Advertisement

Nonlinear Dynamics

, Volume 55, Issue 1–2, pp 31–42 | Cite as

Identification for disturbed MIMO Wiener systems

  • Dan Fan
  • Kueiming Lo
Original Paper

Abstract

The identification of Multi-input Multi-output (MIMO) Wiener systems is concerned in this paper. The system presented is comprised of a multi-dimensional linear subsystem and a memory-less nonlinear block which is made of discontinuous asymmetric piece-wise linear functions. A recursive algorithm is proposed to estimate all the unknown parameters of the system with interference noises. It is shown that the recursive algorithm for the disturbed MIMO Wiener system is convergent. Finally, some simulation results illustrate the identification accuracy and the convergence rate.

Keywords

Convergence rate Interference noise MIMO Wiener systems Parameter identification Recursive estimation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Greblicki, W.: Nonparametric approach to Wiener system identification. IEEE Trans. Circuits Syst. I: Fund. Theory Appl. 44(6), 538–545 (1997) CrossRefMathSciNetGoogle Scholar
  2. 2.
    Greblicki, W.: Nonparametric identification of Wiener systems. IEEE Trans. Inf. Theory 38(5), 1478–1493 (1992) CrossRefGoogle Scholar
  3. 3.
    Greblicki, W.: Nonparametric identification of Wiener systems by orthogonal series. IEEE Trans. Autom. Control 39(10), 2077–2086 (1994) MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Ljung, L.: System Identification: Theory for the User. Prentice-Hall, Upper Saddle River (1999), pp. 141–143 Google Scholar
  5. 5.
    Hsia, T.C.: System Identification Least Squares Methods. Lexington Books, Toronto (1977), pp. 112–113 Google Scholar
  6. 6.
    Korenberg, M.J.: Parallel cascade identification and kernel estimation for nonlinear systems. Ann. Biomed. Eng. 19, 429–455 (1991) CrossRefGoogle Scholar
  7. 7.
    Boyd, S., Chua, L.O.: Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Trans. Circuits Syst. 32(11), 1150–1161 (1985) MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Kalafatis, A.D., Arifin, N., Wang, L., Cluett, W.R.: A new approach to the identification of pH processes based on the Wiener model. Chem. Eng. Sci. 50, 3693–3701 (1995) CrossRefGoogle Scholar
  9. 9.
    Kalafatis, A.D., Wang, L., Cluett, W.R.: Linearizing feedforward-feedback control of pH processes based on Wiener model. J. Process Control 15, 103–112 (2005) CrossRefGoogle Scholar
  10. 10.
    Ralston, J.C., Zoubir, A.M., Boashash, B.: Identification of a class of time-varying nonlinear system based on the Wiener model with application to automotive engineering. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E78-A(9), 1192–1200 (1995) Google Scholar
  11. 11.
    Bloemen, H.H.J., Chou, C.T., Boom, T.J.J., Verdult, V., Verhaegen, M., Backx, T.C.: Wiener model identification and predictive control for dual composition control of a distillation column. J. Process Control 11, 601–620 (2001) CrossRefGoogle Scholar
  12. 12.
    Ling, W.M., Rivera, D.: Nonlinear black-box identification of distillation column models-design variable selection for model performance enhancement. Int. J. Appl. Math. Comput. Sci. 8, 794–813 (1998) Google Scholar
  13. 13.
    Visala, A., Pitkanen, H., Aarne, H.: Modeling of chromatographic separation process with Wiener-MLP representation. J. Process Control 78, 443–458 (2001) Google Scholar
  14. 14.
    Kang, H.W., Cho, Y.S., Youn, D.H.: Adaptive precomensation of Wiener systems. IEEE Trans. Signal Process. 46, 2825–2829 (1998) CrossRefGoogle Scholar
  15. 15.
    den Brinker, A.C.: A comparison of results from parameter estimations of impulse responses of the transient visual system. Biol. Cybern. 61, 139–151 (1989) CrossRefGoogle Scholar
  16. 16.
    Hunter, I.W., Korenberg, M.J.: The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biol. Cybern. 55, 135–144 (1986) MATHMathSciNetGoogle Scholar
  17. 17.
    Chen, G., Chen, Y., Ogmen, H.: Identifying chaotic systems via a Wiener-type cascade model. IEEE Control Syst. Mag. 17, 29–36 (1997) CrossRefGoogle Scholar
  18. 18.
    Billings, S.A., Fakhouri, S.Y.: Theory of separable processes with applications to the identification of nonlinear systems. Proc. IEE 125, 1051–1058 (1977) MathSciNetGoogle Scholar
  19. 19.
    Billings, S.A., Fakhouri, S.Y.: Identification of systems containing linear dynamic and static nonlinear elements. Automatica 18, 15–26 (1982) MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Bai, E.W.: Frequency domain identification of Wiener models. Automatica 39, 1521–1530 (2003) MATHCrossRefGoogle Scholar
  21. 21.
    Gomez, J.C., Baeyens, E.: Identification of block-oriented nonlinear systems using orthonormal bases. J. Process Control 14, 685–697 (2004) CrossRefGoogle Scholar
  22. 22.
    Greblicki, W.: Recursive identification of Wiener systems. Int. J. Appl. Math. Comput. Sci. 11, 977–991 (2001) MATHMathSciNetGoogle Scholar
  23. 23.
    Chan, K.H., Bao, J., Whiten, W.J.: A new approach to control of MIMO processes with static nonlinearities using an extended IMC framework. Comput. Chem. Eng. 30, 329–342 (2005) CrossRefGoogle Scholar
  24. 24.
    Verhaegen, M., Westwick, D.: Identifying MIMO Wiener systems using subspace model identification methods. Signal Process. 52, 235–258 (1996) MATHCrossRefGoogle Scholar
  25. 25.
    Janczak, A.: Instrumental variables approach to identification of a class of MIMO Wiener systems. Nonlinear Dyn. 48, 275–284 (2007) CrossRefMathSciNetGoogle Scholar
  26. 26.
    Vörös, J.: Parameter identification of Wiener systems with discontinuous nonlinearities. Syst. Control Lett. 44(5), 363–372 (2001) MATHCrossRefGoogle Scholar
  27. 27.
    Chen, H.F.: Recursive identification for Wiener model with discontinuous piece-wise linear function. IEEE Trans. Autom. Control 51(3), 390–400 (2006) CrossRefGoogle Scholar
  28. 28.
    Vörös, J.: Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities. Syst. Control Lett. 56(2), 99–105 (2007) MATHCrossRefGoogle Scholar
  29. 29.
    Kalafatis, A.D., Wang, L., Cluett, W.R.: Identification of Wiener-type nonlinear systems in a noisy environment. Int. J. Control 66(6), 923–941 (1997) MATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Rotar, V.: Probability Theory. World Scientific, London (1997), pp. 135–144 Google Scholar
  31. 31.
    Chen, H.F., Guo, L.: Identification and Stochastic Adaptive Control. Birkhäuser, Boston (1991), pp. 24–43 MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.School of Software, Key Lab for ISS of MOETsinghua UniversityBeijingChina
  2. 2.Graduate School of InformaticsKyoto UniversityKyotoJapan

Personalised recommendations