Stabilization of a 3D rigid pendulum

We introduced models for a 3D pendulum, consisting of a rigid body that is supported at a frictionless pivot, in a 2004 CDC paper [Shen, J, Dec. 2004]. In that paper, several different classifications were given and models were developed for each classification. Control problems were posed based on these various models. This paper continues that line of research by studying stabilization problems for a reduced model of the 3D pendulum. Two different stabilization strategies are proposed. The first controller, based on angular velocity feedback only, asymptotically stabilizes the hanging equilibrium. The domain of attraction is shown to be almost global. The second controller, based on angular velocity and reduced attitude feedback, asymptotically stabilizes the inverted equilibrium, providing an almost global domain of attraction. Simulation results are provided to illustrate closed loop properties.