Two-stage instrumental variables identification of polynomial Wiener systems with invertible nonlinearities

• Autorzy: Janczak Andrzej , Korbicz Józef

Identyfikatory

DOI

10.2478/amcs-2019-0042

• Języki publikacji: EN

Abstrakty

EN

A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.

Słowa kluczowe

EN

nonlinear system; parameter estimation; dynamic model; polynomial model

PL

układ nieliniowy; estymacja parametru; model dynamiczny; model wielomianowy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2019
• Tom: Vol. 29, no. 3
• Strony: 571--580
• Opis fizyczny: Bibliogr. 41 poz., rys., tab., wykr.

Twórcy

autor

Janczak Andrzej

• Institute of Control and Computation Engineering, University of Zielona Góra, ul. Szafrana 2, 65-516 Zielona Góra, Poland

autor

Korbicz Józef

• Institute of Control and Computation Engineering, University of Zielona Góra, ul. Szafrana 2, 65-516 Zielona Góra, Poland

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).