Antisloshing Trajectories for High-Acceleration Motions in Automatic Machines

Abstract

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.

Sloshing dynamics estimation for liquid-filled containers performing 3-dimensional motions: modeling and experimental validation

“…Consequently, for lower values of h/R, the prediction models may lose adherence with reality. This also finds confirmation by looking at the correlation between the first natural frequency and the ratio h/R (see equation ( 3)): with the decreasing of h/R, ω 1 tends to lower values, meaning that the fundamentals of the liquid free-surface can be easily excited by the motion-law spectrum, in correspondence of the highest amplitudes [18]. This may result in a more nonlinear behavior and shape of the liquid free-surface that might not be detected by the models, although a higher number of sloshing modes is considered.…”

“…To overcome this drawback, a novel approach, based on the mass-spring-damper model [16], is proposed in [17] for the sloshing-height estimation. This model is validated for 1-dimensional motions in [17] and it is exploited in [18] and [19] to plan antisloshing trajectories. The same technique is used in a software application presented in [20] to execute simulations of liquid sloshing in cylindrical and rectangular containers.…”

Specified-duration shapers for suppressing residual vibrations

“…The four impulses can be obtained by simultaneously solving two residual vibration constraints, two derivative constraints, and a normalization constraint (six unknowns A 1 , A 2 , A 3 , A 4 , t 2 , t 3 with A 4 chosen in advance by the designer). Similarly, if T s is PLOS ONE between 1.5 and 2, Eq (7) states that we should use five impulses; these five impulses can be obtained by simultaneously solving two residual vibration constraints, two derivative constraints, two second-order derivative constraints, and a normalization constraint (eight unknowns A 1 , A 2 , A 3 , A 4 , A 5 , t 2 , t 3 , t 4 , with A 5 chosen in advance by the designer) [21][22][23][24]. For an example that provides a partial justification for using five impulses in this case, refer to the last paragraph of the next section, Analysis of SD shapers.…”

“…Here, the design of an SD shaper with 0.5 < T s � 1 is described. If T s is between 0.5 and 1, we obtain N = 3, as determined by Eq (7), and the impulse vector diagram of the SD shaper can be drawn as shown in Fig 2 . Here, θ 3 is determined from the given shaping time t 3 (= t s ), and θ 2 , I 1 , I 2 , I 3 are unknowns. To ensure residual vibration V is zero when there is no modeling error, the sum of impulse vectors must be zero.…”

“…For example, the forced lateral vibration of a building during earthquakes should be minimized to avoid structural damage [1]. Another example is that when cranes [2][3][4], disk drives [5,6], sloshing liquid containers [7][8][9][10], industrial robots [11], and soft robots [12,13] are operated, residual vibrations should be mitigated swiftly to reduce working hours and increase working efficiency.…”