Stabilization of an underactuated ball-and-beam system using a second-order sliding mode control

This paper presents a stabilization method for an underactuated ball-and-beam system (BABS) based on a second-order sliding mode (SOSM) control. The BABS is an underactuated nonlinear system that is widely used to verify nonlinear control performance. Virtual control is introduced to a second-order BABS subsystem to minimize control performance inaccuracy by using model linearization. An actual virtual controller with variable finite-time tracking is achieved using a second-order sliding mode controller. An adaptive robust method is proposed to solve an uncertainty problem with unknown upper bounds, and then a finite-time convergence theory proof is given. Theory, simulation and experiment results verify the efficiency of the BABS controller.