Instrumental variables approach to identification of a class of MIMO Wiener systems

A new approach to identification of multi-input multi-output (MIMO) Wiener systems using the instrumental variables method is presented. It is assumed that static nonlinear elements are invertible and their inverse characteristics can be expressed or approximated by polynomials of known orders. It is also assumed that the linear part of the Wiener system can be represented by a matrix polynomial form. Based on these assumptions, the Wiener system is transformed introducing a new parameterization and its parameters are estimated using a linear-in-parameters model. To solve the problem of non-consistency of least squares parameter estimates, an instrumental variables method is employed. A numerical example is included to show the effectiveness and the practical feasibility of the presented approach.

[1]  A. Janczak.  Instrumental variables approach to identification of polynomial wiener systems , 2003, 2003 European Control Conference (ECC).

[2]  W. R. Cluett,et al.  Linearizing feedforward-feedback control of pH processes based on the Wiener model , 2005 .

[3]  W. Greblicki.  Nonparametric identification of Wiener systems by orthogonal series , 1994, IEEE Trans. Autom. Control..

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

[5]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[6]  Wlodzimierz Greblicki,et al.  Recursive identification of Wiener systems , 2001 .

[7]  H. Al. Duwaish,et al.  Use of Multilayer Feedforward Neural Networks in Identification and Control of Wiener Model , 1996 .

[8]  Michel Verhaegen,et al.  Identifying MIMO Wiener systems using subspace model identification methods , 1996, Signal Process..

[9]  A. Janczak,et al.  Identification of Nonlinear Systems Using Neural Networks and Polynomial Models: A Block-Oriented Approach , 2004 .

[10]  S. Billings,et al.  Theory of separable processes with applications to the identification of nonlinear systems , 1978 .

[11]  Er-Wei Bai,et al.  Identification of linear systems with hard input nonlinearities of known structure , 2002, Autom..

[12]  Jozef Vörös.  Parameter identification of Wiener systems with discontinuous nonlinearities , 2001, Syst. Control. Lett..

[13]  Aarne Halme,et al.  Modeling of chromatographic separation process with Wiener-MLP representation , 2001 .

[14]  Grazyna Pajunen,et al.  Adaptive control of wiener type nonlinear systems , 1992, Autom..

[15]  Yong Soo Cho,et al.  Adaptive precompensation of Wiener systems , 1998, IEEE Trans. Signal Process..

[16]  H. Bloemen,et al.  Wiener Model Identification and Predictive Control for Dual Composition Control of a Distillation Column , 2001 .

[17]  Er-Wei Bai.  Frequency domain identification of Wiener models , 2003, Autom..

[18]  R. Pearson,et al.  Gray-box identification of block-oriented nonlinear models , 2000 .

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

[20]  Stephen A. Billings,et al.  Identification of systems containing linear dynamic and static nonlinear elements , 1982, Autom..

[21]  Daniel E. Rivera,et al.  Nonlinear black-box identification of distillation column models - design variable selection for model performance enhancement , 1998 .

[22]  W. R. Cluett,et al.  A new approach to the identification of pH processes based on the Wiener model , 1995 .

[23]  T. Wigren.  Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model , 1994, IEEE Trans. Autom. Control..

[24]  W. R. Cluett,et al.  Identification of Wiener-type nonlinear systems in a noisy environment , 1997 .

[25]  Torbjörn Wigren,et al.  Recursive prediction error identification using the nonlinear wiener model , 1993, Autom..

[26]  Enrique Baeyens,et al.  Identification of block-oriented nonlinear systems using orthonormal bases , 2004 .

[27]  Andrzej Janczak,et al.  Comparison of four gradient-learning algorithms for neural network Wiener models , 2003, Int. J. Syst. Sci..

[28]  Andrzej Janczak.  Identification of Nonlinear Systems Using Neural Networks and Polynomial Models , 2005 .