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Modeling of nonlinear block-oriented systems using orthonormal basis and radial basis functions

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents a methodology for modeling the Wiener, Hammerstein and feedback-nonlinear systems via orthonormal basis and radial basis functions. The approach is computationally effective, in particular, in terms of elimination of the disastrous bilinearity effect due to the use of regular or inverse orthonormal basis functions to model the linear dynamic block. Scaling parameters of orthonormal basis and radial basis functions are updated recursively using the stochastic gradient method. The modeling of a nonlinear static block with radial basis functions is particularly recommended for the Hammerstein and feedback-nonlinear systems. A simulation study for the magnetic levitation process confirms the attractiveness of the approach.
Czasopismo
Rocznik
Strony
11--17
Opis fizyczny
Bibliogr. 21 poz., wykr.
Twórcy
autor
  • Opole University of Technology, Department of Electrical, Control and Computer Engineering, ul. Sosnkowskiego 31, 44-272 Opole, Poland, r.stanislawski@po.opole.pl
Bibliografia
  • [1] Bai E.W., An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems, Automatica, Vol. 34, 1998, pp. 333-338.
  • [2] Boukis C., Mandic D.P., Constantinides A.G., Polymenakos L.C., A Novel Algorithm for the Adaptation of the Pole of Laguerre Filters, IEEE Signal Processing Letters, Vol. 13, No. 7, 2006, pp. 429-432.
  • [3] Garulli A., Giarre L., Zappa G., Identification of approximated Hammerstein models in a worst-case setting, IEEE Transactions on Automatic Control, Vol. 47, 2002, pp. 2046-2050.
  • [4] Greblicki W., Nonlinearity recovering in Wiener system driven with correlated signal, IEEE Transactions on Automatic Control, Vol. 49, No. 10, 2004, pp. 1805-1810.
  • [5] Grega W., Piłat P. A., A comparison of nonlinear controllers for magnetic levitation systems, Proc. 5th World Multi-Conference on Systemics, Cybernetics and Informatics, Orlando, Vol. IX, 2001, pp. 188-193.
  • [6] Hasiewicz Z., Hammerstein system identification by the Haar multiresolution approximation, Int. J. Adaptive Control and Signal Processing, Vol. 13, 1999, pp. 191-217.
  • [7] Hunek W.P., Stanisławski R., Latawiec K.J., A comparative analysis of nonlinear block-oriented and ARX-based neural network models for the magnetic levitation process, Proc. XXXIC-SPETO, Ustroń, 23-26 May 2007, pp. 187-188.
  • [8] Janczak A., On identification of Wiener systems based on a modified serial-parallel model, Proc. European Control Conference, Porto, Portugal, 2001, pp. 1852-1857.
  • [9] Kim N.Y., Byun H.G., Kwon K.H., Learning Behaviors of Stochastic Gradient Radial Basis Function Network Algorithms for Odor Sensing Systems, ETRI Journal, Vol. 28, No. 1, 2006.
  • [10] Latawiec K.J., The power of inverse systems in linear and nonlinear modeling and control, Technical University of Opole Press, Opole, 2004.
  • [11] Latawiec K.J., Marciak C., Hunek W., Stanisławski R., A new analytical design methodology for adaptive control of nonlinear block-oriented systems, Proc. 7th World Multi-Conference on Systemics, Cybernetics and Informatics, Orlando, Florida, Vol. XI, 2003, pp. 215-220.
  • [12] Latawiec K.J., Marciak C., Rojek R., Oliveira G.H.C., Linear parameter estimation and predictive constrained control of Wiener/Hammerstein systems, Proc. 13th IF AC Symposium on System Identification (SYSID’2003), Rotterdam, Netherlands, 2003, pp. 359-364.
  • [13] Latawiec K.J., Marciak C., Stanisławski R., Oliveira G.H.C., The mode separability principle in modeling of linear and nonlinear block-oriented systems, Proc. the 10th IEEE MMAR Conference (MMAR’04), Międzyzdroje, Poland, Vol. 1,2004, pp. 479-484.
  • [14] Latawiec K.J., Stanisławski R., Stanisławski W., Oliveira G.H.C., Modelling of a boiler proper by means of multivariable orthonormal basis functions, Proc. 11th IEEE MMAR Conference (MMAR’05), Międzyzdroje, Poland, 2005, pp. 777-780.
  • [15] Ninness B., Gibson S., Quantifying the accuracy of Hammerstein model estimation, Automatica, Vol. 38, 2002, pp. 2037-2051.
  • [16] Oliveira S.T., Optimal pole conditions for Laguerre and two-parameter Kautz models: a survey of known results, Proc. 12th IFAC Symp. on System Identification (SYSID’2000), Santa Barbara, CA, USA, 2000, pp.457-462.
  • [17] Pearson R.K., Pottman M., Gray-box identification of block-oriented nonlinear models, Journal of Process Control, Vol. 10, 2000, pp. 301-315.
  • [18] Piłat A., Time-optimal control for magnetic levitation system, Proc. 7th IEEE MMAR Conference, Międzyzdroje, Poland, Vol. 2, 2001, pp. 873-878.
  • [19] Stanisławski R., Hammerstein system identification by means of orthonormal basis functions and radial basis functions, Emerging Technologies, Robotics and Control Systems, Italy, Vol. 2, 2007, pp. 69-73.
  • [20] Stanisławski R., Latawiec K.J., Hunek W.P., Identification of feedback-nonlinear systems by means of orthonormal basis and radial basis functions, Proc. 13th IEEE IFAC IC MMAR 2007, August 2007, Poland, pp. 611-616.
  • [21] Zhu Y., Identification of Hammerstein models for control using ASYM, Int. Journal of Control, Vol. 73, 2000, pp. 1692-1702.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0062-0002
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