Further results on the identification problem for the class of nonlinear systems S_M
TL;DR: In this paper, the structure of the identification problem based on steady-state frequency response is considered for the class of nonlinear systems S_{M}, and two approaches using amplitude and phase measurements are presented, one of which requires measurements of only the first two harmonics of the steady state response.
Abstract: For the class of nonlinear systems S_{M} , the structure of the identification problem based on steady-state frequency response is considered. Two approaches using amplitude and phase measurements are presented, one of which requires measurements of only the first two harmonics of the steady-state response. Furthermore it is shown that with a minimum phase restriction the system can be identified from amplitude measurements of the first two harmonics. In each case we obtain a considerable reduction in the number of measurements and inputs required by previous approaches.
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DOI•
01 Nov 1980TL;DR: A survey of nonlinear system identification algorithms and related topics is presented by extracting significant results from the literature and presenting these in an organised and systematic way as discussed by the authors, where the limitations, relationships and applicability of the methods are discussed throughout.
Abstract: A survey of nonlinear system identification algorithms and related topics is presented by extracting significant results from the literature and presenting these in an organised and systematic way. Algorithms based on the functional expansions of Wiener and Volterra, the identification of block-oriented and bilinear systems, the selection of input signals, structure detection, parameter estimation and recent results from catastrophe theory and included. The limitations, relationships and applicability of the methods are discussed throughout.
491 citations
TL;DR: It is shown that systems composed of cascade, feedforward, feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only.
446 citations
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.
160 citations
TL;DR: In this paper, a review and an assessment of techniques for automatic test generation for analog systems is presented, respectively, proceeding from approaches based on deterministic and probabilistic estimation, taxonomical and topological analyses.
Abstract: The purpose of this paper is both a review and an assessment of techniques presently available for automatic test generation for analog systems. After recalling the general problems of automatic testing (definitions, faults in analog systems, different types of tests, main operations, and diagnosis procedures), characterization and description modes of analog systems, and the main software ingredients of automatic test equipment, a categorization of known techniques along several criteria can be proposed. Then, several techniques, respectively, proceeding from approaches based on deterministic and probabilistic estimation, taxonomical and topological analyses can be detailed. Techniques specific to linear systems (several of them belonging to the above three categories) are dealt with in a separate section. The main features of the techniques that are described are summed up in five synoptic tables. As a conclusion, several research areas that need further investigation in view of a possible industrial implementation of automatic analog test generation techniques are identified. Two appendixes deal briefly with fault tolerance and fault simulation in analog systems. An extensive bibliography ( \sim 500 entries) is provided.
123 citations
27 Aug 2003
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'.
Abstract: 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.
119 citations
Additional excerpts
...…this idea (Baumgartner and Rugh, 1975; Bendat, 1990; Bendat, 1998; Billings and Fakhouri, 1980; Billings and Fakhouri, 1982; Chen, 1995; Korenberh and Hunter, 1986; Korenberg, 1991; Sjöberg et al., 1995; Tan and Godfrey, 2002; Wysocki and Rugh, 1976; Wysocki and Wilson, 1979; Weiss et al., 1998)....
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References
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TL;DR: In this paper, the identification of zero-memory multipoles and two-poles of class n_1 was studied, where the test signals are sine waves of different amplitudes and frequencies, and the measured quanity is the describing function of the device.
Abstract: The identification problem involves the determination of the identity of a black box from the observation of its responses to a set of input signals. In this paper attention is focused on the identification of zero-memory multipoles and two-poles of class n_1 . The test signals are sine waves of different amplitudes and frequencies, and the measured quanity is the describing function of the device. In the case of two-poles of class n_1 , it is found that the describing function is related to the characteristic function by an integral equation of second order which can be solved explicitly by the use of the Fourier-Hankel transformation.
107 citations
TL;DR: In this paper, a solution to the identification problem for a class of nonlinear systems, based on steady-state frequency response, is presented, which is composed of certain interconnections of stable linear dynamic systems and integer power nonlinearities.
Abstract: A solution to the identification problem for a class of nonlinear systems, based on steady-state frequency response, is presented. This class is composed of certain interconnections of stable linear dynamic systems and integer power nonlinearities. Two kinds of measurements are considered. The first involves obtaining the amplitude and relative phase of each harmonic of the steady-state frequency response, while the second involves measuring the amplitudes only. In each case we find the number of measurements sufficient to identify a system for which the highest power present and the bounds on the dimensions of the linear subsystems are known.
53 citations
01 Dec 1973
TL;DR: In this paper, a structure theory based on the representation of input/output behavior by rational functions in several variables is developed for nonlinear systems composed of linear dynamic subsystems in cascade with static power nonlinearities.
Abstract: Nonlinear systems composed of linear dynamic subsystems in cascade with static power nonlinearities are considered A structure theory is developed based on the representation of input/output behavior by rational functions in several variables An algorithm is given which solves the minimal complete realization problem for two forms of the representation A basis for identification of the representation from input/output experiments is also developed Examples are worked in detail to illustrate the results
31 citations