Experimental bifurcation analysis of an impact oscillator - Tuning a non-invasive control scheme

Emil Bureau, Frank Schilder, Ilmar Santos, Jon Juel Thomsen, Jens Starke

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We investigate a non-invasive, locally stabilizing control scheme necessary for an experimental bifurcation analysis. Our test-rig comprises a harmonically forced impact oscillator with hardening spring nonlinearity controlled by electromagnetic actuators, and serves as a prototype for electromagnetic bearings and other machinery with build-in actuators. We propose a sequence of experiments that allows one to choose optimal control-gains, filter parameters and settings for a continuation method without a priori study of a model. Depending on the algorithm for estimating the Jacobian required by Newton's method we find two almost disjoint sets of suitable control parameters. Control-based continuation succeeds reliably in producing the full bifurcation diagram including both stable and unstable equilibrium states for an appropriately tuned controller.
Original languageEnglish
JournalJournal of Sound and Vibration
Volume332
Issue number22
Pages (from-to)5883–5897
ISSN0022-460X
DOIs
Publication statusPublished - 2013

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