A New Nonlinear Control for Asymptotic Stabilization of a Class of Underactuated Systems: An Implementation to Slosh-Container Problem

In this paper, a new control law is proposed for the nonlinear underactuated system. It is proved that the proposed control achieves asymptotic stability of the whole system. A broad class of underactuated systems, termed as commensurate underactuated systems, is identified where numbers of actuated and unactuated degrees of freedom are equal; for which the proposed control can be used as the general stabilizing control. The design methodology is simple and uses the prevalent total energy like Lyapunov function. The control strategy is tested on slosh-container system, a benchmark underactuated system of the class considered herein. We discern some important features of the proposed control law and analyze its effectiveness through physical interpretations. The findings are verified through simulations and experimental results for the slosh-container system.