Modal Coupling in Micromechanical Vibratory Rate Gyroscopes

The authors present modeling approaches to describe the coupling of modes in a resonant vibratory rate gyroscope. Modal coupling due to off-diagonal stiffness and damping terms is considered. Three analytical modeling approaches are presented in the context of a$z$-axis micromechanical vibratory rate gyroscope fabricated in an integrated polysilicon surface-micromachining process. The first approach is based on frequency-response analysis of the gyroscope output. The second approach takes the route of state-space-based system identification to identify the modal-coupling parameters. A third approach based on measured vibration data identifies the coupling parameters due to stiffness and damping. These three methods are then applied to predict the extent of displacement and force coupling between the drive and the sense axes of an existing device as a function of varying degrees of matching between the resonant frequencies associated with the drive and the sense modes. Experimental data show that as the resonant frequencies of the drive and sense 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 instability for an open-loop sensing implementation.