Modeling and identification of the doubly decoupled X-axis micromachined gyroscope

This paper presents the experimental modeling and system identification of a doubly decoupled x-axis gyroscope with novel torsional sensing comb capacitors. The doubly decoupled design is very efficient to suppress mechanical coupling of the gyroscope. Because the motion coupling of sensing and driving mass is through the proof mass, the driving and sensing movements can be totally independent. For a micromachined inertial device, it is very important to estimate the modal frequencies, damping ratios, and the vibrational orientation for important sensor dynamic modes of the sensor. Reduced high-order, mufti-input/multi- output time-domain models are required to capture important characteristics of the sensor dynamics, such as closely spaced modal frequencies and damping ratios. The sensor´s error analysis motivates the importance of estimating the vibration orientation and modal frequency split, because both the parameters contribute to the quadrature and in-phase bias errors when estimating the angular rate of rotation. The orientation of the nodal axes, however, is determined from further analysis since this information is not immediately available from the identified MIMO model. Based on the vibration and mode theories, we give the detailed equivalent model parameters, and these parameters will be compared with the calculated value of the finite element method and frequency response test value. The result will give the main error source of the quadrature component and the in-phase component.