Almost Globally Asymptotically Stable Switched PD Control for a Spherical Pendulum

This paper presents a methodology to control a spherical pendulum on a stationary base in an upright position. This is based on the application of a nonlinear PD controller and a linear feedback controller in a small domain around the vertically upward equilibrium. The controller is designed to transition from the nonlinear to the linear region once it becomes sufficiently close to its equilibrium point. The region of asymptotic stability of the pendulum encompasses all initial conditions apart from the vertically downward position. Numerical experiments illustrating the performance of the controller are also provided.