On Feedback and Anticipatory Control of Pendular Systems

摘要

The stability or stabilization of an inverted pendulum is a textbook example for analytical mechanics or control theory because it is a simple and generally used model of several engineering problems. In this paper we study the behavior of an excited inverted pendulum in the post-critical region. A simple feedback control is applied to avoid chaotic oscillations. While our problem is originated by an astronautical device (dumbbell satellite) the controller changes the length of the pendulum as the angular position is varied. We use two approaches in numerical simulation. The one is of recursive nature while the other is an incursive one and we detect that the qualitative picture of the trajectories may be different even for the same parameter values.