Embedded input shaper: Difference between trapezoidal profile and S-curve profile

Abstract

In this paper, we discuss the relation between the motion profile and pre-filter. As previously reported in various literatures [1-3], a tuned motion profile can effectively reduce residual vibration by placing inherent zeros of the motion profile at the vibratory pole of systems similar to the role of the input shaping technique. From the results, we factorize the motion profile into a basis function and an input shaper. In contrast to the previously reported impulse-sequence-based input shapers, the input shaper extracted from the motion profile has unique characteristics. Thanks to the characteristics of the input shaper extracted from the motion profile, it has advantages to reduce the vibrations caused by not only the modeled vibratory mode but also unmodeled dynamics which exist in higher frequency ranges.