Rapid sloshing-free transport of liquids in arbitrarily shaped containers

Abstract

We present a model-based feedforward control strategy suitable for designing swift rest-to-rest maneu-vers for liquids in arbitrarily shaped containers. We employ the commonly used equivalent pendulummodel to represent the sloshing dynamics and suggest a novel parameter identification scheme suitablefor arbitrary container shapes and any number of sloshing modes. By computing natural modes andfluid reaction forces and torques for imposed harmonic container motions via a finite element model,we obtain data for the identification scheme. A fitting procedure then yields highly accurate parameters for a physical pendulum model, where each pendulum represents one sloshing mode. We alsoprovide a thorough analysis of parameter identifiability and guidelines for obtaining robust parameterestimates. The proposed feed forward control method uses a virtual tray pendulum on which we placethe container (in the form of its equivalent pendulum model). Designing the virtual tray such thatthe fluid’s dominant sloshing mode becomes uncontrollable for displacements of the tray pendulumpivot effectively zeros out any sloshing motion in this mode. We then exploit the flatness property ofthe resulting system to design rest-to-rest maneuvers where any residual sloshing motion (in highermodes) can be exactly stopped at the end of the maneuver. The effectiveness of the proposed methodis demonstrated through extensive simulations and experimental results using a Martini cocktail glass,whose shape is challenging in terms of sloshing. The experimental results show the successful, accurate suppression of sloshing, validating the efficacy of the proposed concept.