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Motion-induced vibration can be greatly reduced by properly shaping the reference command. Input shaping is one type of reference shaping method that is based largely on linear superposition. In this paper we document the impact of nonlinear crane dynamics on the effectiveness of input shaping. As typical bridge cranes are driven using Cartesian motions, they behave nearly linearly for low- and moderate-velocity motions. On the other hand, the natural rotational motions of tower cranes make them more nonlinear. The nonlinear equations of motion for both bridge and tower cranes are presented and experimentally verified using two portable cranes. The effectiveness of input shaping on the near-linear bridge crane is explained. Then, a command-shaping algorithm is developed to improve vibration reduction during the more nonlinear slewing motions of the tower crane. Experimental results demonstrate the effectiveness of the proposed approach over a wide range of operating conditions.
Blackburn et al. (Wed,) studied this question.