CFP last date
20 January 2025
Reseach Article

Identification of Hammerstein Systems using Triangular basis Functions

by Khaled Elleuch, Abdessattar Chaari
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 24 - Number 1
Year of Publication: 2011
Authors: Khaled Elleuch, Abdessattar Chaari
10.5120/2911-3827

Khaled Elleuch, Abdessattar Chaari . Identification of Hammerstein Systems using Triangular basis Functions. International Journal of Computer Applications. 24, 1 ( June 2011), 42-45. DOI=10.5120/2911-3827

@article{ 10.5120/2911-3827,
author = { Khaled Elleuch, Abdessattar Chaari },
title = { Identification of Hammerstein Systems using Triangular basis Functions },
journal = { International Journal of Computer Applications },
issue_date = { June 2011 },
volume = { 24 },
number = { 1 },
month = { June },
year = { 2011 },
issn = { 0975-8887 },
pages = { 42-45 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume24/number1/2911-3827/ },
doi = { 10.5120/2911-3827 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:09:53.879290+05:30
%A Khaled Elleuch
%A Abdessattar Chaari
%T Identification of Hammerstein Systems using Triangular basis Functions
%J International Journal of Computer Applications
%@ 0975-8887
%V 24
%N 1
%P 42-45
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

A new identification method is proposed for Hammerstein systems in presence of dead zone input nonlinearities. To describe and identify the nonlinear system, a new decomposition technique using the triangular basis functions is employed. Then a parameterized model is derived to represent the entire system. The approximation by Triangular basis functions for the description of the static nonlinear block conducts to a linear regressive model, so parameter matrices characterizing the considered model can be estimated. After this stage, Singular Values Decomposition (SVD) technique has been applied to separate the coupled parameters of matrixes. The numerical simulation results illustrate that the proposed approach can be a promising tool for identifying Hammerstein systems with dead zone nonlinearities.

References
  1. J. Wang, A. Sano, D. Shook, T. Chen, B. Huang 2007. A blind approach to closed-loop identification of Hammerstein systems. Int. J. Control 80 (2) 302–313.
  2. Bai E.W. 2002. Identification of linear systems with hard input nonlinearities of known structure”, Automatica, vol. 38, no. 5, pp. 853–860.
  3. Vörös J. 1997. Parameter Identification of Discontinuous Hammerstein Systems. Automatica 33 No. 6, 1141–1146.
  4. Kara T., and Eker I. 2004. Nonlinear modelling and identification of a DC motor for bidirectional operation with real time experiments. Energy Conversion and Management, vol. 45, pp. 1087-1106.
  5. T. H. van Pelt and D. S Bernstein 2001. Nonlinear system identification using Hammerstein and nonlinear feedback models with piecewise linear static maps. Int. J. Control, vol. 74, n° 18, pp. 1807-1823.
  6. Khaled ELLEUCH and Abdessattar CHAARI 2010. Modelling and Estimation of Hammerstein System with Preload Nonlinearity. Leonardo Journal of Sciences (LJS), Issue 16 (9), p. 13-20.
  7. Vörös J. 2005. Identification of Hammerstein systems with time-varying piecewise-linear characteristics nonlinearities. Journal of electrical engineering, vol. 57, No. 1, pp. 42–46.
  8. Elleuch K., M. Kharrat, A. Chaari and M. Chaabane 2009. Modeling and identification of block-oriented heat transfer process. Int. J. of Information and Systems Sciences, vol. 5, n° 1. , pp. 41-56.
  9. D.Q. Wang, F. Ding 2008. Extended stochastic gradient identification algorithms for Hammerstein–Wiener ARMAX systems. Comput. Math. Appl. 56 (12) 3157–3164.
  10. Tao G. and M. Tian 1998. Discrete-time adaptive control of systems with multisegment piecewise-linear nonlinearities. IEEE Trans. Autom. Control, vol. 43, no. 5, pp. 719–723.
  11. Kung, M. C. and Womack, B. F. 1984b. Discrete time adaptive control of linear systems with preload nonlinearity, Automatica 20, 477-479.
  12. Vörös J. 2002. Modelling and parameter identification of systems with multi segment piecewise-linear characteristics IEEE Transactions on Automatic Control, vol. AC 47, N° 1, pp. 184-188.
  13. Billings S., S. Fakhouri. 1982. Identification of systems containing linear dynamic and static nonlinear elements. Automatica, pp. 15–26.
  14. Vörös J. 1999. Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities. IEEE Transactions on Automatic Control (44). pp. 2145-2149.
  15. Vörös J. 2010. Recursive Identification of Systems with Noninvertible Output Nonlinearities. Informatica, Vol. 21, No. 1, 139–148.
  16. Gomez J.C., E. Baeyens 2004. Identification of block-oriented nonlinear systems using orthonormal bases. Journal of Process Control 14, pp. 685–69.
Index Terms

Computer Science
Information Sciences

Keywords

Identification SVD technique Dead-zone nonlinearity