Two-mass MEMS velocity sensor: Internal feedback loop design

This paper presents theoretical and experimental results about the design of an internal feedback loop in a new capacitive micro-electro-mechanical-system velocity sensor. The sensor comprises two mass-spring inertial sensing systems connected in a series, termed the principal and secondary systems. The secondary system output is fed to an electrostatic actuator that acts between the sensor frame and the proof mass of the principal system. The aim of this internal feedback loop is to generate a sky-hook damping effect on the principal system, so that, in the frequency band of interest, the output of the sensor is proportional to the base velocity. The sensor is fabricated on a silicon-on-isolator wafer. The sensor interface and the controller are implemented on a printed circuit board. The design of the control loop is carried out offline using measured frequency response functions for the displacements of the two proof masses with respect to: 1) the base acceleration, and 2) the voltage signal driving the electrostatic actuator. This paper shows that, below 1 kHz, the measured output signal of the closed loop sensor is proportional to the velocity of the base, and above the fundamental resonance, the output signal rolls off with a phase lag of-90°C.