Input shaping is an effective method for suppressing motion-induced oscillation in flexible systems. This technique works well on systems with continuously-variable actuation. However, many systems only have a finite number of actuation states. For example, some relay-driven cranes have three actuation states: off, low-speed, and full speed. The discretizing effect of finite-state actuation can reduce the effectiveness of input shaping. This paper investigates the detrimental effects of discretization. The operational effects of finite-state input shaping are evaluated by using experimental results from a human-operated bridge crane, and a 3-D simulation of this crane.
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