Adaptive stabilization of a reaction wheel pendulum on moving LEGO platform

In this paper an adaptive control algorithm of a reaction wheel pendulum on a movable platform is proposed. Obtained hybrid control system allows to stabilize a pendulum fixed on the movable platform at the top unstable equilibrium. Tasks of swinging up and stabilizing of a pendulum is solved in conditions of a full parametric uncertainty of a plant and constrained control channel. In contrast to other approaches, this algorithm has adaptive adjusting of controller's parameters in ldquoon-linerdquo mode without any preliminary identification procedure. The second goal of this work is a development of applications used in an educational process because an investigation of control theory problems with real plants very important for students and their experience.

I. Introduction

The pendulum is one of the most interest objects to research complex dynamics of mechanical system since Galileo's time. Now control tasks of pendulum systems don't lose an actuality and cause increasing interest from both Russian and foreign researchers. The interest is caused because pendulum systems represent analogs of lot technological and physical processes. For example, one of practical tasks where proposed algorithm can be applied is rocket stabilization at the start, when rocket can be approximately represent as inverted pendulum.