Stabilization Control of a MEMS Accelerometer With Tuned Quasi-Zero Stiffness

In this paper, a novel MEMS accelerometer with tuned quasi-zero stiffness stabilized and operated in a closed-loop is proposed. By using the electrostatic softening effect of the double-sided comb-finger capacitors and the triangular capacitors, the effective stiffness of the accelerometer can be adjusted to quasi-zero. The variation of the electrostatic stiffness arising from the thermal drift of the proposed quasi-zero stiffness accelerometer can be greatly reduced when utilizing the double-sided comb-finger capacitors. For a high-sensitivity and high-linearity acceleration measurement, a traditional proportional-integral-derivative (PID) controller and a proportional-integral sliding mode (PISM) controller are designed for the stabilization near the border of pull-in. The parameters of the controller are tuned to ensure that the proof mass is stably positioned at the desired position. Both the simulation and experiment validate the feasibility of two controllers, showing distinct transient characteristics and long-term stability performance. Compared to the open-loop accelerometer with untuned stiffness, the sensitivity of the closed-loop accelerometer is increased over 40 times while the long-term stability of the closed-loop accelerometer with quasi-zero stiffness is remarkably improved for both controllers. The PID-controlled accelerometer with quasi-zero stiffness has an Allan bias instability as low as 22.51 ng and narrow bandwidth of 0.36 Hz. The PISM controlled accelerometer with quasi-zero stiffness has a linearly varied Allan bias instability from 37 ng to
$2.02 ~\mu \text{g}$
depending on the switching gain which determines the acceleration input range. However, the bandwidth of the PISM control system exhibits a nonlinear and wide-range variation with respect to the switching gain.