Robust negative input shapers for vibration suppression

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/highmode excitation trade-off. Experimental results from a portable bridge crane verify the theoretical predictions.