Averaging Second-Order Control Systems: Spatial Invariance
In the mechanics of fluids, structures, and mechanisms, it is well-known that the relative importance of various physical effects change as characteristic length scales are reduced (e.g. friction forces become more important and inertial forces become less important). The guiding principles for controlling mechatronic systems using very small-scale actuators and sensors also change. Motion control for small-scale devices in which control forces are produced by magnetostrictive, electrostrictive, or electrostatic effects involve transduction and rectification of oscillatory signals. Vibrating beams, plates, and membranes as well as electrostatic comb motors have been incorporated in a wide variety of devices, but connections with recent work in the nonlinear control theory of systems with oscillatory inputs have remained unexplored. We summarize recent developments in the control of mechanical systems with oscillatory inputs and pay particular attention to how these results depend on length scales. The talk will be illustrated by videos of recent laboratory experiments, and we shall briefly discuss the B.U. micropendulum experiment.