A Digital Control Structure for Lissajous Frequency-Modulated Mode MEMS Gyroscope

Abstract

This article proposes a digital control structure for a doubly decoupled gyroscope working in the Lissajous frequency-modulated (LFM) mode based on digital phase-locked loops (PLLs), which demodulates the angular rate signal directly from the readable digital gyroscope resonance frequency, eliminating the need for specific frequency readout circuits. The resonance frequencies of the LFM gyroscope working modes contain a mode mismatch frequency modulated by input angular rate, respectively, which are tracked by two digital PLLs followed by subsequent digital demodulation and filtering. A linearized model of the digital PLL is built to analyze noise and control characteristics for different PI parameters. The impact of different amplitude–phase extraction architectures on the extracted phase signal is also addressed in this article. Contrast experiments are carried out using the same gyroscope with large internal thermal stress due to the silicon-glass bonding process and no stress relief structure around the sensing element, working in the traditional amplitude-modulated (AM) mode and the LFM mode. Overall, the LFM working mode maintains its low-temperature sensitivity and high stability in spite of the large internal thermal stress in the gyroscope compared to AM working modes. The maximum scale factor variation over the temperature range from 10 °C to 50 °C is 1000 ppm for the LFM mode compared to 51 900 ppm for the AM closed mode. The maximum zero rate output drift over the same temperature range is 0.1248 °/s for the LFM mode and 10.7139 °/s for the AM closed mode. The scale factor nonlinearity is 329 ppm with an angular rate input range of ±50 °/s for the LFM mode compared to 1902 ppm for the AM closed mode. The LFM mode zero-bias fluctuation for ten days is less than 0.12 °/s. The angle random walk (ARW) and the bias instability (BI) of the LFM gyroscope are 0.316 °/ $\surd \text{h}$ and 2 °/h, respectively.