Design and optimization of input shapers for liquid slosh suppression

Abstract

The need for fast maneuvering and accurate positioning of flexible structures poses a control challenge. The inherent flexibility in these lightly damped systems creates large undesirable residual vibrations in response to rapid excitations. Several control approaches have been proposed to tackle this class of problems, of which the input shaping technique is appealing in many aspects. While input shaping has been widely investigated to attenuate residual vibrations in flexible structures, less attention was granted to expand its viability in further applications. The aim of this work is to develop a methodology for applying input shaping techniques to suppress sloshing effects in open moving containers to facilitate safe and fast point-to-point movements. The liquid behavior is modeled using finite element analysis. The input shaper parameters are optimized to find the commands that would result in minimum residual vibration. Other objectives, such as improved robustness, and motion constraints such as deflection limiting are also addressed in the optimization scheme. Numerical results are verified on an experimental setup consisting of a small motor-driven water tank undergoing rectilinear motion, while measuring both the tank motion and free surface displacement of the water. The results obtained suggest that input shaping is an effective method for liquid slosh suppression.