Convex Optimization on Differential Pair of Actuation Voltages for Quasi-Static MEMS Mirrors in Scanning Applications

This work presents how an optimal, differential pair of actuation voltages for an electrostatic, quasi-static MEMS mirror is determined through convex optimization to achieve the lowest power consumption and tracking error, as well as the robustness and stability in its scanning applications, while it tracks a given angle profile (trajectory) at a frame rate of 60 Hz, for example, below its torsional resonance, 650 Hz. To this end, a strongly nonlinear electrostatic differential actuation in its governing equation is transformed into discrete affine equality constraints with a set of convex inequality constraints and a cost function that promotes the lowest actuation voltage pair, as well as the lowest power consumption.