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Cranes are the primary heavy lifters for a wide variety of industries. However, all cranes share the same important limitation on efficiency: payload oscillation. Given the significance of cranes, it is not surprising that a large amount of research has been dedicated to eliminating this oscillation. Much of this research has been directed toward feedback control methods. Another portion of the work has focused primarily on command-shaping methods. This paper explores the problems with using feedback for crane control, which include the difficulty in sensing the crane payload, widely varying system dynamics, and human-operator compatibility. In light of these problems, input shaping is shown to be a favorable solution.

Input shaping is a control method that limits motion-induced oscillation in vibratory systems by intelligently shaping the reference command. As with any control method, the robustness of input shaping to parameter variations and modeling errors is an important consideration. For input shaping, there exists a fundamental compromise between robustness to such errors and system rise time. For all types of shapers, greater robustness requires a longer duration shaper, which degrades rise time. However, if a shaper is allowed to contain negative impulses, then the shaper duration may be shortened with only a small cost of robustness and possible high-mode excitation. This paper presents a thorough analysis of the compromise between shaper duration, robustness, and possible high-mode excitation for several negative input-shaping methods. In addition, a formulation for specified negative amplitude, specified insensitivity shapers is presented. These shapers provide a continuous spectrum of solutions for the duration/robustness/high-mode excitation trade-off. Experimental results from a portable bridge crane verify the theoretical predictions.