Stabilization of the inverted pendulum on a skate

Abstract

In the classical control theory literature, the inverted pendulum stabilization problem has been addressed in two ways: as an application of the vibrational control principle, or by imagining that the pivot is on a cart moved according to a suitable feedback law. Several other stabilization methods have been recently proposed. In this paper we propose a new approach: the pendulum is assembled on an ice skate, subject to some constraints and equipped with a driving device. The upper equilibrium position is stabilized provided that the speed of the skate is sufficiently large.