In this paper we show that it is possible to retrieve structural information about complex block-oriented nonlinear systems, starting from linear approximations of the nonlinear system around different setpoints. The key idea is to monitor the movements of the poles and zeros of the linearized models and to reduce the number of candidate models on the basis of these observations.Besides the well known open loop single branch Wiener-, Hammerstein-, and Wiener-Hammerstein systems, we also cover a number of more general structures like parallel (multi branch) Wiener-Hammerstein models, and closed loop block oriented models, including linear fractional representation (LFR) models.
The work presented illustrates how the choice of input perturbation signal and experimental design improves the derived model of a nonlinear system, in partic-
G(k):Final frequency response estimate when averaged over realisations
This paper focuses on a state-space based approach for the identification of a rather general nonlinear blockstructured 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.
In this paper, two nonlinear optimization methods for the identification of nonlinear systems are compared. Both methods estimate all the parameters of a polynomial nonlinear state-space model by means of a nonlinear least-squares optimization. While the first method does not estimate the states explicitly, the second estimates both states and parameters adding an extra constraint equation. Both methods are introduced and their similarities and differences are discussed utilizing simulation and experimental data. The unconstrained method appears to be faster and more memory efficient, while the constrained method is robust towards instabilities.
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