Nonlinear control of the Reaction Wheel Pendulum

In this paper we introduce the Reaction Wheel Pendulum, a novel mechanical system consisting of a physical pendulum with a rotating bob. This system h as several attractive features both from a pedagogical standpoint and from a research standpoint. From a pedagogical standpoint, the dynamics are the simplest among the various pendulum experiments available so that the syste m can be introduced to students earlier in their education. At the same tim e, the system is nonlinear and underactuated so that it can be used as a be nchmark experiment to study recent advanced methodologies in nonlinear cont rol, such as feedback linearization, passivity methods, backstepping and hy brid control. In this paper we discuss two control approaches for the probl ems of swingup and balance, namely, feedback linearization and passivity ba sed control. We first show that the system is locally feedback linearizable by a local diffeomorphism in state space and nonlinear feedback. We compar e the feedback linearization control with a linear pole-placement control f or the problem of balancing the pendulum about the inverted position. For t he swingup problem we discuss an energy approach based on collocated partia l feedback linearization, and passivity of the resulting zero dynamics. A h ybrid/switching control strategy is used to switch between the swingup and the balance control. Experimental results are presented. (C) 2001 Elsevier Science Ltd. All rights reserved.