Vibration Suppression Based on Improved Adaptive Optimal Arbitrary-Time-Delay Input Shaping

Abstract

Vibration suppression is important for high-precision motion control because positioning accuracy is an essential figure of merit for a servosystem. The paper presents a vibration-suppression method based on improved adaptive optimal arbitrary-time-delay (IAOAT) input shaping. First, analyzing a conventional optimal-arbitrary-time-delay (OAT) input shaper yields an OAT input shaper with five pulses that completely suppresses two-mode vibrations when the natural frequency and damping ratio are exactly known. Next, embedding an adaptive algorithm in the shaper gives a conventional adaptive optimal arbitrary-time-delay (AOAT) input shaper that handles unknown natural frequencies and damping ratios. Note that the conventional AOAT input shaper contains five pulses that have to be updated, but the delay times of the pulses are prescribed. Then, the IAOAT method extends the symmetry of pulse amplitudes for zero damping ratio to a nonzero case and reduces the number of pulses to three. A recursive-least-squares (RLS) algorithm is devised to update these parameters. This shaper features the smallest number of parameters and high robust performance. Finally, comparisons with other input-shaping methods show the effectiveness and superiority of the developed method over others.