The residuals of liquid free-surface wave oscillations induced by a rest-to-rest crane maneuver of a suspended liquid container are eliminated using a command-shaped profile. The dynamics of liquid sloshing are modeled using an equivalent mechanical model based on a series of mass-spring damper systems. The proposed model considers the excited frequencies of the container swing motion and liquid sloshing modes. The objective is to design a discrete-time shaped acceleration profile with a variable command length, that controls the moving crane-jib, while suppressing the sloshing modes. Simulations are conducted to illustrate the command effectiveness in eliminating liquid sloshing with a wide variation range of system and command-designing parameters; liquid depth, cable length, command duration, and the employing of higher sloshing modes in representing the sloshing dynamics. The command sensitivity of the input command to changes of the system parameters are treated as well. A refined and smooth input command based on suppressing the residuals of multi-modes is also introduced. Furthermore, the command effectiveness was supported by a comparison with the time-optimal flexible-body control and multi-mode zero vibration input shaper.

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