Robert T. M’Closkey

Modal Parameter Tuning of an Axisymmetric Resonator via Mass Perturbation

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.

Frequency Tuning of a Disk Resonator Gyro Via Mass Matrix Perturbation

Electrostatic tuning of the resonant modes in microelectromechanical vibratory gyroscopes is often suggested as a means for compensating manufacturing aberrations that produce detuned resonances. In high performance sensors, however, this approach places very stringent requirements on the stability of the bias voltages used for tuning. Furthermore, the bias voltage stability must be maintained over the operating environment, especially with regard to temperature variations. An alternative solution to this problem is to use mass perturbations of the sensor’s resonant structure for resonant mode tuning. This paper presents a new mass perturbation technique that only relies on the sensor’s integrated actuators and pick-offs to guide the mass perturbation process. The algorithm is amenable to automation and eliminates the requirement that the modal nodes of the resonator be identified by direct measurement.

Phase Compensation Strategies for Modulated-Demodulated Control With Application to Pulsed Jet Injection

Modulated-demodulated control is an effective method for asymptotic disturbance rejection and reference tracking of periodic signals, however, conventional static phase compensation often limits the loop gain in order to avoid sensitivity function peaking in a neighborhood of the frequencies targeted for rejection or tracking. This paper introduces dynamic phase compensation for modulated-demodulated control which improves disturbance rejection characteristics by inverting the plant phase in a neighborhood of the control frequency. Dynamic phase compensation is implemented at baseband which enables the use of low-bandwidth compensators to invert high frequency dynamics. Both static and dynamic phase compensation methods are used to demonstrate a novel application of repetitive control for pulsed jet injection. In this application pulsing an injectant has been shown to produce advantageous effects such as increased mixing in many energy generation and aerospace systems. The sharpness of the pulse can have a large impact on the effectiveness of control. Modulated-demodulated control is used to maximize the sharpness of a pulsed jet of air using active forcing by tracking a square wave in the jet’s temporal velocity profile.

Wafer-scale etch process for precision frequency tuning of MEMS gyros

A technique which retains wafer-scale processing and packaging compatibility is described for customizing the dynamics of individual silicon resonators. The approach uses laser ablation of a protective conformal layer (parylene) to expose silicon in regions that are targeted for mass removal by subsequent DRIE. The technique is demonstrated on a planar axisymmetric resonator design whereby the frequency mismatches of a subset of the wafers resonators are reduced to less than 100 mHz.

Semi-analytical modeling of anchor loss in plate-mounted resonators

HIGHLIGHTSSemi‐analytical method to determine frequency and damping of plate‐mounted miniature resonators.Approach combines finite element models with Lamb wave theory.Numerical examples include cantilevers mounted on plates.Good agreement between obtained results and those from conventional transient FE simulations. ABSTRACT A semi‐analytical technique for estimating the energy loss in a resonator mounted to an infinite plate substrate is proposed in this paper. In a plate, only Lamb waves have to be considered, leading to a simplified characterization of the energy carried away from a vibrating source on the plate surface. Instead of employing absorbing elements at the boundaries of the plate‐resonator finite element model, it is shown how the semi‐analytical approach of stitching together analytical Lamb wave expressions to the finite element model can be utilized. The approach is demonstrated for single and double cantilever configurations on a plate. The results have excellent agreement with those of conventional transient finite element simulations.

Compensation of Nonlinear Harmonic Coupling for Pulsed-Jet-Velocity Shaping

This paper describes an approach to periodic reference tracking in a pulsed-jet-injection experimental study. The objective was to match the jet’s temporal velocity profile to a periodic reference. The challenge lies in controlling the highly nonlinear and poorly understood dynamics associated with the jet velocity. Although the actuator maintains good authority over the jet velocity, the nonlinear jet dynamics creates a high degree of coupling among neighboring harmonics that depends on the forcing level and the desired waveform. The coupling is quantified by demodulating the jet-velocity measurement into baseband components centered at the harmonic frequencies represented in the desired waveform. An empirical input–output relationship is developed by perturbing the baseband components and measuring their effect on neighboring harmonics, and it is shown that this relationship can be modeled as a linear multi-input/multi-output system. This knowledge is exploited to create stabilizing feedback controls th...

Decoupling of a Disk Resonator From Linear Acceleration Via Mass Matrix Perturbation

Axisymmetric microelectromechanical (MEM) vibratory rate gyroscopes are designed so the central post which attaches the resonator to the sensor case is a nodal point of the two Coriolis-coupled modes that are exploited for angular rate sensing. This configuration eliminates any coupling of linear acceleration to these modes. When the gyro resonators are fabricated, however, small mass and stiffness asymmetries cause coupling of these modes to linear acceleration of the sensor case. In a resonator postfabrication step, this coupling can be reduced by altering the mass distribution on the resonator so that its center of mass is stationary while the operational modes vibrate. In this paper, a scale model of the disk resonator gyroscope (DRG) is used to develop and test methods that significantly reduce linear acceleration coupling.

Integration of a Signal Processing and Control ASIC With the JPL Micro-Gyroscope

This paper describes the integration of a vibratory rate sensor—the JPL microgyro—with a special purpose control ASIC developed at UCLA. The digital ASIC has a flexible control architecture that can be customized for individual sensors. We describe this process for one sensor prototype and include experimental results demonstrating the efficacy of the ASIC.Copyright