A unified approach for the parametric identification of SISO/MIMO Wiener and Hammerstein systems

Abstract Hammerstein and Wiener models are nonlinear representations of systems composed by the coupling of a static nonlinearity N and a linear system L in the form N–L and L–N respectively. These models can represent real processes which made them popular in the last decades. The problem of identifying the static nonlinearity and linear system is not a trivial task, and has attracted a lot of research interest. It has been studied in the available literature either for Hammerstein or Wiener systems, and either in a discrete-time or continuous-time setting. The objective of this paper is to present a unified framework for the identification of these systems that is valid for SISO and MIMO systems, discrete- and continuous-time settings, and with the only a priori knowledge that the system belongs to the set including Wiener and Hammerstein models.

[1]  Han-Fu Chen,et al.  Recursive identification for Wiener model with discontinuous piece-wise linear function , 2006, IEEE Transactions on Automatic Control.

[2]  E. Bai,et al.  Block Oriented Nonlinear System Identification , 2010 .

[3]  Yucai Zhu,et al.  Multivariable System Identification For Process Control , 2001 .

[4]  Michel Verhaegen,et al.  Identification of the deterministic part of MIMO state space models given in innovations form from input-output data , 1994, Autom..

[5]  Vito Cerone,et al.  Parameter bounds for discrete-time Hammerstein models with bounded output errors , 2003, IEEE Trans. Autom. Control..

[6]  W. Greblicki,et al.  Nonparametric system identification , 2008 .

[7]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[8]  K. Narendra,et al.  An iterative method for the identification of nonlinear systems using a Hammerstein model , 1966 .

[9]  Liuping Wang,et al.  Identification of time-varying pH processes using sinusoidal signals , 2005, Autom..

[10]  David T. Westwick,et al.  Identification of Hammerstein models with cubic spline nonlinearities , 2004, IEEE Transactions on Biomedical Engineering.

[11]  José Luis Figueroa,et al.  Wiener and Hammerstein uncertain models identification , 2009, Math. Comput. Simul..

[12]  Johan Schoukens,et al.  Computing an initial estimate of a Wiener-Hammerstein system with a random phase multisine excitation , 2005, IEEE Transactions on Instrumentation and Measurement.

[13]  X. Jing.  Frequency domain analysis and identification of block-oriented nonlinear systems , 2011 .

[14]  Fouad Giri,et al.  Parameter identification of Hammerstein systems containing backlash operators with arbitrary-shape parametric borders , 2011, Autom..

[15]  Stanko Strmcnik,et al.  Identification of nonlinear systems using a piecewise-linear Hammerstein model , 2005, Syst. Control. Lett..

[16]  Heinz Unbehauen,et al.  Continuous-time approaches to system identification - A survey , 1990, Autom..

[17]  Fouad Giri,et al.  An Analytic Geometry Approach to Wiener System Frequency Identification , 2009, IEEE Transactions on Automatic Control.

[18]  Dietmar Bauer,et al.  Asymptotic properties of subspace estimators , 2005, Autom..

[19]  Martin Enqvist.  Identification of Block-oriented Systems Using the Invariance Property , 2010 .

[20]  Marc Rébillat,et al.  Identification of cascade of Hammerstein models for the description of nonlinearities in vibrating devices , 2011 .

[21]  Sirish L. Shah,et al.  Identification of Hammerstein models using multivariate statistical tools , 1995 .

[22]  Ioan Doré Landau,et al.  Digital Control Systems , 2014 .

[23]  W. Rudin.  Real and complex analysis , 1968 .

[24]  Lars-Henning Zetterberg,et al.  Identification of certain time-varying nonlinear Wiener and Hammerstein systems , 2001, IEEE Trans. Signal Process..

[25]  Jie Bao,et al.  Identification of MIMO Hammerstein systems using cardinal spline functions , 2006 .