Zero-phase velocity tracking of vibratory systems with actuation constraints

In this paper, a novel filter for precise tracking of constant velocity signals is presented, which allows the reduction of residual vibrations along with the compliance with kinematic constraints that affect the actuation system. A technique achieving both these two objectives at the same time is the main contribution of the work. The filter is based on a cascade of smoothers, i.e. dynamic filters that act on the input signal by increasing its continuity level. Unfortunately, when applied to a generic input composed by ramp (and step) functions, the filter introduces a phase delay not acceptable in many applications where moving parts have to be mated, such as high-speed automatic machines. In order to guarantee a perfect synchronization between the original and the filtered reference signal, once the transient is terminated, a proper compensation scheme has been designed. Moreover, the expressions of the smoothers parameters which assure vibration cancellation at specific frequencies and compliance with given bounds on velocity and acceleration have been analytically deduced. By means of an extensive experimental activity, the effectiveness of the proposed approach has been demonstrated, by comparing its performances with the results of well established approaches for vibrations suppression or signal derivatives limitation.