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Modeling and Identification of Hammerstein System by using Triangular Basis Functions

Authors: A. Chaari, K. Elleuch


This paper deals with modeling and parameter identification of nonlinear systems described by Hammerstein model having Piecewise nonlinear characteristics such as Dead-zone nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the triangular basis functions leads to a particular form of Hammerstein model. The approximation by using Triangular basis functions for the description of the static nonlinear block conducts to a linear regressor model, so that least squares techniques can be used for the parameter estimation. Singular Values Decomposition (SVD) technique has been applied to separate the coupled parameters. The proposed approach has been efficiently tested on academic examples of simulation.

Keywords: Identification, singular values decomposition, Hammerstein model, Piecewisenonlinear characteristic, Dead-zone nonlinearity, Triangular basisfunctions

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[1] Bai E.W., "Identification of linear systems with hard input nonlinearities of known structure," Automatica, 2002, vol. 38, no. 5, pp. 853-860.
[2] Kara T., and Eker I., "Nonlinear modelling and identification of a DC motor for bidirectional operation with real time experiments," 2004, Energy Conversion and Management, vol. 45, pp. 1087-1106.
[3] T. H. van Pelt and D. S Bernstein, "Nonlinear system identification using Hammerstein and nonlinear feedback models with piecewice linear static maps," 2001, Int. J. Control, vol. 74, n┬░ 18, pp. 1807-1823.
[4] Vörös J., "Parameter Identification of Discontinuous Hammerstein Systems," 1997, Automatica 33 No. 6, 1141-1146.
[5] Vörös J., "Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities," 1999, IEEE Transactions on Automatic Control (44). pp. 2145-2149.
[6] Vörös J., "Modelling and parameter identification of systems with multi segment piecewise-linear characteristics," 2002, IEEE Transactions on Automatic Control, vol. AC 47, N┬░ 1, pp. 184-188.
[7] Elleuch K., M. Kharrat, A. Chaari and M. Chaabane, "Modeling and identification of block-oriented heat transfer process," Int. J. of Information and Systems Sciences, 2009, vol. 5, n┬░ 1. , pp. 41-56.
[8] Ljung L., "System Identification: Theory for the User," 1999, second ed., Prentice-Hall, Inc., Englewood Cliffs, NJ.
[9] Chidambaram M., "Computer Control of Processes, 2001," New York: CRC.
[10] Kung, M. C. and Womack, B. F., "Discrete time adaptive control of linear systems with preload nonlinearity," 1984b, Automatica 20, 477- 479.
[11] Guo F., G. Bretthauer, "Identification of MISO Wiener and Hammerstein systems," 2003, Proceedings of the 7th European Control Conference, TEE, University of Cambridge, UK, September.
[12] Vörös J., "Identification of Hammerstein systems with time-varying piecewise-linear characteristics nonlinearities," 2005, Journal of electrical engineering, vol. 57, No. 1, pp. 42-46.
[13] Zhu Y., "Estimation of an N-L-N Hammerstein-Wiener model", 2002, Automatica, vol. 38, no. 9, pp. 1607-1614.
[14] Vörös J., "Recursive Identification of Systems with Noninvertible Output Nonlinearities" 2010, Informatica, , Vol. 21, No. 1, 139-148.
[15] Billings S., S. Fakhouri, "Identification of systems containing linear dynamic and static nonlinear elements," Automatica, 1982, pp. 15-26.
[16] Gomez J.C., E. Baeyens, "Identification of nonlinear systems using orthonormal bases," 2001, Proceedings of the IASTED International Conference on Intelligent Systems and Control, Clearwater, FL, USA, November, pp. 126-131.
[17] Gomez J.C., E. Baeyens, "Identification of block-oriented nonlinear systems using orthonormal bases," 2004, Journal of Process Control 14, pp. 685-697.
[18] Chaari A., K. Elleuch, M. Kharrat and S. Kamoun, "Identification of discrete time nonlinear system described by Hammerstein model: Application to a thermal system," ICGST, Automatic Control and Systems Engineering, ACSE journal, 2006, Vol. 6, Issue (2): pp. 63-69.
[19] Dolanc G. and S. Strmcnik, "Identification of nonlinear systems using a piecewise-linear Hammerstein model," Syst. Contr. Lett., 2005, vol. 54, no. 2, pp. 145-158.
[20] Gu, X., Bao, Y. and Lang, Z., "A parameter identification method for a class of discrete time nonlinear systems," 1988,. In Proc. 12fh IMACS World Congress, Paris, Vol. 4, pp. 627-629.
[21] Golub G., C. Van Loan, "Matrix Computations," 1989, second ed., The Johns Hopkins University Press, Baltimore and London.
[22] Hasiewicz Z., M. Pawlak, and P. Sliwinski, "Nonparametric identification of nonlinearities in block-oriented systems by orthogonal wavelets with compact support," Feb. 2005, IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 2, pp. 427-442.
[23] Lang Z. Q., "Controller design oriented model identification method system, Identification of Hammerstein system," 1993, Automatica, vol. 29, n┬░. 3, pp. 767-771.
[24] Ninness B., F. Gustafsson, "A unifying construction of orthonormal bases for system identification," 1997, IEEE Transactions on Automatic Control AC-42 (4), pp. 515-521.
[25] Pearson R., M. "Pottmann, Gray-box identification of block-oriented nonlinear models," 2000, Journal of Process Control 10, pp. 301-315.
[26] Tao G. and M. Tian, "Discrete-time adaptive control of systems with multisegment piecewise-linear nonlinearities," May.1998, IEEE Trans. Autom. Control, vol. 43, no. 5, pp. 719-723.
[27] Vörös J., "Recursive Identification of Systems with Noninvertible Output Nonlinearities" 2010, Informatica, , Vol. 21, No. 1, 139-148.