Journal ArticleDOI
Robustness Issues of the Best Linear Approximation of a Nonlinear System
Reads0
Chats0
TLDR
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.Abstract:
In many engineering applications, linear models are preferred, even if it is known that the system is disturbed by nonlinear distortions. A large class of nonlinear systems, which are excited with a ldquoGaussianrdquo random excitation, can be represented as a linear system G BLA plus a nonlinear noise source Y S . The nonlinear noise source represents that part of the output that is not captured by the linear approximation. In this paper, 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. This shows that the alternative ldquolinear representationrdquo of a nonlinear system is robust, making its use in the daily engineering practice very attractive. This result also opens perspectives to a new generation of dynamic system analyzers that also provide information on the nonlinear behavior of the tested system without increasing the measurement time.read more
Citations
More filters
Journal ArticleDOI
Nonlinear System Identification: A User-Oriented Road Map
Johan Schoukens,Lennart Ljung +1 more
TL;DR: The selection of topics and the organization of the discussion are strongly colored by the personal journey of the authors in this nonlinear universe.
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
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
More filters
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.