System Identification I

This chapter contains sections titled: Historical Review Supervised Multilayer Networks Unsupervised Neural Networks: Kohonen Network Unsupervised Networks: Adaptive Resonance Theory Network Model Validation Summary References Recommended Exercises

Nonlinear System Identification

Nonlinear system identification in structural dynamics: 10 more years of progress

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

This paper studies the impact of nonlinear distortions on linear system identification. It collects a number of previously published methods in a fully integrated approach to measure and model these systems from experimental data. First 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'. The class of nonlinear systems covered by this approach is described and the properties of the extended linear representation are studied. These results are used to design the experiments; to detect the level of the nonlinear distortions; to measure efficiently the 'best' linear approximation; to reveal the even or odd nature of the nonlinearity; to identify a parametric linear model; and to improve the model selection procedures in the presence of nonlinear distortions.

Identification of Linear Systems with Nonlinear Distortions

Nonlinear system-identification of the filling phase of a wet-clutch system

In this paper we discuss how to identify a mathematical model for a (non)linear dynamic system starting from experimental data. In the initial step, the frequency response function is measured, together with the properties of the disturbing noise and the nonlinear distortions. This uses nonparametric preprocessing techniques that require very little user interaction. On the basis of this information, the user can decide on an objective basis, in an early phase of the modelling process, to use either a simple linear approximation framework, or to build a more involved nonlinear model. We discuss both options here: i) Identification of linear models in the presence of nonlinear distortions, including the generation of error bounds; and ii) Identification of a nonlinear model. For the latter, a double approach is proposed, using either unstructured nonlinear state space models, or highly structured block oriented nonlinear models. The paper is written from a users perspective.

System identification in a real world

This paper focuses on a state-space based approach for the identification of a rather general nonlinear block-structured model. The model has several Single-Input Single-Output (SISO) static polynomial nonlinearities connected to a Multiple-Input Multiple-Output (MIMO) dynamic part. The presented method is an extension and improvement of prior work, where at most two nonlinearities could be identified. The location of the nonlinearities or their relation to other parts of the model does not have to be known beforehand: the method is a black-box approach, in which no states, internal signals or structural properties need to be measured or known. The first step is to estimate a partly structured polynomial (nonlinear) state-space model from input-output measurements. Secondly, an algebraic approach is used to split the dynamics and the nonlinearities by decomposing the multivariate polynomial coefficients.

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Identification of a block-structured model with several sources of nonlinearity

A new method is proposed to solve the model inversion problem that is part of model based iterative learning control (ILC) for nonlinear systems. The model inversion problem consists of finding the input signal corresponding to a given output signal. This problem is formulated as a nonlinear dynamic optimization problem in time domain and solved efficiently using a constrained Gauss-Newton algorithm. A nonlinear ILC algorithm based on this model inversion approach is validated numerically and experimentally. The considered application is an electric circuit described by a polynomial nonlinear state-space model. The nonlinear ILC algorithm shows fast convergence and accurate tracking control.

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A. Van Mulders

Papers

Nonlinear system-identification of the filling phase of a wet-clutch system

System identification in a real world

Identification of a block-structured model with several sources of nonlinearity

Model based nonlinear iterative learning control: A constrained Gauss-Newton approach

Identification of a Block-Structured Model with Localised Nonlinearity