Effects of DAC interpolation on the dynamics of a high speed linear actuator

This works deals on the dynamics of linear actuators with an experimental set on high speed actuators. These devices are subjected to different undesired dynamic phenomena such as vibrations due to the conjunct presence of finite stiffness and non-zero inertia associated to other eventual dynamical characteristics. Specifically, the attention of this paper is associated to vibrations due to command motion distortion associated to discretization and to successive conversion to a continuous function through DAC (Digital to Analog Converter). To reduce undesired dynamical phenomena, different DACs implement interpolation algorithms. This work analyzes numerically and experimentally the effects of different interpolation approaches in the time domain. Results show how: increasing sample dimension decreases error; truncation affects asymptotic error over the sample dimension; the effect of the type of interpolation is sensible only with a low sample dimension. Then experimental trials was realized showing that: linear interpolation exhibits an increment of measured acceleration with decreasing sample size; Hermite interpolation produced measured acceleration that does not depend on sample size; Bezier interpolation produced the lowest measured acceleration. Thus, the best interpolation method can be adopted, according with the constraints of the specific problem.

I. Introduction

Linear actuators are widely adopted in different application fields [1]–[7]. The presence of finite stiffness, associated to non-zero inertia and eventual kinematical discontinuities produces undesired dynamical phenomena, such as vibrations, especially in high speed applications, thus different works in literature are devoted to limit negative effects [8]–[11] or to employ these characteristics for their positive effects [12]–[15]. This work focuses the attention to a specific cause of vibration, the discretization of the commanded motion. In fact the commanded motion is sent directly to the actuator as a continuous command, but it is subjected to a discretization, a digital elaboration and a successive conversion to a continuous command [16]–[20]. To reduce the distortion of the commanded motion, that is one of the causes of vibration in actuators, different approaches involves the use of interpolation algorithms [21]–[24]. This work is devoted to verify the ability to smooth vibration phenomena associated to discretization, specifically with interpolators in the time domain, comparing different approaches adopted in literature.