Automatic Mode-Matching in MEMS Vibrating Gyroscopes Using Extremum Seeking Control

In order to enhance the sensitivity and to reduce the readout circuit complexity of any angular velocity microsensor (vibrating gyroscope), it is crucial to reduce the frequency mismatch of its resonant modes of vibration. Achieving a good matching accuracy during fabrication is rather difficult because of tolerances and process variations that detrimentally affect the manufacturing precision. Moreover, even assuming to achieve a good frequency matching through fabrication or postfabrication calibration, it is very likely that parametric variations induced by the external environment during the normal operation of the device disrupt any initial tuning. For these reasons, in this paper, an alternative way to accomplish the frequency-matching condition is suggested, which exploits a real-time adjusting mechanism based on an automatic mode-matching control loop. In particular, this paper describes the details of an adaptive controller capable of automatically matching the resonant frequencies of the two main modes of vibration of a single-axis vibrating microgyroscope, under the provision that there is an underlying mechanism through which the frequency mismatch can be controlled by adjusting a suitable tunable parameter. The controller is designed by considering the requirement of reducing its complexity, so that it can be easily implemented on cheap sensors. Owing to a key observation that allows the recast of the frequency-matching problem as a maximization problem, the proposed mode-matching controller is actually designed as a standard perturbation-based extremum-seeking controller, which can be implemented by using few analog electronic components. The proposed solution has been tested on the LISY300AL yaw-rate microelectromechanical system gyroscope manufactured by STMicroelectronics, showing that a mode matching of nearly 1 Hz or less can be easily attained.