Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions

Sasa S. Nikolic; Miroslav B. Milovanovic; Nikola B. Dankovic; Darko B. Mitic; Stanisa Lj. Peric; Andjela D. Djordjevic; Petar S. Djekic

doi:10.5755/j02.eie.33838

Authors

Sasa S. Nikolic Department of Control Systems, Faculty of Electronic Engineering, University of Nis, Serbia https://orcid.org/0000-0003-2745-3862
Miroslav B. Milovanovic Department of Control Systems, Faculty of Electronic Engineering, University of Nis, Serbia https://orcid.org/0000-0003-0535-0790
Nikola B. Dankovic Department of Control Systems, Faculty of Electronic Engineering, University of Nis, Serbia https://orcid.org/0000-0003-0986-5695
Darko B. Mitic Department of Control Systems, Faculty of Electronic Engineering, University of Nis, Serbia https://orcid.org/0000-0001-9483-0176
Stanisa Lj. Peric Department of Control Systems, Faculty of Electronic Engineering, University of Nis, Serbia https://orcid.org/0000-0003-4766-195X
Andjela D. Djordjevic Department of Control Systems, Faculty of Electronic Engineering, University of Nis, Serbia https://orcid.org/0000-0003-2611-1246
Petar S. Djekic Academy of Applied Technical and Preschool Studies-Nis, Serbia https://orcid.org/0000-0001-9506-7301

DOI:

https://doi.org/10.5755/j02.eie.33838

Keywords:

Hammerstein-Wiener models, Identification system, Improved orthogonal functions, Nonlinear systems

Abstract

Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, and a new improvement is proposed, which is consisted of the basic structure of Hammerstein-Wiener models with an improved orthogonal function of Müntz-Legendre type. We present an extension of generalised Malmquist polynomials that represent Müntz polynomials. Also, a detailed mathematical background for performing improved almost orthogonal polynomials, in combination with Hammerstein-Wiener models, is proposed. The proposed approach is used to identify the strongly nonlinear hydraulic system via the transfer function. To compare the results obtained, well-known orthogonal functions of the Legendre, Chebyshev, and Laguerre types are exploited.