Multi-mode, mode-matched, mems-based Coriolis vibratory gyroscope

A microelectromechanical sensor system, comprising:

• a vibratory gyroscope apparatus, further comprising:
• a resonating proof mass having a top surface and a plurality of side surfaces substantially perpendicular to the top surface, wherein the proof mass is configured to facilitate in-plane motion at a mode-matched frequency, wherein the proof mass is a substantially square shape having four side surfaces;
• and four comb capacitors,
• each coupled to one of the four side surfaces, and configured to provide an in-plane sense metric while operating at the mode-matched frequency,
• a plurality of serpentine springs configured to facilitate translational motion of the proof mass in directions substantially perpendicular to the top surface;
• a gyroscope controller configured to receive, measure, and adjust the control signal for at least two orthogonal sense modes, wherein the vibratory gyroscope apparatus is configured to simultaneously operate in the at least two orthogonal sense modes while maintaining mode-matching across a plurality of sense modes;
• an actuator electrically coupled to the proof mass configured to apply a periodic oscillatory signal;
• a plurality of electrodes each electrically coupled to each of the plurality of comb capacitors;
• a laser Doppler vibrometer configured to optically determine vibration amplitude of the proof mass and provide an out-of-plane sense metric;
• a phase locked loop configured to fix the mode-matched frequency;
• and
• an automatic gain control configured to hold the mode-matched frequency constant.