http://iet.metastore.ingenta.com
1887

On the interpretation and practice of dynamical differences between Hammerstein and Wiener models

On the interpretation and practice of dynamical differences between Hammerstein and Wiener models

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IEE Proceedings - Control Theory and Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

It is suggested that the differences between the Hammerstein and Wiener models be interpreted and understood in terms of the system eigenvalues. In particular, it is shown that the Wiener representation should be preferred when the system dynamics vary with the operating point. Conversely, when only the system gain varies with the operating point, Hammerstein models generally outperform the Wiener representation. The paper also points out connections between such models and the more general non-linear autoregressive model with exogenous inputs (NARX) polynomial representation. From a practical control engineering point of view, the results presented seem to be more helpful than other ways of distinguishing between such model types. The main ideas are illustrated by means of three examples that use simulated and measured data.

References

    1. 1)
    2. 2)
    3. 3)
      • S.A. Billings , S.Y. Fakhouri . Identification of systems containing linear dynamic and static nonlinear elements. Automatica , 1 , 15 - 26
    4. 4)
    5. 5)
      • D. Schröder , C. Hintz , M. Rau . Intelligent modeling, observation, and control for nonlinear systems. IEEE Trans. Mechatronics , 2 , 122 - 131
    6. 6)
    7. 7)
      • J. Abonyi , R. Babuska , A. Ayala-Botto , F. Szeifert , L. Nagy . Identification and control of nonlinear systems using fuzzy Hammerstein models. Ind. Eng. Chem. Res. , 4302 - 4314
    8. 8)
    9. 9)
    10. 10)
    11. 11)
      • P. Palumbo , L. Piroddi . Seismic behavious of buttress dams: Non-linear modelling of a damaged buttress based on ARX/NARX models. J. Sound Vib. , 3 , 405 - 422
    12. 12)
    13. 13)
      • Billings, S.A., Leontaritis, I.J.: `Identification of nonlinear systems using parametric estimation techniques', Proc. IEE Conf. Control and its Applications, 1981, Warwick, p. 183–187.
    14. 14)
      • M.J. Korenberg , S.A. Billings , Y.P. Liu , P.J. McIlroy . Orthogonal parameter estimation algorithm for nonlinear stochastic systems. Int. J. Control , 1 , 193 - 210
    15. 15)
      • M. Kortmann , H. Unbenhauen . Structure detection in the identification of nonlinear systems. Trait. Signal , 5 , 5 - 25
    16. 16)
      • L.A. Aguirre , S.A. Billings . Improved structure selection for nonlinear models based on term clustering. Int. J. Control , 3 , 569 - 587
    17. 17)
      • Corrêa, M.V.: `Grey-box identification of nonlinear systems using rational and polynomial model representations', 2001, PhD, PPGEE, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil, In Portoguese.
    18. 18)
      • L.A. Aguirre , E.M. Mendes . Nonlinear polynomial models: Structure, term clusters and fixed points. Int. J. Bifurcation Chaos , 2 , 279 - 294
    19. 19)
      • L.A. Aguirre , M. Corrêa , C.C.S. Cassini . Nonlinearities in NARX polynomial models: Representation and estimation. IEE Proc. D, Control Theory Appl. , 4 , 343 - 348
    20. 20)
    21. 21)
      • L. Ljung . (1987) System identification, theory for the user.
    22. 22)
    23. 23)
      • L.A. Aguirre , A.V.P. Souza . An algorithm for estimating fixed points of dynamical systems from time series. Int. J. Bifurcation Chaos , 11 , 2203 - 2213
    24. 24)
      • A. Visala , H. Pitkänen , A. Halme . Modeling of chromatographic separation process with Wiener-MLP representation. J. Process Control , 443 - 458
    25. 25)
    26. 26)
      • E.M.A.M. Mendes , S.A. Billings . An alternative solution to the model structure selection problem. IEEE Trans. Man Cyber. - Part A , 21 , 597 - 608
    27. 27)
http://iet.metastore.ingenta.com/content/journals/10.1049/ip-cta_20045152
Loading

Related content

content/journals/10.1049/ip-cta_20045152
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address