On Correlation of Anisoelasticity, Angular Gain, and Temperature in Whole-Angle CVGs

• Published in: IEEE sensors journal 2022-03, Vol.22 (5), p.4175-4185
• Main Authors: Vatanparvar, Daryosh, Shkel, Andrei M.
• Format: Article
• Language: English
• Subjects: anisoelasticity; Control stability; Control systems; Control theory; Controllers; Drift; Ellipticity; Feedback control; Feedback loops; Gyroscope; Gyroscopes; Mathematical analysis; Mathematical models; Oscillators; Precession; Proportional integral; quadrature; Quadratures; Sensitivity; Sensors; Straight lines; TCF; temperature; Temperature sensors; Vibratory gyroscopes; Voltage control; whole-angle
• ISSN: 1530-437X; 1558-1748
• DOI: 10.1109/JSEN.2021.3139920

In Coriolis Vibratory Gyroscopes (CVG) operating in the Whole-Angle (WA) mode, due to the presence of anisoelasticity in the mechanical structure, the oscillation pattern deviates from an ideal straight line and turns into an elliptical shape. In a conventional WA control architecture, the ellipticity is quantified using the quadrature variable, and a feedback control loop is utilized to minimize quadrature, thus compensating for anisoelasticity in the gyroscope structure. In this paper, using simulation and experimental results, we demonstrated that while a Proportional-Integral (PI) controller can be adapted as the feedback loop to suppress quadrature by several orders of magnitude, it cannot fully eliminate the ellipticity. The effect of residual quadrature on precession was numerically modeled and the corresponding angular drift and angle bias errors were characterized. The simulation results were verified through experimental data of a Micro-Electro-Mechanical (MEM) CVG. Furthermore, we modeled and evaluated the drift in angular gain due to variations in anisoelasticity. A Temperature Coefficient of Frequency (TCF) mismatch between the resonant modes, as the main mechanism causing anisoelasticity variations, was experimentally demonstrated to cause angular-gain temperature sensitivity in WA mode of operation. Our findings suggest that in the case of using a PI quadrature controller, residual quadrature and the corresponding effects on precession, including the angular-gain temperature sensitivity, can be reduced by a combination of increasing the feedback control gain and operating in a mode-matched condition. By following these two strategies, temperature sensitivity of angular gain in the MEM gyroscope was reduced by two orders of magnitude. We demonstrated an angular gain variation below 10 ppm for WA operation in a temperature range from 15 °C to 45 °C. By employing an active temperature controller, sub-ppm angular gain stability was experimentally demonstrated, realizing high-accuracy direct angle measurements for prolonged operation.