Mode-matching in vibrating microgyros using extremum seeking control

For MEMS vibrating gyroscopes that operate with an open loop sensing interface, the mode-matching condition is essential in order to achieve enhanced sensitivity and uniform performance on the whole sensor bandwidth. Matching the vibrating modes of the sensor during fabrication is rather unfeasible, because the fabrication process tolerances and defects detrimentally affect the manufacturing precision. Moreover, system parameter changes induced by the influence of the external environment can disrupt an initial trimming operated on the device in order to establish mode-matching. So, the only effective way to achieve mode-matching consists of exploiting feedback control. In this paper, we propose an adaptive add-on controller capable of achieving the mode-matching condition in vibratory microgyros operating with an open loop sensing interface. After recasting the mode-matching condition as a maximization problem, we use an extremum seeking control to perform the task of tuning the resonant frequencies of the sensor vibrating modes. The effectiveness of the proposed control scheme is shown by several numerical simulations.