Combined frequency-prediction error identification approach for Wiener systems with backlash and backlash-inverse operators

Giri, F.; Radouane, Abdelhadi; Brouri, Adil; Chaoui, F.Z.

doi:10.1016/j.automatica.2013.12.030

Cited by 38 publications

(37 citation statements)

References 25 publications

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“…As the proposed nonlinear mathematical model is linear in parameters it can be directly applied in on-line identification of nonlinear dynamic systems with input backlash and output saturation using the known recursive least-squares algorithm [46,47]. Moreover, the presented identification method can be easily extended for systems with the so-called general input backlash [48][49][50][51] and also other types of static nonlinearities can be considered in the output block.…”

Section: Resultsmentioning

confidence: 99%

Identification of nonlinear block-oriented systems with backlash and saturation

Vörös

2019

Journal of Electrical Engineering

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A new approach to modeling and identification of discrete-time nonlinear dynamic systems with input backlash and output saturation nonlinearities is presented. The proposed three-block cascade mathematical model results from successive applications of the key-term separation principle. This provides special nonlinear model description that is linear in parameters. An iterative technique with internal variable estimation is proposed for estimation of all the model parameters based on measured input/output data and minimizing the least-squares criterion. Illustrative example of cascade system identification with backlash and saturation is included.

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Section: Resultsmentioning

confidence: 99%

Identification of nonlinear block-oriented systems with backlash and saturation

Vörös

2019

Journal of Electrical Engineering

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“…Frequency-domain approaches can be used to exploit the nonlinear behavior of the block-oriented nonlinear system, which is not visible in the time-domain, e.g. (Giri et al, 2014).…”

Section: Other Approachesmentioning

confidence: 99%

“…The structured nature of block-oriented nonlinear systems can be exploited by carefully designing the input signal used during the estimation, e.g. step signals, sine wave signals, sinesweeps or phase-coupled multisines (Giri et al, 2014;Tiels et al, 2015;Rébillat et al, 2016;Castro-Garcia et al, 2016). Most of the methods described in the following sections make use of Gaussian input signals (Definition 1) to exploit Bussgang's Theorem (see Section 3).…”

Section: Other Approachesmentioning

confidence: 99%

Identification of block-oriented nonlinear systems starting from linear approximations: A survey

2017

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Block-oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use. Many different identification approaches were developed over the years to estimate the parameters of a wide range of block-oriented nonlinear models. One class of these approaches uses linear approximations to initialize the identification algorithm. The best linear approximation framework and the -approximation framework, or equivalent frameworks, allow the user to extract important information about the system, guide the user in selecting good candidate model structures and orders, and prove to be a good starting point for nonlinear system identification algorithms. This paper gives an overview of the different block-oriented nonlinear models that can be identified using linear approximations, and of the identification algorithms that have been developed in the past. A non-exhaustive overview of the most important other block-oriented nonlinear system identification approaches is also provided throughout this paper.

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“…It is well known that many industrial processes are inherently nonlinear and when the operating point changes it is difficult to represent adequately a given process by means of a linear model. Therefore, to achieve the required system performance, advanced control methods based on nonlinear process models are identification of Wiener systems, and many different identification methods have been developed that are based on correlation analysis (e.g., Billings and Fakhouri, 1987;1982;Van Vaerenbergh et al, 2013), frequency analysis (Giri et al, 2014;Brouri and Slassi, 2015), nonlinear optimization (Wigren, 1993;Al-Duwaish et al, 1996;Janczak, 2005;Vörös, 2007;Ławryńczuk, 2013;Zhou et al, 2013), linear regression (Janczak, 2005;2018;Stanisławski et al, 2014), nonparametric regression (Greblicki, 1997;2001), and subspace approach (Westwick and Verhaegen, 1996;Baeyens, 2002, 2005;Ase and Katayama, 2015).…”

Section: Introductionmentioning

confidence: 99%

Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities

Janczak

Korbicz

2019

International Journal of Applied Mathematics and Computer Science

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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.

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Combined frequency-prediction error identification approach for Wiener systems with backlash and backlash-inverse operators

Cited by 38 publications

References 25 publications

Identification of nonlinear block-oriented systems with backlash and saturation

Identification of nonlinear block-oriented systems with backlash and saturation

Identification of block-oriented nonlinear systems starting from linear approximations: A survey

Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities

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