Nano-precision control of micromirrors using output feedback

Micromirror arrays may be used as spatial light modulators, to vary the amplitude and phase of an incident image. The difficulty of controlling analog micromirrors to within a fraction of a wavelength of the incident light, that is, to within a few nanometers, has led to the development and successful commercialization of digital devices, in which the components take one of only two possible configurations. In this paper we revisit true analog operation, in light of past advances in nonlinear control. Our focus is electrostatically actuated mirrors, for which control objectives include extending the range of motion, improving transient performance, improving positioning accuracy and preventing electrode contact. We consider two models of individual micromirrors, suitable for controller design. The first treats each micromirror as a rigid body, and allows arbitrary rotation and translation. This model is developed in the context of dynamics on the Lie group SE(3). We simulate the performance of an observer-based controller for this system. The second model, based on work by Pelesko, is developed directly from a PDE representation of an electrostatically forced membrane. We show via simulation that an unstable equilibrium point of this model may be stabilized by proportional output feedback.