H∞ Design of an EM-ΣΔ Feedback for MEMS Gyroscopes

In this work, we propose a systematic and flexible method for designing the electronic filter of electro-mechanical ΣΔ (EM-ΣΔ) feedbacks, widely used for the closed-loop operation of high-performance MEMS gyroscopes. We formulate the filter design as an optimization problem based on the H
_∞
norm of weighted closed-loop transfer functions with an appropriate H
_∞
criterion. The desired closed-loop system specifications are then expressed through weighting filters, which can be chosen by the system designer. Practical implementations demonstrate the effectiveness of our method. When compared to the results of an established filter, we obtain performance improvements of 30% for the scale factor nonlinearity, 40% for the RMS noise, 35% for the angle-random walk, to cite a few.