This paper reports real-time tuning of the JPL-Boeing micromachined vibratory rate sensor. The ideal sensor is designed to operate in a degenerate condition in which two modes of vibration have equal resonant frequencies. This condition achieves the best possible signal-to-noise ratio thereby maximizing sensor performance. A frequency split between the two modes, however, is inevitable in actual devices and leads to degraded performance. To modify the sensor dynamics to a desired condition, we have studied the bias potential effect on the sensor dynamics and successfully implemented a real-time tuning process via electrostatic forces to reduce the frequency split to less than 0.1 Hz when the nominal modal frequencies are near 4.4 kHz. A closed-loop identification method is employed for rapid and precise empirical frequency response estimates of the sensor dynamics. An LMI-based parameter estimation scheme produces an excellent fit of the model to the frequency response data and this enables the successful implementation of a steepest descent algorithm. Transformations for decoupling the MIMO sensor dynamics are also motivated and demonstrated. © 2005 AACC.

High-performance vibratory gyroscopes require two degenerate modal frequencies for maximizing the rate-induced signals relative to noise produced by signal conditioning electronics. The present paper introduces a systematic approach for tuning these modes in vibratory gyros that employ electrostatic actuation. The key contribution shows how a parametric model, which captures the dependence of the sensor dynamics on the bias electrodes' potentials, can be fit to empirical frequency response data by solving a generalized eigenvalue problem. The models typically have 20 to 30 parameters for which the frequency response data imposes up to several hundred constraints. Subsequent analysis of the identified model enables the direct computation of the bias potentials which yield degenerate modal frequencies. The results are illustrated on a JPL-Boeing MEMS gyro prototype. © 2006 IEEE.

It is well known that the poles, zeros and delay of a system play an important role in determining the associated feedback performance limitations. In this paper, we first derive an approximate transfer function for a modulated and demodulated system of a particular form. We next analyse the behaviour of the poles, zeros and delay of this transfer function when the modulation frequency is varied. Some implications of these results are also briefly discussed. © 2005 Elsevier Ltd. All rights reserved.

We consider feedback performance limitations for modulated and demodulated control systems whose base systems have non-minimum phase (NMP) zeros or unstable poles. We first derive a transfer function for the modulated system and then show how the poles and zeros of this function are related to those of the base system. We next analyse the behaviour of the poles and zeros, when the modulation frequency is varied. Bode and Poisson Integral constraints for the modulated system are then considered. The effect of a base system delay is also discussed. Performance limitations, linear systems, control applications, poles and zeros.

© 2015 IEEE. This paper reports the permanent frequency mismatch reduction of the primary wineglass modes in a planar axisymmetric resonator by strategic mass loading. The resonator consists of a set of concentric rings that are affixed to neighboring rings by a staggered system of spokes. The outer layers of spokes are targets for mass deposition. This paper develops modified ring equations that guide the mass perturbation process, and despite the fact that the deposited mass and deposition locations are quantized, it is possible to systematically reduce the frequency difference of the wineglass modes to effective degeneracy such that two modes cannot be distinguished in a frequency response plot. Results on five resonators are reported with nominal wineglass modes near 14 kHz, quality factors of 50k, and frequency mismatches exceeding 30 Hz in some cases, but with postperturbation mismatches smaller than 80 mHz. Furthermore, it is also shown that the quality factors remain unchanged.

A special-purpose integrated circuit that accomplishes the real-time control and filtering tasks for the JPL-Boeing micromachined gyroscopes using a flexible, low-power implementation is presented. Our exposition focuses on the integration of the circuit and a prototype sensor, the synthesis and implementation of the control filters, and the subsequent performance of the closed-loop system. Identified sensor models are also presented because the control approach and, hence, the circuit architecture, is motivated by special features of the sensor dynamics. © 2005 IEEE.

We report on the development of a new microelectronic mechanical system (MEMS)-based quartz resonator technology that allows for the processing and integration of VHF to UHF high-Q oscillators and filters with high-speed silicon or III-V electronics. This paper describes the first demonstration of prototype oscillators and filters using this newly developed technology. We present impedance, Q, and temperature sensitivity data of UHF resonators along with phase noise and Allan deviation measurements. Our first 2-pole filter data showing low insertion loss are also presented. Finally, the results of power handling measurements are described for applications where high levels of background signals are present. © 2005 IEEE.

This paper presents the optimized design and analysis of a new circular quartz resonator for VHF-UHF filtering applications. The resonator is designed for ease of packaging and integration with on-chip electronics using a new quartz-MEMS process that is being developed at HRL Laboratories. A key feature of this design is the removal of the metal electrodes from the active regions in order to enhance the mechanical gain. As an example of this design, we have modeled a 9.8μm thick circular plate (383-μm-diameter) with a 10-μm-thick double-sided circular resonator as the active region. The 200 μm diameter resonator has a 0.1 μm step above each face of the plate. The entire structure is composed of AT-cut quartz. This design provides a high degree of energy trapping for the fundamental thickness-shear mode at approximately 168 MHz. Around the resonator on each face of the plate is a pair of opposing 600 Å-thick annular Al electrodes. The width of the electrodes is 40 μm and a 1.5 μm gap exists between the inner edge of the electrodes and the central areas. We will present numerical results showing that this electrode arrangement provides effective acoustic coupling to the thickness shear mode of the central resonator area. A frequency sweep provides a plot of the motional impedance of the resonator and is a very effective tool for assessing the acoustic coupling between the electrodes and TS mode as function of the electrode-mesa gap. We will also demonstrate a trade-off between Au and Al electrodes for this design.