Dynamics of MEMS-Based Angular Rate Sensors Excited via External Electrostatic Forces

This paper investigates the dynamic behavior of rotating MEMS-based vibratory gyroscopes which employs a thin ring as the vibrating flexible element. The mathematical model for the MEMS ring structure as well as a model for the nonlinear electrostatic excitation forces are formulated. Galerkin’s procedure is employed to reduce the equations of motion to a set of ordinary differential equations. Understanding the effects of nonlinear actuator dynamics is considered important for characterizing the dynamic behavior of such devices. A suitable theoretical model to generate nonlinear electrostatic force that acts on the MEMS ring structure is formulated. Dynamic responses in the driving and the sensing directions are examined via time responses, phase diagram, and Poincare’ map plots when the input angular motion and the nonlinear electrostatic force are considered simultaneously. The analysis is envisaged to aid fabrication of this class of devices as well as for providing design improvements in MEMS Ring-based Gyroscopes.