Liquid Container Transfer Considering the Suppression of Sloshing for the Change of Liquid Level

We consider a tank containing a fluid. The tank is subjected to directly controlled translations and rotations. The fluid motion is described by linearized wave equations under shallow water approximations. For irrotational flows, a new variational formulation of Saint-Venant equations is proposed. This provides a simple method to establish the equations when the tank is moving. Several control configurations are studied: one and two horizontal dimensions; tank geometries (straight and nonstraight bottom, rectangular and circular shapes), tank motions (horizontal translations with and without rotations). For each configuration, we prove that the linear approximation is steady-state controllable and provide a simple and flatness-based algorithm for computing the steering open-loop control. These algorithms rely on operational calculus. They lead to second order equations in space variables whose fundamental solutions define delay operators corresponding to convolutions with compact support kernels. For each configurations, several controllability open-problems are proposed and motivated.

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“…Gathering these last two stationarity equations we get A differentiation with respect to yields (7) which is indeed identical to (2).…”

Section: Variational Formulationsmentioning

confidence: 84%

Dynamics and solutions to some control problems for water-tank systems

Petit

Rouchon

2002

IEEE Trans. Automat. Contr.

102

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“…Furthermore, the H ∞ -theory was additionally applied to increase the motion's robustness in [8]. In [9,10], optimal control theory was used to implement an optimal closed-loop feedback controller in order to minimize the liquid slosh. Hereby, it must be mentioned that a closed-loop feedback controller requires appropriate measurement possibilities of the process state values.…”

Section: Introductionmentioning

confidence: 99%

Controlling Liquid Slosh by Applying Optimal Operating-Speed-Dependent Motion Profiles

2020

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In this paper, an investigation is presented that demonstrates the application of a new approach for enabling the reduction of liquid slosh by implementing optimized motion profiles over a continuous range of operating speeds. Liquid slosh occurs in the packaging process of beverages. Starting by creating a dynamic process model, optimal control theory is applied for calculating optimal motion profiles that minimize residual vibration. Subsequently, the difficulty of operating speed dependency of the herewith synthesized motion profiles is examined. An approach in which the optimal motion profiles are consolidated into a characteristic map of motion specifications, which can be executed by a programmable logic controller in real time, is discussed. Eventually, the success of this novel approach is demonstrated by the comparison with state-of-the-art motion profiles and conventional motion implementation.

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“…Another possibility is the modeling with concentrated parameters and physical substitution models such as the pendulum model, also discussed in [7]. This approach leads to an ordinary differential equation of order two, which can be easily considered in common motion optimization algorithms in an efficient way [16,17].…”

Section: Introductionmentioning

confidence: 99%

Modeling Transient Liquid Slosh Behavior at Variable Operating Speeds Induced by Intermittent Motions in Packaging Machines

Troll

Majschak

2020

Applied Sciences

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The present paper deals with the problem of modeling liquid slosh occurring in the packaging process of containers filled with liquid. Sloshing effects are induced by one-dimensional intermittent motions and are undesired due to the necessity of quality control processes, such as weighing. Therefore, motion optimizations are often applied with the intention to minimize the residual vibrations. Valid process models are required to do so. The aim of this paper is to derive models for describing the liquid slosh behavior for different motions and for common practical circumstances, e.g., different container geometries as well as machine operating speeds, and to state the model's limits of use. Known model approaches are discussed, and their assumptions are reviewed experimentally. This leads to a set of limited ranges of operating speeds in which the applied models' assumptions are valid. The models are derived for these sets from experimental data, and a comparison is executed that enables the determination of the models' validity concerning their operating speed dependency. Finally, the validity of the derived models is investigated by comparing their predictive efficiency of describing the vibration for different motion profiles.

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Liquid Container Transfer Considering the Suppression of Sloshing for the Change of Liquid Level

Cited by 18 publications

References 3 publications

Dynamics and solutions to some control problems for water-tank systems

Dynamics and solutions to some control problems for water-tank systems

Controlling Liquid Slosh by Applying Optimal Operating-Speed-Dependent Motion Profiles

Modeling Transient Liquid Slosh Behavior at Variable Operating Speeds Induced by Intermittent Motions in Packaging Machines

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