Control-Based Continuation of Unstable Periodic Orbits

J. Sieber, B Krauskopf, DJ Wagg, SA Neild, Alicia Gonzalez-Buelga

Research output: Contribution to journalArticle (Academic Journal)peer-review

24 Citations (Scopus)

Abstract

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.
Translated title of the contributionControl-Based Continuation of Unstable Periodic Orbits
Original languageEnglish
Number of pages9
JournalJournal of Computational and Nonlinear Dynamics
Volume6 Issue 1
DOIs
Publication statusPublished - Sep 2011

Fingerprint

Dive into the research topics of 'Control-Based Continuation of Unstable Periodic Orbits'. Together they form a unique fingerprint.

Cite this