A mode-matched force-rebalance control for a MEMS vibratory gyroscope

The force-to-rebalance (FTR) closed-loop control is widely used in MEMS vibratory gyroscopes. However, most of these applications may operate in split modes, as mode matching is usually conducted open loop. There is a lack of discussion explicitly addressing the significance of mode matching in the FTR operation mode. This paper investigates the influence of mode mistuning on the FTR closed-loop control of a MEMS Coriolis vibratory gyroscope (CVG), and proposes a novel tuning method using real time control forces to achieve a mode-matched FTR control. The analysis and design of the FTR is based on the time averaged equations of motion, where the sense mode vibration is decomposed into the quadrature and in-phase channels with cross coupling determined by the frequency mismatch between the drive and sense modes of vibration. The control design is treated as a 2 × 2 multivariable control problem using the individual channel design (ICD) framework. Independent control design for each of the two channels allows the bandwidth of the quadrature loop to be significantly less than the in-phase loop. The characteristics of mode mistuning can be extracted from the real time feedback forces. Using this information, the desirable mode-matched uncoupled FTR can be implemented. The FTR closed-loop control eliminates the influences of frequency mismatch on the zero rate output and linearity of the scale factor. It therefore relaxes the degree to which the modes need to be tuned. It is shown in this study that matching the modes in the FTR control scheme improves noise performance and measurement accuracy over the non-tuned case. Experimental results of real time FTR control and Allan deviation tests are provided to verify the analysis.