On the control of vibratory actuators

Recent technological developments have resulted in the commercial availability of electric motors which operate on principles which are entirely different from those which govern the operation of standard electrical machines. For a given maximum torque output these new actuators can be both smaller and less massive than the usual designs. However, because they generate their output in a two stage process involving the conversion of electrical energy into a high frequency elastic vibration as an intermediate step, the optimization of the performance and control of these motors requires the consideration of a number of new and interesting problems. The literature on the operation of these devices is sparse and largely informal. In particular, it does not seem to include a quantitative analysis which would allow one to explore their suitability for high performance closed loop applications. In this paper we use the Euler-Bernoulli beam model together with some ideas from system theory to derive the appropriate transfer functions for these systems. Actuators based on standing waves, suitable for generating translational motion, are considered in detail; the modifications required to treat the traveling wave/rotational motion case are briefly indicated.