Torque Multiplication and Singularity Avoidance in the Control of Electrostatic Torsional Micro-Mirrors

The present work addresses the control of torsional micro-mirrors assisted by a constant bias voltage. It is shown that such a configuration will have an effect of torque multiplication and hence, it will reduce the dynamic range of actuation signal. A nonlinear controller using backstepping and barrier functions is developed, which can guarantee closed-loop stability in a restricted range covering a big portion of the physically allowable one, while eliminating the singularities due to uncontrollability and contact dynamics. In this study, the actuation voltage is taken as a state variable. This would further simplify the implementation of experimental systems. The development of the control algorithm has been demonstrated through a rectangular micro-mirror and the performance of the system is verified by numerical simulations. As a generic model is used in the design, the control algorithm developed can be applied to any device with the same structure regardless of the geometric shape.