Tilt-angle stabilization of electrostatically actuated micromechanical mirrors beyond the pull-in point

Recently proposed optical subsystems utilizing microelectromechanical system (MEMS) components are being developed for use in optical crossconnects, add-drop multiplexers, and spectral equalizers. Common elements to these subsystems are electrostatically actuated micromechanical mirrors that steer optical beams to implement the subsystem functions. In the past, feedback control methods were used to obtain precise mirror orientations to minimize loss through optical switch fabrics or to stabilize attenuation through spectral equalizers. However, the mirror tilt angle range is limited because of inherent instability beyond a critical tilt angle (pull-in angle), and the usual feedback schemes do not counteract this effect. This work presents a feedback control method to enable operation of electrostatic micromirrors beyond the pull-in angle, yielding advantages including greater scalability of switch arrays and increased dynamic range of optical attenuators. Both static and dynamic tilting behaviors of electrostatic micromirrors under the feedback control are studied. In addition, a practical implementation of the feedback control system by using linear voltage control law is developed. A voltage slightly larger than the pull-in voltage is first applied when the mirror is at small angle positions, and the voltage is then linearly reduced as the mirror approaches the desired position. Experimental measurements, showing that tilt angles beyond the pull-in point can be achieved, are in good agreement with theoretical analysis.