Anti-sloshing control: Flatness-based trajectory planning and tracking control with an integrated extended state observer

The phenomenon of sloshing causes a significantly negative impact on a wide range of industries. A time-optimal flatness-based trajectory planning and Lyapunov-based model predictive control (LMPC) is proposed for trajectory tracking of a transmitting cylindrical container filled with liquid. Firstly, this research presents an equivalent discrete model based on a mass-spring-damper system. Subsequently, after the flatness of the adopted non-linear model for 2D is established, time-optimal trajectories are introduced. A control method called LMPC is shown to solve the problem of orbital tracking, which allows setting limits for state variables. In addition, to ensure system performance, a linear extended state observer (LESO) is integrated to cope with system uncertainties. Finally, the efficiency of the proposed approach for liquid sloshing suppression and tracking is illustrated by simulations.