This paper studies the design of anti-sloshing trajectories for application in automatic machines for packaging liquid products, with specific reference to cylindrical containers and emphasis on prescribed motion durations. Different strategies, based on a discrete linear model of the sloshing phenomenon and applicable in real-time, are analyzed to perform anti-sloshing feedforward control of the container motion: FIR filters (input shapers and others), dynamic-model inversion, and IIR filters. Unlike the previous literature, these strategies are applied to highly dynamical motion laws, with maximum accelerations from 4m=s2 to 13m=s2. The effectiveness of the proposed anti-sloshing trajectories is assessed by experiments.

This paper studies the phenomenon of sloshing in the field of automatic machines for packaging of liquid products, with specific reference to containers with planar motions. After introducing two equivalent discrete models based on a mass-spring-damper system borrowed from the literature (one linear and one non-linear), a novel method is proposed to evaluate the sloshing height of the liquid, namely the deviation of its free surface at the wall of the container from the equilibrium condition. The merits of this method are that it is easy to use, requiring no experimental evaluation of the system parameters or computationally-expensive fluidodynamical simulations, and it gives good results also for highly dynamical motions. Moreover, though this paper focuses on cylindrical containers performing rectilinear movements, the technique therein presented can be extended to containers of arbitrary shape and generic planar motions. The method is validated by experimental tests using cylindrical containers of different dimensions and a large number of rectilinear motion laws with maximum accelerations up to 12m/s 2 . The results are compared with those that may obtained by using other methods of equal complexity available in the literature, showing the effectiveness of the proposed technique.

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