Coupling of resonant modes in micromechanical vibratory rate gyroscopes

Abstract

Analytical models are presented to describe the resonant modal coupling behaviour of z-axis micromechanical vibratory rate gyroscopes fabricated in an integrated polysilicon surface micromachining process. The models are then applied to predict the extent of displacement and force coupling between the drive and sense axes of this device as a function of varying degrees of matching between the resonant frequencies associated with these modes. Two modelling approaches are presented. The first approach is based on linear vibration analysis. The second approach- a state-space based system identification method- is used to calculate the anisoelasticity parameters. It is shown that, as the resonant frequencies of the two modes are brought closer together, an improvement in overall resolution and scale factor of the device is obtained at the expense of an enhanced coupling of forces to displacements between the two axes and the onset of electrostatic instability for an open-loop sensing implementation.