Control-based continuation of unstable periodic orbits

J. Sieber, B. Krauskopf, D. Wagg, S. Neild, A. Gonzalez-Buelga

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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.
Original languageEnglish
Pages (from-to)011005
Number of pages1
JournalJournal of Computational and Nonlinear Dynamics
Issue number1
Publication statusPublished - 2011


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