Abstract
System identification refers to the experimental approach that consists of determining system models by fitting experimental data to a suitable model structure [14] in some optimal ways. Linear model structures can be based upon when the physical system remains in the vicinity of a nominal operation point so that the linearity assumption is satisfied. When a wide range of operation modes are involved, the linear assumption may not be valid and a nonlinear model structure becomes necessary to capture the system (nonlinear) behaviour. In relatively simple cases, suitable nonlinear model structures are obtained using the mathematical modelling approach that consists of describing the system phenomena using basic laws of physics, chemistry, etc. Then, system identification methods may be resorted to assign suitable numerical values to the (unknown) model parameters. When the mathematical modelling approach is insufficient, system identification must rely on ‘universal’ black-box or grey-box nonlinear model structures. These include NARMAX models [9], multi-model representations [15], neuro-fuzzy models [3], Volterra series [19], non-parametric models [14] and others.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Balestrino, A., Landi, A., Ould-Zmirli, M., Sani, L.: Automatic nonlinear auto-tuning method for Hammerstein modeling of electrical drives. IEEE Transactions on Industrial Electronics 48, 645–655 (2001)
Boyd, S., Chua, L.O.: Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Transactions on Circuits and Systems 32, 1150–1161 (1985)
Brown, M., Harris, H.C.: Neurofuzzy adaptive modelling and control. Prentice Hall, New Jersey (1994)
Dempsey, E., Westwick, D.: Identification of Hammerstein models with cubic spline nonlinearities. IEEE Transactions on Biomedical Engineering 51, 237–245 (2004)
Eskinat, E., Johnson, S., Luyben, W.L.: Use of Hammerstein models in identification of nonlinear systems. AIChE Journal 37, 255–268 (1991)
Hammerstein, A.: Nichtlineare integralgleichung nebst anwendungen. Acta Mathematica 54, 117–176 (1930)
Hunt, K.J., Munih, M., Donaldson, N.D., Barr, F.M.D.: Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle. IEEE Transactions on Biomedical Engineering 45, 998–1009 (1998)
Hunter, I.W., Korenberg, M.J.: The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biological Cybernetics 55, 135–144 (1986)
Johansen, T.A., Foss, B.A.: Constructing NARMAX models using ARMAX models. International Journal of Control 58, 1125–1153 (1993)
Jurado, F.: A method for the identification of solid oxide fuel cells using a Hammerstein model. Journal of Power Sources 154, 145–152 (2006)
Kalafatis, A., Wang, L., Cluett, W.R.: Identification of time-varying pH processes using sinusoidal signals. Automatica 41, 685–691 (2005)
Kim, J., Konstantinou, K.: Digital predistortion of wideband signals based on power amplifier model with memory. IEE Electronics Letters 37, 1417–1418 (2001)
Lee, Y.J., Sung, S.W., Park, S., Park, S.: Input test signal design and parameter estimation method for the Hammerstein–Wiener processes. Industrial and Engineering Chemistry Research 43, 7521–7530 (2004)
Ljung, L.: System identification: Theory for the user. Prentice-Hall, Englewood Cliffs (1999)
Murray-Smith, R., Johansen, T.A.: Multiple model approaches to modelling and control. Taylor & Francis, London (1997)
Palanthandalam-Madapusi, H.J., Ridley, A.J., Bernstein, D.S.: Identification and prediction of ionospheric dynamics using a Hammerstein–Wiener model with radial basis functions. In: American Control Conference, Portland, OR, USA, pp. 5052–5057 (2005)
Palanthandalam-Madapusi, H.J., Bernstein, D.S., Ridley, A.J.: Space Weather Forecasting: Identifying periodically switching block-structured models for predicting magnetic-field fluctuations. IEEE Control Systems Magazine 27, 109–123 (2007)
Park, H.C., Sung, S.W., Lee, J.: Modeling of Hammerstein–Wiener processes with special input test signals. Industrial and Engineering Chemistry Research 45, 1029–1038 (2006)
Schetzen, M.: The Volterra and Wiener theories of non-linear systems. Krieger Publishing Co. (1980), (reprint Edition with Additional Material, Malabar, Fla)
Srinivasan, R., Rengaswamy, R., Narasimhan, S., Miller, R.: Control loop performance assessment - Hammerstein model approach for stiction diagnosis. Industrial and Engineering Chemistry Research 44, 6719–6728 (2005)
Sung, S.: System identification method for Hammerstein processes. Industrial and Engineering Chemistry Research 41, 4295–4302 (2002)
Wang, J., Sano, A., Chen, T., Huang, B.: Identification of Hammerstein systems without explicit parameterization of nonlinearity. International Journal of Control 82, 937–952 (2009)
Wiener, N.: Nonlinear problems in random theory. Wiley, New York (1958)
Zhu, Y.: Distillation column identification for control using Wiener model. In: American Control Conference, San Diego, California, vol. 5, pp. 3462–3466 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer London
About this chapter
Cite this chapter
Bai, EW., Giri, F. (2010). Introduction to Block-oriented Nonlinear Systems. In: Giri, F., Bai, EW. (eds) Block-oriented Nonlinear System Identification. Lecture Notes in Control and Information Sciences, vol 404. Springer, London. https://doi.org/10.1007/978-1-84996-513-2_1
Download citation
DOI: https://doi.org/10.1007/978-1-84996-513-2_1
Publisher Name: Springer, London
Print ISBN: 978-1-84996-512-5
Online ISBN: 978-1-84996-513-2
eBook Packages: EngineeringEngineering (R0)