Open-loop oscillatory stabilization of an n-pendulum

This paper presents new results on the behaviour of an n-link pendulum which is controlled by means of an oscillatory input forcing one end link. Drawing on recent research on the oscillatory control of second order non-linear systems, we adopt the averaged potential as the primary tool in our equilibrium and stability analysis. While such control of single-degree-of-freedom systems has been studied in fair detail by Weibel and Baillieul, researchers are only beginning to explore the issues which arise in the control of multi-degree-of-freedom systems. Of specific interest is the behaviour when the system possesses bifurcations and more than one stable equilibrium. In this paper, we present a study of the bifurcations and stability of a periodically forced cart and n-pendulum on an inclined plane. Periodic open-loop forcing of the single degree-of-freedom pendulum has previously been shown to be a robust and effective means of stabilizing the inverted equilibrium, and this robustness carries over to the m...