Decomposition of generalized frequency response functions for nonlinear systems using symbolic computation

Billings, S.A.; Yusof, Mohd Ismail

doi:10.1080/00207179608921712

Cited by 8 publications

(2 citation statements)

References 16 publications

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“…, where all frequency variables are limited by the sampling frequency. In addition, as the nonlinear degree M in an identified NARX model is often selected to be low to reduce complexity and avoid possible unstable models (Napoli & Piroddi, 2010;Zhu et al, 2015), Billings, 1989, Billings & Yusof, 1996, the specific form of function , p m p C  can be determined using computer codes conducting symbolic computations.…”

Section: The Generalized Output Bound Characteristic Function (Gobcf)mentioning

confidence: 99%

A new convergence analysis for the Volterra series representation of nonlinear systems

Zhu

Lang

2020

Automatica

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The convergence of the Volterra series representation of nonlinear systems is the fundamental requirement for the analysis of nonlinear systems in the frequency domain. In the present study, a new criterion is derived to determine the convergence of the Volterra series representation of nonlinear systems described by a NARX (Nonlinear Auto Regressive with eXegenous input) model. The analysis is performed based on a new function known as Generalized Output Bound Characteristic Function (GOBCF), which is defined in terms of the input, output and parameters of the NARX model of nonlinear systems. Compared to the existing results, the new criterion provides a much more rigorous and effective approach to the analysis of the convergence conditions and properties of the Volterra series representation of nonlinear systems. Two case studies have been used to demonstrate the effectiveness of the new convergence analysis criterion and the advantages of the new analysis over those produced by existing approaches.

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Section: The Generalized Output Bound Characteristic Function (Gobcf)mentioning

confidence: 99%

A new convergence analysis for the Volterra series representation of nonlinear systems

Zhu

Lang

2020

Automatica

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“…A symbolic procedure is proposed in Reference [21] to address this issue but unfortunately produces an overly complicated solution since permutations for general frequency inputs are considered. Thus, a limit of up to a 5th order general frequency response function is calculated in Reference [21]. For SIDF applications where n is an odd integer, the values of jo 1 ; jo 2 ; .…”

Section: Combinatorial Analysismentioning

confidence: 99%

Convergence and computation of describing functions using a recursive Volterra series

Glass

Franchek

2004

Intl J Robust & Nonlinear

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SUMMARYPresented in this paper is a comparison of algorithms for computing an approximation to the sinusoidal input describing function (SIDF) for the nonlinear differential equationThe importance of this nonlinear differential equation comes from the context of nonlinear feedback controller design. Specifically, this equation is either a linear lead or lag controller (depending on the coefficient values) augmented with a nonlinear, polynomial type term. Consequently, obtaining a SIDF representation of this nonlinear differential equation or creating a process to obtain SIDFs for other similar differential equations, will facilitate nonlinear controller design using classical loop shaping tools. The two SIDF approximations studied include the well-established harmonic balance method and a Volterra series based algorithm. In applying the Volterra series, several theoretical issues were addressed including the development of a recursive solution that calculates high order Volterra transfer functions, and the guarantee of convergence to an arbitrary accuracy. Throughout the paper, case studies are presented.

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The Identification and Analysis of Nonlinear Systems in the Frequency Domain

Billings

2013

Nonlinear System Identification

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Decomposition of generalized frequency response functions for nonlinear systems using symbolic computation

Cited by 8 publications

References 16 publications

A new convergence analysis for the Volterra series representation of nonlinear systems

A new convergence analysis for the Volterra series representation of nonlinear systems

Convergence and computation of describing functions using a recursive Volterra series

The Identification and Analysis of Nonlinear Systems in the Frequency Domain

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