Three-dimensional sloshing control of a planar-conveyed rectangular container using an adjustable-smooth robust command

Abstract

A rectangular water-filled container is guided along a planar trajectory that is specifically designed to minimize transient wave oscillations and eliminate residual sloshing at the end of a rest-to-rest maneuver. The proposed input command utilizes equidistant multi-steps profile designed for a multi-mode linear damped system, relying solely on the natural frequencies and modal damping ratios. This approach is particularly advantageous for complex systems where deriving or accessing comprehensive mathematical models is challenging or infeasible. The dynamics of three-dimensional sloshing, resulting from longitudinal and transverse motions, were simulated using finite element analysis. The input command is engineered to (i) maximize actuator utilization to minimize maneuver duration, (ii) adhere to zero residual vibration constraints, and (iii) reduce step-to-step differences to mitigate jerks, such as inrush currents. The flexibility of the design allows for adjusting the step intervals to synchronize with actuator sampling times - avoiding delays and inaccuracies - and modifying the total duration to balance between transient wave suppression, maneuver time, and robustness against parameter uncertainties. Numerical simulations and experimental tests of a planar-conveyed water-filler rectangular container across a broad range of system and design parameters validate the efficacy of the proposed command shaping strategy.