Modeling of nonlinearities in vibratory ring gyroscopes

This paper presents a behavioral model for the ring gyroscope, taking into consideration the effects due to nonlinearity of actuation electrodes. Closed-form expressions for the nonlinear electrostatic force due to any actuation electrode are obtained, and are used as exciting force for the mechanical part of the gyroscope, which is usually modeled as a set of mass-spring-damper systems representing each mode. Nonlinearity of detection electrodes as well as Brownian noise are modeled too. Numerical solution for the equations of motion was done using Simulink to verify the model. The evolution of vibration induced errors due to nonlinearity of actuation and detection electrodes is explained in details. The model helps quantify some important parameters and limitations for the ring gyroscope.