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research
Control-based continuation of unstable periodic orbits
Authors
A. Gonzalez-Buelga
Bernd Krauskopf
+3 more
Simon Neild
J. Sieber
David Wagg
Publication date
1 January 2011
Publisher
'ASME International'
Doi
Cite
Abstract
Copyright © 2010 American Society of Mechanical Engineers (ASME)We present an experimental procedure to track periodic orbits through a fold (saddle-node) bifurcation and demonstrate it with a parametrically excited pendulum experiment where the tracking parameter is the amplitude of the excitation. Specifically, we track the initially stable period-one rotation of the pendulum through its fold bifurcation and along the unstable branch. The fold bifurcation itself corresponds to the minimal amplitude that supports sustained rotation. Our scheme is based on a modification of time-delayed feedback in a continuation setting and we show for an idealized model that it converges with the same efficiency as classical proportional-plus-derivative control
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