Open Access
Non-parametric identification of higher order sinusoidal output describing functions
Pwjm Pieter Nuij,M Maarten Steinbuch,Okko H. Bosgra +2 more
- pp 2361-2371
TLDR
The HOSODF can be defined for the class of causal, stable, time invariant non-linear systems which give a sinusoidal response to a specific harmonic excitation of non- linear systems.Abstract:
In this paper the concept of the Higher Order Sinusoidal Output Describing Functions (HOSODF) is presented. HOSODF can be defined for the class of causal, stable, time invariant non-linear systems which give a sinusoidal response to a specific harmonic excitation. The HOSODF relate the magnitude and phase of the individual harmonics, which together compose that specific input signal, to the sinusoidal output signal of such a system. HOSODF are the dual of the Higher Order Sinusoidal Input Describing Functions (HOSIDF). Like the HOSIDF, the HOSODF are the results of an extension of linear techniques towards non-linear systems analysis. Using the HOSODF, the non-linear systems under investigation can be modeled as a cascade of the HOSODF and a Virtual Harmonics Compressor (VHC). The VHC is defined as a non-linear component which transforms a harmonic input signal y(t) into a sinusoidal output signal y(t) with frequency ω, amplitude â and phase φ. This input signal y(t) consists of an infinite amount of harmonics of the output signal y(t) with frequency nω, amplitude â and phase nω with n = 0, 1, ...∞. Special attention is paid to the non-parametric identification of the HOSODF. The identification requires control of the frequency and amplitude of the sinusoidal output of the system within its domain of possible sinusoidal output signals. This specific state of these non-linear systems can be reached by incorporating the system under test in a feedback loop. In this loop the desired sinusoidal output is defined as the control objective of a dedicated repetitive controller consisting of a memory loop with positive feedback. The design of the learning filter required for stability is also addressed. As a spinoff of the identification technique, the authors see opportunities for advanced non-linear control of shaker systems aimed at sinusoidal excitation of non-linear systems.read more
Citations
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Identification of Linear Systems with Nonlinear Distortions
TL;DR: A theoretical framework is proposed that extends the linear system description to include the impact of nonlinear distortions: the nonlinear system is replaced by a linear model plus a 'nonlinear noise source'.
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Brief paper: Spectral analysis of block structured nonlinear systems and higher order sinusoidal input describing functions
TL;DR: A mapping from the parameters defining the nonlinear and LTI dynamics to the output spectrum is derived, which allows analytic description and analysis of the corresponding higher order sinusoidal input describing functions.
Journal ArticleDOI
A comparative overview of frequency domain methods for nonlinear systems
TL;DR: This paper provides a comparative overview of four classes of frequency domain methods for nonlinear systems: Volterra based models, nonlinear frequency response functions / Bode plots, describing functions and linear approximations in the presence of nonlinearities.
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Frequency domain‐based nonlinearity detection and compensation in Lur'e systems
DJ David Rijlaarsdam,Agung Chris Setiadi,Pwjm Pieter Nuij,Joannes Schoukens,M Maarten Steinbuch +4 more
TL;DR: In this article, the authors proposed a frequency domain-based method for detection and optimal compensation of performance degrading nonlinear effects in Lur'e-type systems, where a sinusoidal response is necessary and sufficient to show the existence of an equivalent linear and time invariant dynamical model that fully captures the system dynamics for a well defined set of input signals and initial conditions.
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Book Review: Nonlinear System Theory: The Volterra/Wiener ApproachNonlinear System Theory: The Volterra/Wiener approach: RughWilson J. (Johns Hopkins University Press, 1981, 325 pp., $22.75)
TL;DR: In this paper, the authors present a book on multivariable system theory and design for postgraduate students with a focus on pole assignment, frequency domain, design techniques and robust servomechanism problem.
References
More filters
Journal ArticleDOI
An iterative method for the identification of nonlinear systems using a Hammerstein model
Kumpati S. Narendra,P. Gallman +1 more
TL;DR: In this article, an iterative method is proposed for the identification of nonlinear systems from samples of inputs and outputs in the presence of noise, which consists of a no-memory gain (of an assumed polynomial form) followed by a linear discrete system.
Journal ArticleDOI
The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs
E. Bedrosian,S.O. Rice +1 more
TL;DR: Results, both old and new, which will aid the reader in applying Volterra-series-type analyses to systems driven by sine waves or Gaussian noise are presented.
Journal ArticleDOI
Digital control of repetitive errors in disk drive systems
Kok Kia Chew,Masayoshi Tomizuka +1 more
TL;DR: A modified prototype repetitive controller is applied as a plug-in module to a Winchester disk drive with a preexisting analog feedback controller to demonstrate its efficacy in the reduction of this periodic component.
Journal ArticleDOI
Brief Repetitive control for systems with uncertain period-time
TL;DR: A robust repetitive controller structure is proposed that uses multiple memory-loops in a certain feedback configuration, such that small changes in period-time do not diminish the disturbance rejection properties.
Journal ArticleDOI
Parametric and nonparametric identification of linear systems in the presence of nonlinear distortions-a frequency domain approach
TL;DR: A related linear dynamic system (RLDS) approximation to the nonlinear system (NLS) is defined, and it is shown that the differences between the NLS and the RLDS can be modeled as stochastic variables with known properties.
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