Analysis and Design of Nonlinear Systems in the Frequency Domain

Abstract

Nonlinear system analyses have been widely applied in engineering practice, where the frequency domain approaches have been developed to satisfy the requirement of the analysis and design of nonlinear systems.However, there exist many problems with current techniques including the challenges with the nonlinear system representation using physically meaningful models, and difficulties with the evaluation of the frequency properties of nonlinear systems. In the present work, some new approaches, that have potential to be used to systematically address these problems, are developed based on the NDE (Nonlinear Differential Equation) model and the NARX (Nonlinear Auto Regressive with eXegenous input) model of nonlinear systems.In this thesis, the background of the frequency domain analysis and design of nonlinear systems is introduced in Chapter 1, and the existing approaches are reviewed in Chapter 2. In general, the frequency ABSTRACT II(3) The Output Frequency Response Function (OFRF) in terms of physical parameters of concern is introduced for the NARX Model with parameters of interest for Design (NARX-M-for-D). Moreover, a new concept known as the Associated Output Frequency Response Function (AOFRF) is introduced to facilitate the analysis of the effects of both linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems.(4) Nonlinear damping can achieve desired isolation performance of a system over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Both simulation and laboratory experiments are studied, demonstrating the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems. CATALOGUE III AcknowledgementsI would like to thank Prof. Z Q Lang, my supervisor, for his great support and supervision on my PhD study. He has provided a lot of suggestions on my research and writing so that I can complete the project and this PhD thesis.I also want to express my thankfulness to the research and work staffs of the department for their kind help on my study, and also would like to acknowledge the support of Engineering Faculty Scholarship for my PhD study at Sheffield.