Command generation using specified-negative-amplitude input shapers

Residual vibrations can be greatly reduced by using specially-shaped command signals. Input shaping is a technique that reduces vibration by convolving a sequence of impulses with any desired system command. The resulting shaped input is then used to drive the system. Many types of useful impulses sequences have been proposed. Most of these have contained only positively valued impulses. However, the system rise time can be improved by using some negative impulses. A new type of impulse sequence containing negative impulses is proposed. These sequences are designed to fill the performance gap between all-positive sequences and the negative sequences previously developed