Gantry cranes are traditionally modeled as a simple pendulum. However, a quay-side container crane has a multicable hoisting mechanism which can not be modeled as a simple pendulum. In this paper, a two-dimensional four-bar-mechanism model of a container crane is developed. The model is then reduced to a double pendulum with a kinematic constraint. A nonlinear approximation of the oscillation frequency of the simplified model is developed. The resulting frequency approximation is used to determine the switching times for a bang-off-bang input-shaping controller. The performance of the controller is numerically simulated on the full model, and is compared to the performance of similar controllers, which are based on a nonlinear frequency approximation of a simple pendulum and a linear frequency approximation of a constraint double pendulum. The sensitivity of the controller performance to the oscillation frequency is investigated. A delayed-position feedback controller is applied at the end of the transfer maneuver to eliminate residual oscillations without affecting the shaped commands of the input-shaping controller.
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