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.