Unity-magnitude Input Shapers and Their Relation to Time-optimal Control

Input shaping reduces residual vibrations by convolving a sequence of impulses, an input shaper, with the desired system command. Using negative impulses in the shaper leads to faster maneuvers. Unfortunately, when negative input shapers are used, there is no guarantee that the shaped command will satisfy actuator limitations. A new type of negative input shaper is presented that satisfies actuator limits for a large class of unshaped commands. The performance of these input shapers is compared to the time-optimal control and other types of input shapers.