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Journal of Vibration and Control, Vol. 13, No. 5, 603-616 (2007)
DOI: 10.1177/1077546307074245

Nonlinear Stability of a Delayed Feedback Controlled Container Crane

Thomas Erneux

Université Libre de Bruxelles Optique Nonlinéaire Théorique Campus Plaine, C.P. 231 1050 Bruxelles, Belgium, terneux{at}ulb.ac.be

Tamás Kalmár-Nagy

Department of Aerospace Engineering, Texas A&M University, College Station, TX 77845, USA

A simplified model of a container crane subject to a delayed feedback is investigated. The conditions for a Hopf bifurcation to stable/unstable limit-cycle solutions are determined. It is shown that a subcritical Hopf bifurcation to unstable oscillations cannot be ruled out and the undesired coexistence of stable large amplitude oscillations and a stable equilibrium endangers the robustness of time-delay control strategies. The bifurcation is analyzed both analytically and numerically using a continuation method.

Key Words: Sway reduction • Hopf bifurcation • stable oscillations


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