Improved output‐feedback second order sliding mode control design with implementation for underactuated slosh‐container system having confined track length

Abstract

In this study, a new second order sliding mode controller is designed through a novel non‐linear sliding surface proposal for a slosh‐container system. A linear sliding surface based controller using second order sliding mode is also derived for the comparison purpose. Both the controllers need only output measurements. The super‐twisting algorithm is employed to ensure the finite time convergence of system trajectories to a second order sliding set. In sliding phase, the asymptotic stability of the system states to a desired origin is proved by proposing a new Lyapunov function for the system. A slosh‐container system representing underactuated interconnected non‐linear dynamics is considered. It is shown that how the consideration of limited track length of container affects the stability conditions. To generate a position trajectory for container from the control input signal, a new approach is employed for the implementation purpose. It is demonstrated through simulations and experimental results that the proposed controller based on the novel non‐linear sliding surface outperforms the other controller based on the linear surface and it is more suitable on various practical aspects. This also validates the theoretical findings of the study.