Nonlinear Stability of a Delayed Feedback Controlled Container Crane

Author:

Erneux Thomas1,Kalmár-Nagy Tamás2

Affiliation:

1. Université Libre de Bruxelles Optique Nonlinéaire Théorique Campus Plaine, C.P. 231 1050 Bruxelles, Belgium,

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

Abstract

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.

Publisher

SAGE Publications

Subject

Mechanical Engineering,Mechanics of Materials,Aerospace Engineering,Automotive Engineering,General Materials Science

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