Experimental Bifurcation Analysis Using Control-Based Continuation

Emil Bureau

Research output: Book/ReportPh.D. thesisResearch

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Abstract

The focus of this thesis is developing and implementing techniques for performing experimental bifurcation analysis on nonlinear mechanical systems. The research centers around the newly developed control-based continuation method, which allows to systematically track branches of stable and unstable equilibria under variation of parameters. As a test case we demonstrate that it is possible to track the complete frequency response, including the unstable branches, for a harmonically forced impact oscillator with hardening spring nonlinearity, controlled by electromagnetic actuators. The method requires the constitution of a non-invasive and locally stabilizing control scheme, which must be tuned without a-priori study of a model. We propose a sequence of experiments that allows to choose optimal control-gains, filter parameters and settings for a continuation method. This experimental tuning procedure is applied to our test rig, resulting in a reliable non-invasive, locally stabilizing control. The use of stabilizing control makes it difficult to determine the stability of the underlying uncontrolled equilibrium. Based on the idea of momentarily modifying or disabling the control and study the resulting behavior, we propose and test three different methods for assessing stability of equilibrium states during experimental continuation. We show that it is possible to determine the stability without allowing unbounded divergence, and that it is under certain circumstances possible to quantify instability in terms of finite-time Lyapunov exponents. A software toolbox for the Matlab continuation platform COCO has been developed and will be made freely available. This toolbox implements functions necessary for interfacing a numerical continuation code with a real experiment, as well as provide means for simulating control-based continuation experiments. Finally, the feasibility of implementing the method for rotating machinery is discussed.
Original languageEnglish
PublisherDTU Mechanical Engineering
Number of pages145
ISBN (Print)978-87-7475-377-3
Publication statusPublished - 2014
SeriesDCAMM Special Report
NumberS163
ISSN0903-1685

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