Robust multi-steps input command for liquid sloshing control

Abstract

A robust input command based on multiple steps for eliminating the residual vibrations of a multimode linear system is proposed. Only the system resonant frequencies are needed to determine the step magnitudes in the shaped command. The command duration is selectable to help in designing an optimum command that compensates between the reduction in the transient vibration, the enhancement in the command robustness, and the increase in the total maneuver time. The induced transient and residual sloshing oscillations of a suspended water-filled container are suppressed using the proposed command. The dynamics of the sloshing is numerically simulated using finite element method that accommodates the interactions between the fluid, structural, and multi-body dynamics. A short move time penalty is incurred with the price of significant reduction in the liquid sloshing. The performance of the shaped command to the system parameters and the robustness to their uncertainty are investigated. An improved robust input command in the presence of uncertainties in the cable length and water depth is also introduced. The effectiveness and excellence of the proposed command is demonstrated through a comparison with multimode zero-vibration input shaper and time-optimal flexible-body control.