Stabilization of a ball and sphere system using feedback linearization and sliding mode control

In this paper, we consider the problem of control of a laboratory experiment, called the ball and sphere system. This system consists of two dc motors that drive a big sphere to roll in two directions and to keep a small ball staying on the top of the sphere. This system is inherently nonlinear, unstable, and underactuated. The control of this system is a challenging task. In this paper, we show that around the equilibrium of the system can be decoupled into two independent ball and wheel systems. Based on full-state-feedback linearization and sliding mode control, a controller is designed to achieve the closed-loop stability of the system. The simulation and experimental results are given to demonstrate and validate the effectiveness of the control scheme.