Control-based continuation: Bifurcation and stability analysis for physical experiments

Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The idea is to apply the method of numerical continuation to a feedback-controlled physical experiment such that the control becomes non-invasive. Since in an experiment it is not (generally...

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Vydané v:Mechanical systems and signal processing Ročník 84; s. 54 - 64
Hlavný autor: Barton, David A.W.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Ltd 01.02.2017
Predmet:
Bifurcation theory
Feedback control
Numerical continuation
System identification
Bifurcation theory
System identification
Feedback control
Numerical continuation
ISSN:0888-3270, 1096-1216
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Shrnutí:Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The idea is to apply the method of numerical continuation to a feedback-controlled physical experiment such that the control becomes non-invasive. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target becomes a proxy for the state. Control-based continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses a periodic auto-regressive model with exogenous inputs (ARX) to approximate the time-varying linearisation of the experiment around a particular periodic orbit, thus providing the missing stability information. This method is demonstrated using a physical nonlinear tuned mass damper. •We outline the control-based continuation method.•We propose a new method for calculating the stability of the periodic orbits.•We apply this method to a nonlinear experiment.
ISSN:0888-3270
1096-1216
DOI:10.1016/j.ymssp.2015.12.039