PhD Thesis

Methods for Control of Liquid Slosh

Mattias Grundelius


Horizontal movement of liquid containers is a common operation in an industrial packaging machine. During the movement the acceleration of the container induces motion of the liquid within the container, this is referred to as liquid slosh or liquid vibration. If there is too much slosh the liquid might wet the sealing surfaces of the container and even contaminate the machine. There is no measurement of the slosh so the only way to control the slosh is through the acceleration reference that defines the movement.

The work presented in this thesis is focused on development of systematic methods for calculation of acceleration references that move the container as fast as possible without too much slosh. The methods are based on a simple model of the slosh phenomenon which is derived from fluid dynamics and system identification. The acceleration reference is calculated both directly using optimal control techniques with various cost functions and constraints and iteratively using iterative learning control.

To enable practical evaluation of the acceleration references and the use of iterative learning control an experimental setup has been used where it is possible to measure the surface elevation on one side of the container using an infrared laser displacement sensor. The experimental evaluations show that it is possible to achieve fast movements by solving a minimum energy optimal control problem and tuning of the model parameters. It is also shown that the iterative learning control methods are successful in finding good acceleration references in practice using only a simple model of the slosh phenomenon.

A method that utilize tilting of the container is also derived, this enables faster movements with less slosh. The methods simultaneously calculates the horizontal and rotational acceleration references by solving a minimum energy optimal control problem. Experiments show that the method is successful if the maximum allowed surface elevation is not too large.


Slosh, Fluid dynamics, Motion control, Optimal control, Iterative learning control

PhD Thesis ISRN LUTFD2/TFRT--1062--SE, Department of Automatic Control, Lund University, Sweden, October 2001.

Download full document