Modeling and identification of the Jet Propulsion Laboratory vibratory rate microgyroscope

This dissertation presents the experimental modeling and system identification of the Jet Propulsion Laboratory MEMS vibratory rate gyroscope. The primary objective is to estimate the modal frequencies, damping ratios, and the orientation of the vibrational nodes for important sensor dynamic modes with respect to the electrode-pick-offs in the sensor. An adaptive lattice filter is initially used to identify a high-order two-input/two-output transfer function describing the dynamics of the sensor in the neighborhood of lightly damped degrees of freedom. A three-mode model is then developed from the identified input/output model to determine the nodal axes' orientation. The identified model, which is extracted from several seconds of input/output data, also yields the frequency split between the sensor's modes that are exploited in detecting the rotation rate. The nodal axes' orientation and modal frequency split give direct insight into the source of quadrature measurement error that corrupts detection of the sensor's angular rate.; A new frequency-domain identification technique that estimates the mass, damping, and stiffness matrices based on an “impedance” model, is also investigated. A normalized coprime factor controller is synthesized to add damping to the dominant sensor modes using velocity feedback for efficient generation of frequency response data via the correlation method. Two identification methods are performed: (1) a least-squares approximation that minimizes the Frobenius norm of the error and, (2) a minimax optimization problem that minimizes the maximum singular value of the error on a frequency-by-frequency basis. The advantage of the second method is that the positive definiteness of the mass, damping, and stiffness matrices is guaranteed. The two methods give similar estimates of the nodal axes' orientations and are comparable to the time-domain sensor model and optical interferometric images.