On the inverted pendulum on a cart moving along an arbitrary path

Authors:	Consolini Luca, Universita' degli Studi di Parma, Italy Tosques Mario, Universita' degli Studi di Parma, Italy
Topic:	2.3 Non-Linear Control Systems
Session:	Nonlinear Controller Design
Keywords:	Nonlinear control, time-varying systems, feedback stabilization, non-minimum phase systems, mechanical systems.

Abstract

This article discusses a problem of stabilization for an inverted pendulum on a cart. In this work the cart does not travel along an horizontal line, which is the case commonly considered in the literature, but along an arbitrary path in the horizontal-vertical plane. The main obstacle encountered lies in the fact that the feedback controlled system becomes unstable in some "critical regions" along the cart path curve (close to the points where the path is vertical). The overall closedloop system is characterized by an alternation of periods of stability and instability and its state is proved to be stable under some conditions, which involve the geometry of the path. Simulations results are provided for the case in which the path is a circle.