A complete solution to asymmetric S-curve motion profile: Theory & experiments

In this paper, we propose the asymmetric S-curve motion profile that enables easy manipulation of jerks during the arrival time in order to effectively reduce the residual vibration. To derive the complete closed form solution to the asymmetric S-curve, a design parameter the so-called jerk ratio is introduced to scale down the jerks during the deceleration period so that the velocity profile is in an asymmetric S-curve. Thanks to the jerk ratio, the motion parameters are remarkably simplified in analytic forms for short, medium and long distances. The effectiveness of the proposed approach is validated by experiments with the AC motor control system. As the jerk ratio increases, the residual vibration decreases, but, the motion profile is lengthened as expected by simulations.