Identification for Hammerstein nonlinear systems based on universal spline fractional order LMS algorithm

Cheng, Songsong; Wei, Yiheng; Sheng, Dian; Wang, Yong

doi:10.1016/j.cnsns.2019.104901

Cited by 29 publications

(14 citation statements)

References 27 publications

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“…Furthermore, using (24) one can derive the expression of the linear subsystem output for sinusoidal excitation in terms of intermediate simulated input…”

Section: B Identification Of the Nonlinearitymentioning

confidence: 99%

“…The state-space model approach for fractional Hammerstein process was described in [23]. Neural network based nonlinear fractional process modeling verified in real time with wind turbines was depicted in [24]. Recently, Wang et al [1] presented a fully parametric identification (FPI) technique using two algorithms for a fractional Hammerstein process.…”

Section: Introductionmentioning

confidence: 99%

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Identification scheme for fractional Hammerstein models with the delayed Haar wavelet

Kothari

Mehta

Prasad

et al. 2020

IEEE/CAA J. Autom. Sinica

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The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix (HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.

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“…Furthermore, using (24) one can derive the expression of the linear subsystem output for sinusoidal excitation in terms of intermediate simulated input…”

Section: B Identification Of the Nonlinearitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Identification scheme for fractional Hammerstein models with the delayed Haar wavelet

Kothari

Mehta

Prasad

et al. 2020

IEEE/CAA J. Autom. Sinica

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show abstract

“…Dentre os modelos orientados a blocos mais populares estão os sistemas Hammerstein (Castro- Garcia et al, 2018;Cheng et al, 2018Cheng et al, , 2019 e os sistemas Wiener (Trinh et al, 2019). A estrutura chamada de Hammerstein-Wiener é um modelo orientado por blocos composto por duas partes não lineares, uma na entrada e uma na saída, e uma parte linear entre os dois blocos (Zhu, 2001), sendo sua utilização bem estabelecida na área de identificação, presentes nos mais diversos estudos (Li & Ren, 2018;Schoukens et al, 2015).…”

Section: Identificação Do Sistema Não Linearunclassified

Otimização Multiobjetivo Aplicada no Controle de um Sistema Não Linear do Tipo Aeropêndulo

Kagami

Angonese

Pereira

et al. 2020

Anais Do Congresso Brasileiro De Automática 2020

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A parametrização de controladores é um problema constantemente estudado, tanto para aplicações na área industrial, quanto acadêmica. A utilização da otimização multiobjetivo, apoiada por metaheurísticas no auxílio a esta tarefa tem sido cada vez mais comum, visto que possibilita a obtenção de múltiplas soluções de maneira mais simples e rápida, quando confrontada por métodos clássicos. Neste artigo, o Algoritmo Genético de Classificação Não Dominada II (NSGA-II) é utilizado para a obtenção dos ganhos de um controlador Proporcional-Integral-Derivativo (PID) cujo propósito é estabilizar um sistema não linear aeropêndulo, identificado por um modelo Hammerstein-Wiener. O conjunto de soluções obtido pelo algoritmo NSGA-II mostrou-se inviável para análise e simulação individual devido à sua elevada quantidade, de modo que o método de auxílio à tomada de decisão multicritério Processo Analítico Hierárquico (AHP), foi adotado, a solução apontada como preferencial pelo método AHP apresentou rápido tempo de estabilização e mínimo de sobressinal.

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“…some linear combination of preset basis functions [6, 13, 35, 43–45, 50].…”

Section: Introductionmentioning

confidence: 99%

Hammerstein system with a stochastic input of arbitrary/unknown autocorrelation – nonparametric estimator of the static nonlinear subsystem

Lin

Wong

2021

IET Signal Processing

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This study proposes the first estimator in the open literature (to the present authors' best knowledge) to nonparametrically estimate a Hammerstein system's nonlinear static subsystem when excited by an input that is temporally self-correlated with an unknown spectrum, an unknown variance and an unknown mean (instead of the input as commonly presumed to be white and zero-mean). This proposed nonparametric estimator is analytically proved here to be asymptotically unbiased and pointwise consistent. The proposed estimate's associated finite-sample convergence rate is also derived analytically. | INTRODUCTIONA Hammerstein system comprises two subsystems in series: (i) a nonlinear, static (memoryless) subsystem, trailed by (ii) a linear, dynamic, time-invariant, asymptotically stable subsystem. Please see Figure 1 for a schematic showing these two subsystems and their associated signals, which are described in great details in Section 1.This study proposes a new estimate for the nonlinear static subsystem's input-output nonlinearity m(⋅). This estimator relies on observations of only the input and the output of the overall Hammerstein system (i.e. {(U n , Y n ), ∀n}), but not on any observation of any intrasystem signal/noise (e.g. {W n , Z n , V n , X n , P n , ∀n}).This proposed estimator also does not require any prior/simultaneous identification of the nonlinear static subsystem.This is an open access article under the terms of the Creative Commons Attribution-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited and no modifications or adaptations are made.

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Identification for Hammerstein nonlinear systems based on universal spline fractional order LMS algorithm

Cited by 29 publications

References 27 publications

Identification scheme for fractional Hammerstein models with the delayed Haar wavelet

Identification scheme for fractional Hammerstein models with the delayed Haar wavelet

Otimização Multiobjetivo Aplicada no Controle de um Sistema Não Linear do Tipo Aeropêndulo

Hammerstein system with a stochastic input of arbitrary/unknown autocorrelation – nonparametric estimator of the static nonlinear subsystem

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