Proceedings ArticleDOI
Robustness Issues of the Equivalent Linear Representation of a Nonlinear System
Joannes Schoukens,John Lataire,R. Pintelon,Gerd Vandersteen +3 more
- pp 332-335
TLDR
In this paper, it was shown that the power spectrum SYS of the nonlinear noise source YS is a robust characteristic, making its use in the daily engineering practice very attractive.Abstract:
In many engineering applications, linear models are preferred, even if it is known that the system is nonlinear. A large class of nonlinear systems, excited with a 'Gaussian' random excitation, can be represented as a linear system GBLA plus a nonlinear noise source YS. The nonlinear noise source represents that part of the output that is not captured by the linear approximation. It was shown before that the GBLA is an invariant for a wide class of excitations with a user specified power spectrum. In this paper it is shown that also the power spectrum SYS of the nonlinear noise source YS is a robust characteristic. This shows that the alternative 'linear representation' of a nonlinear system is a robust one, making its use in the daily engineering practice very attractive.read more
Citations
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Journal ArticleDOI
Identification of block-oriented nonlinear systems starting from linear approximations: A survey
Maarten Schoukens,Koen Tiels +1 more
TL;DR: 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 are given.
Journal ArticleDOI
Linear System Identification in a Nonlinear Setting: Nonparametric Analysis of the Nonlinear Distortions and Their Impact on the Best Linear Approximation
TL;DR: In this paper, a linear dynamic time-invariant model is identified to describe the relationship between the reference signal and the output of the system, and the power spectrum of the unmodeled disturbances are identified to generate uncertainty bounds on the estimated model.
Journal ArticleDOI
Robustness Issues of the Best Linear Approximation of a Nonlinear System
TL;DR: It is shown that the best linear approximation G BLA and the power spectrum S Y S of the nonlinear noise source Y S are invariants for a wide class of excitations with a user-specified power spectrum, showing that the alternative ldquolinear representationrdquo of a nonlinear system is robust, making its use in the daily engineering practice very attractive.
Journal ArticleDOI
Parametric Identification of Parallel Hammerstein Systems
TL;DR: The linear dynamic parts of the system are modeled by a parametric rational function in the z - or s-domain, while the static nonlinearities are represented by a linear combination of nonlinear basis functions.
Journal ArticleDOI
Improved (non-)parametric identification of dynamic systems excited by periodic signals—The multivariate case
TL;DR: In this paper, the authors extended the results of [1] to multiple-input, multiple-output (MIMO) systems where all inputs and outputs are disturbed by noise (i.e., an errors-in-variables framework).
References
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Book
System Identification: A Frequency Domain Approach
Rik Pintelon,Joannes Schoukens +1 more
TL;DR: Focusing mainly on frequency domain techniques, System Identification: A Frequency Domain Approach, Second Edition also studies in detail the similarities and differences with the classical time domain approach.
Book
The Volterra and Wiener Theories of Nonlinear Systems
TL;DR: In this article, a complete and detailed development of the analysis, design and characterization of non-linear systems using the Volterra and Wiener theories, as well as gate functions, is presented.
Journal ArticleDOI
Linear approximations of nonlinear FIR systems for separable input processes
Martin Enqvist,Lennart Ljung +1 more
TL;DR: A necessary and sufficient condition on the input signal for the optimal LTI approximation of an arbitrary nonlinear finite impulse response (NFIR) system to be a linear finite impulse Response (FIR) model is presented.
Journal ArticleDOI
Identification of linear systems with nonlinear distortions
TL;DR: In this article, the impact of nonlinear distortions on linear system identification was studied and a theoretical framework was proposed that extends the linear system description to include nonlinear distortion: the nonlinear system is replaced by a linear model plus a nonlinear noise source.
Linear models of nonlinear systems
TL;DR: In this thesis, it is described how robust control design of some nonlinear systems can be performed based on a discrete-time linear model and a model error model valid only for bounded inputs.
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