Dynamics and Control of Three-Dimensional Slosh in a Moving Rectangular Liquid Container Undergoing Planar Excitations

While significant work has been directed at suppressing the 2-D slosh, less success has been achieved with reducing the 3-D slosh in a moving rectangular container. Control of the 3-D slosh in a moving rectangular liquid container is very challenging because there are two fundamental modes and an infinite number of high modes. The dynamics of the 3-D slosh in a moving rectangular container are derived. The theoretic analysis shows that both the two fundamental and high modes have large impacts on the sloshing dynamics. A command smoothing technique is designed to suppress slosh for the two fundamental and high modes. Comparing with the combined input shaper and the low-pass filter scheme, the presented smoother provides more robustness to variations in the sloshing frequency. Simulations over a large range of various working conditions and system parameters are conducted to analyze the liquid sloshing dynamics and the robustness of the method. Experimental results obtained from a moving rectangular liquid container validate the simulated sloshing dynamics behavior and the effectiveness of the method.