Estimation of optimal time-delay in adaptive command shaping filter for residual vibration suppression

In the previously introduced direct adaptive command shaping filter the time-delay value is fixed and only the magnitudes of the impulses are learned. However, the performance of the direct adaptive time-delay command shaping filter depends on the select time-delay. In this paper, the authors introduce a new scheme to adapt the time-delay which is to be used in conjunction with the direct adaptive command shaping for the improved vibration suppression in flexible motion system. In order to formulate the time-delay adaptation scheme, the authors have analyzed the effect of the time-delay value on the performance of the direct adaptive command shaping filter. By modifying the direct adaptation formula based on the analysis result the authors have established a set of equations to adapt the time-delay toward the optimal value. Experimental results show the effectiveness of the proposed time-delay adaptation approach for the improved vibration suppression.