Rao, Identification of continuous systems, System and control series, Amsterdam, 1987.

D Neumann and R. Isermann, Comparison of some parameter estimation methods for continuous-time models, in: IFAC, Identification and System Parameter Estimation, pp. 851- 856, 1988.

Marco Araújo, Nonlinear System Identification and Behavior Modeling. (2009) International Review of Automatic Control (IREACO), 2 (4), pp. 372-375.

J.-L Battaglia, Le Lay L., Batsale J.-C., Oustaloup A., Cois O, Heat flux estimation through inverted non integer identification models, International Journal of Thermal Science, vol. 39,n°3, p.374-389, 2000.

R. Darling and J. Newman, On the short behavior of porous intercalation electrodes, J. Electrochem. Soc., 144(9), 3057-3063, 1997.

M. Amairi, M. Aoun, S. Najar, M. N. Abdelkrim, New method for the resolution of fractional orders differential equations: application to the simulation of fractional systems, (2010) International Review of Modelling and Simulations (IREMOS), 3 (3), pp. 265-271.

B. Mathieu, L. Le Lay, A. Oustaloup, “Identification of non integer order systems in the time domain”, in: Proc. IEEE-SMC CESA’96, Symposium on Control, Optimization and Supervision, Lille, France.1996.

L. Le Lay, Identification fréquentielle et temporelle par modèle non entier, Thèse de doctorat de l'Université Bordeaux I, Talence, France, 20 octobre, 1998.

J.-C. Trigeassou, T. Poinot, J. Lin, A. Oustaloup, F. Levron, Modeling and identification of a non integer order system, in: Proc ECC'99, European Control Conference. Karlsruhe, Germany, 1996.

O. Cois, A. Oustaloup, E. Battaglia, J.-L. Battaglia, Non integer model from modal decomposition for time domain system identification, in: Proc. IFAC SYSID’2000, Symposium on System Identification, Santa Barbara, USA, 2000.

A. Oustaloup, La dérivation non entière: théorie, synthèse et applications (Hermès Editeur, Paris, 1995).

Matignon, D. Représentations en variables d’état de modèles de guides d’ondes avec dérivation fractionnaire, Thèse de Doctorat. Université de Paris XI, ORSAY, 1994.

Miller, K.S., Ross, B., An introduction to the fractional calculus and fractional differential equations (John Wiley and Sons New-York, 1993).

Oldham, K.B., Spanier, J. The fractional calculus (Academic Press New-York, 1974).

J. Lin, Modélisation et identification des systèmes d’ordre non entier, Thèse de Doctorat, Université de Poitiers, France, 2001.

D. Heleschewitz and D. Matignon, Diffusive realizations of fractional intego-differential operators: structural analysis under approximation, Conference IFAC, System, Structure and Control. Vol2, pp.243-248, Nantes, France, July 1998.

Montseny G., Diffusive representation of pseudo differential time operators , Proceedings ESSAIM, Vol 5, 1998, pp. 159-175.

J. Richalet, A. Rault, R. Pouliquen, Identification des processus par la méthode du modèle (Gordon and Breach, 1971).

D.W. Marquardt, An algorithm for Least-Squares estimation of Non-Linear Parameters, J. Soc. Industr. Appl. Math., 11(2), pp. 431-441, 1963.

J.-C. Trigeassou, Recherche de modèles expérimentaux assistée par ordinateur (Lavoisier- Tec et Doc Paris 1988).

D. M. Himmelblan, Applied non linear programming (Mc Graw Hill. 1972).

T. Djamah, S. Djennoune, M. Bettayeb, fractional order system identification, JTEA 2008 May Hammamet Tunisia.

A. Jalloul, K. Jelassi, J.C. Trigeassou, P. Melchior, A Fractional Order Approach to the Modeling of Induction Machines, (2011) International Review on Modelling and Simulations (IREMOS), 4 (4), pp. 1522-1532.


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2019 Praise Worthy Prize