Reference Command Shaping Using Specified-Negative-Amplitude Input Shapers for Vibration Reduction

Residual vibrations can be greatly reduced by using specially-shaped reference command signals. Input shaping is one such technique that reduces vibration by convolving a sequence of impulses with any desired reference command. Several types of useful impulse sequences have been developed. Most of these have contained only positively valued impulses. However, rise time can be improved by using some negative impulses in the sequence. Unfortunately, the use of negative impulses can excite unmodeled high modes. A new type of impulse sequence containing negative impulses is proposed. These sequences are designed to fill the performance gap between all-positive impulse sequences and the negative sequences previously developed. A proof governing the worst case scenario provides an upper bound on high-mode excitation. The resulting class of impulse sequences allows the designer to make a precise trade off between rise time and vibration reduction.