Zhu, Y.-P., Lang, Z.-Q. and Guo, Y.-Z. (2021) Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria. Nonlinear Dynamics, 104 (3). pp. 2553-2571. ISSN 0924-090X
Abstract
In engineering practice, a nonlinear system stable about several equilibria is often studied by linearizing the system over a small range of operation around each of these equilibria, and allowing the study of the system using linear system methods. Theoretically, for operations beyond a small range but still within the stable regime of an equilibrium, the system behaves nonlinearly, and can be described and investigated using the Volterra series approach. However, there is still no available approach that can systematically transform the model of a nonlinear system into a form that can be studied over the whole stable regime about an equilibrium so as to facilitate the system study using the Volterra series approach. This transformation is, in the present study, referred to as nonlinear model standardization, which is the extension of the well-known concept of linearization to the nonlinear case. In this paper, a novel approach to nonlinear model standardization is proposed for nonlinear systems that can be described by a Nonlinear AutoRegressive model with eXogeneous input (NARX) or a nonlinear differential equation (NDE) model. The proposed approach is then used in three case studies covering the applications in nonlinear system analysis, nonlinear system design, and nonlinearity compensation, respectively, demonstrating the significance of the proposed nonlinear model standardization in a wide range of engineering practices.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 The Authors. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Nonlinear systems; Equilibria; NARX / NDE model; Frequency domain; Standardization |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Funding Information: | Funder Grant number Engineering and Physical Science Research Council EP/R032793/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 14 May 2021 07:25 |
Last Modified: | 21 Feb 2022 11:34 |
Status: | Published |
Publisher: | Springer Nature |
Refereed: | Yes |
Identification Number: | 10.1007/s11071-021-06429-9 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:174110 |