The purpose of this research is to create a tool for electrostatically suspending planar, disk-shaped objects towards the effort to measure and analyze stem motion of planar disk-shaped resonators as a function of mass perturbations. Planar disk-shaped resonators, generally, operate as sensors which measure an object's rate of rotation. When measuring the vibratory response, resonant modes appear in degenerate pairs which are exploited in measurements to achieve exceptional signal-to-noise ratios relative to various noise sources. However, assorted errors and nonidealities in a resonator's fabrication ``detune'' the resonant frequencies. The resonator may be ``tuned'' by converging the split frequencies together through systematic mass modifications with post-fabrication techniques. No quantitative analysis has demonstrated changes in the dynamics at the resonator stem as a result of the mass perturbations. By electrostatically suspending a disk resonator, hard-mounts are removed, and repeatable and controllable boundary conditions are established for comparing analogous resonators. The electrostatic suspension of a disk is representative of an ``electrostatic bearing'' .

Two systems are modeled and analyzed to assess the dynamics of an electrostatically controlled object and assistin the design of stabilizing controllers. Inherently, each system is unstable and requires feedback control to adjust the forces acting on the electrostatically suspended body until a desired reference is achieved. Further, electrical measurements representative of the body's pose require compensation to achieve stability due to the colocation of the force actuation and sensing pick-off. A single degree of freedom system is initially fabricated and analyzed both experimentally and through the use of a modeling paradigm to aid in the development of the more complicated suspension platform, debug the electronics interface, and determine the methods of signal conditioning. The modeling paradigm, fabrication techniques, and electronics interface are then extended to a suspended disk platform. The model indicates the suspension system is not strongly stabilizable if only the electrode-disk gap measurements are available. Consequently, an unstable controller is proposed that stabilizes the disk. To control the lateral degrees of freedom, measurements of the disk's lateral position are used to regulate its in-plane motion. Comparisons of the model results and experimental results are given.

Coriolis Vibratory Gyroscope (CVG) is considered the most critical component in a strap down

inertial navigation unit. It measures the rate of rotation through the Coriolis coupling, or exchange

of angular momentum, between a pair of resonance modes with very close resonance frequency,

often referred to as a degenerate mode pair. The measurement error, however, is closely related to

how close the degenerate mode pair match in frequencies. Further the errors also drifts over time,

making precise calibration nearly impossible.

There is a particular class of CVGs with radial symmetry in their geometric design. Such

symmetry permits the simultaneous actuation and measurement of multiple Coriolis mode pairs.

Such design opens up the possibility of operating more than one pair of degenerate modes on

the same resonator. The UCLA resonator (URES) was designed to exploit the benefits of this

possibility. The first challenge to overcome is the simultaneous modal frequency match of two

Coriolis mode pairs. The two mode pairs of interest are the n = 2 mode, which is elliptical

in shape, and the n = 3 mode, which is trilobal in shape. The as etched resonator typically

exhibit frequency mismatch on the order of 10Hz for both mode pairs. A technique using mass

perturbation has been developed to simultaneously reduce the frequency mismatch of both mode

pairs to within 0.1 Hz. Once tuned, a system identification procedure is performed to determine the

modal properties of both mode pairs, from which the drive and sense electrodes and the peripheral

electronics can be optimally configured to maximize signal to noise ratio, and reduce quadrature

error.

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A new control architecture is then implemented to simultaneously operate both mode pairs

on the tuned resonator as two independent Coriolis sensors, thus allowing the extraction of two

independent rate measurements from the same resonator. The noise and long term stability performance

of both mode pairs are characterized. Angle random walk (ARW), bias stability, and

scale factor for each mode pair are first characterized with the other mode pair turned off. The

performance parameters are subsequently compared to those when the two mode pairs are simultaneously

operated. Degradation in the noise performance due to nonlinearity in the electronics was

analyzed, and an effective mitigation using frequency domain filtering was implemented. Correlation

between the n = 2 and n = 3 bias drift was observed, and studied in detail in this research.

Further a blending filter architecture is introduced to optimally combine the two rate measurements

to yield a single superior rate measurement, in terms of both the sensors noise characteristics and

its long term bias stability.

Lastly, a novel in-situ technique is introduced to adaptively identify a finite-impulse-response

(FIR) model for the parasitic feedthrough signal between the input port and the output port of a

microelectromechanical (MEMS) resonator. The identified FIR model is then used as a filter to

cancel the parasitic signal leaving a clean resonance peak. Experiments conducted on multiple

two-input-two-output resonator devices show that the filters can adapt to different devices without

precise knowledge of the devices’ parameters. The filters also track the changes in the parasitic

feedthrough over time, providing consistent cancellation. Suppressions of more than 30 dB on the

parasitic feedthrough signals are obtained on all tested devices.