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Mapping from parametric characteristics to generalized frequency response functions of nonlinear systems

Jing, X.J., Lang, Z.Q. and Billings, S.A. (2008) Mapping from parametric characteristics to generalized frequency response functions of nonlinear systems. Research Report. ACSE Research Report no. 975 . Automatic Control and Systems Engineering, University of Sheffield

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Abstract

Based on the parametric characteristic of the nth-order GFRF (Generalised Frequency Response Function) for nonlinear systems described by an NDE (nonlinear differential equation) model, a mapping function from the parametric characteristics to the GFRFs is established, by which the nth-order GFRF can directly be written into a more straightforward and meaningful form in terms of the first order GFRF, i.e., an ndegree polynomial function of the first order GFRF. The new expression has no recursive relationship between different order GFRFs, and demonstrates some new properties of the GFRFs which can explicitly unveil the linear and nonlinear factors included in the GFRFs, and reveal clearly the relationship between the nth-order GFRF and its parametric characteristic, and also the relationship between the nth-order GFRF and the first order GFRF. The new results provide a novel and useful insight into the frequency domain analysis and design of nonlinear systems based on the GFRFs. Several examples are given to illustrate the theoretical results.

Item Type: Monograph (Research Report)
Copyright, Publisher and Additional Information: The Department of Automatic Control and Systems Engineering research reports offer a forum for the research output of the academic staff and research students of the Department at the University of Sheffield. Papers are reviewed for quality and presentation by a departmental editor. However, the contents and opinions expressed remain the responsibility of the authors. Some papers in the series may have been subsequently published elsewhere and you are advised to cite the later published version in these instances.
Keywords: Generalised Frequency Response Function (GFRF), Nonlinear systems, Parametric characteristics, Nonlinear differential equation (NDE), Volterra series
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) > ACSE Research Reports
Depositing User: Miss Anthea Tucker
Date Deposited: 12 Oct 2012 13:54
Last Modified: 07 Jun 2014 07:04
Status: Published
Publisher: Automatic Control and Systems Engineering, University of Sheffield
URI: http://eprints.whiterose.ac.uk/id/eprint/74629

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