Non-linear control of electrically driven micromirrors by means of inverse dynamics

Abstract

Based on a unified mathematical approach for modelling electromechanical systems (EMS), this paper shows a method to control dynamically the motion of an electrically driven micromirror on a nominal trajectory. For every time interval, this is done in three steps: Inverse dynamics of the mechanical subsystem, calculation of appropriate charges to produce the control forces electrically, and inverse dynamics of the electrical subsystem. The usage of an augmented PD-control law in the first step guarantees global exponential stability of the mirror on the nominal trajectory. The second step is carried out by an optimization method of linear programming. In the third step, the voltages are computed neglecting the dynamics of the electrical subsystem. Finally, these voltages are applied at the simulation model of the micromirror.