Robust Negative Input Shapers for Vibration Suppression

Abstract

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.

Command shaping for flexible systems: A review of the first 50 years

“…Successful applications of input shaping have also been reported on the related problems of controlling XY stages, [128][129][130][131][132][133] flexible robotic arms, 18,28,51,62,65,66,68, and voice coil motors. 157 Implementation on these types of industrial machines may require the input-shaping algorithm to deal with friction, 116,158,159 saturation, 75,160 or rate limiting.…”

Reducing swing of model helicopter sling load using input shaping

“…These robust shapers are slightly longer in duration, but are more effective when there are errors in the estimated ζ and ω n . For a comprehensive description of these and other input shapers, see [15], [38].…”

On the derivative constraints of input shaping control

“…Some previous studies [7,20,[24][25][26][27][28][29][30][31][32] describe that the ZVD input shaper is derived from zero vibration constraints and an additional constraint…”