Andrei M. Shkel

Dynamics and control of micromachined gyroscopes

We summarize principles of operation of micromachined gyroscopes, analyze dynamics of ideal and non-ideal systems, and propose an approach for formulation and solving problems of control. The suggested approach uses active nonlinear feedback control for drive and compensation of errors. Both non-adaptive and adaptive strategies are presented. These strategies can be used for a broad class of micromachined vibratory gyroscopes including those for angle and angular rate measurement.

Experimental evaluation and comparative analysis of commercial variable-capacitance MEMS accelerometers

This paper reports the experimental analysis of commercially available variable-capacitance MEMS accelerometers, characterized under standardized tests. Capacitive MEMS sensors of the same low-level input acceleration range with various mechanical sensing element designs, materials, fabrication technologies and price ranges were selected for evaluation. The selected sensors were characterized using ANSI and NIST certified testing equipment and under the same testing conditions; and their sensitivity, resolution, linearity, frequency response, transverse sensitivity, temperature response, noise level and long-term stability were tested and compared. The experimental results are then interpreted to provide an insight to advantages and disadvantages for using a particular mechanical design, fabrication technology, sensor material and the techniques for electronics integration and packaging of each specific sensor design.

Type I and Type II Micromachined Vibratory Gyroscopes

All Micromachined Vibratory Gyroscopes (MVG) are based on the principle that the Coriolis forces produced by rotation of the gyro cause a transfer of energy between two of the gyros modes of vibration. Vibratory Gyroscopes can be classified into two broad types, angle gyroscopes (or Type I) and rate gyroscopes (or Type II). Gyroscopes of the first type measure orientation angles directly, while gyroscopes of the second type measure rotational rate. Most MVG implementations to date are found exclusively in the angular rate measuring variety, however there are opportunities for implementation on the micro-scale angle gyroscopes. This paper introduces a unified approach for description of MVGs and emphasizes the differences between the two types of devices. We also review our recent results in development of Type I and Type II gyroscopes. I. INTRODUCTION All vibratory gyroscopes use the Coriolis acceleration that arises in rotating reference frames to measure rotation. The Coriolis forces produced by vibration of the sensing element and rotation of the system cause a transfer of energy between two of the gyros modes of vibration. Vibratory gyros divide naturally into two classes depending on whether the two modes are of the same kind or different. In the classical tuning fork gyro (Fig. 1), for example, the two modes are different. One consists of a flexural vibration of the tines and the other a torsional vibration about the stem. Vibratory gyros utilizing similar modes include the vibrating string, the vibrating rectangular bar, the vibrating cylinder, and the hemispherical resonator gyro, Fig. 2. Vibratory gyros utilizing similar modes can be operated in the whole angle mode (direct angle measurement mode) or the open-loop mode(or force-to-rebalance modes) to measure rotational rate. Conventionally, different modes gyros are used for angular rate measurement. We introduced the classification of vibratory gyroscopes based on phenomena they measure - angle gyroscopes (or Type I) and rate gyroscopes (or Type II). Almost all reported to date Micromachined Vibratory Gy- roscopes (MVG) are of Type II. They operate on the Coriolis principle of a vibrating proof mass suspended above the substrate. The proof mass is supported by anchored flexures, which serve as the flexible suspension between the proof mass and the substrate, making the mass free to oscillate in two orthogonal directions: the drive direction and the sense direction. In Type II implementation, the overall dynamical

Nonresonant micromachined gyroscopes with structural mode-decoupling

This paper reports a novel four-degrees-of-freedom (DOF) nonresonant micromachined gyroscope design concept that addresses two major MEMS gyroscope design challenges: eliminating the mode-matching requirement and minimizing instability and drift due to mechanical coupling between the drive and sense modes. The proposed approach is based on utilizing dynamical amplification both in the 2-DOF drive-direction oscillator and the 2-DOF sense-direction oscillator, which are structurally decoupled, to achieve large oscillation amplitudes without resonance. The overall 4-DOF dynamical system is composed of three proof masses, where second and third masses form the 2-DOF sense-direction oscillator, and the first mass and the combination of the second and third masses form the 2-DOF drive-direction oscillator. The frequency responses of the drive and sense direction oscillators have two resonant peaks and a flat region between the peaks. The device is nominally operated in the flat regions of the response curves belonging to the drive and sense direction oscillators, where the gain is less sensitive to frequency fluctuations. This is achieved by designing the drive and sense anti-resonance frequencies to match. Consequently, by utilizing dynamical amplification in the decoupled 2-DOF oscillators, increased bandwidth and reduced sensitivity to structural and thermal parameter fluctuations and damping changes are achieved, leading to improved robustness and long-term stability over the operating time of the device.

Inherently robust micromachined gyroscopes with 2-DOF sense-mode oscillator

Commercialization of reliable vibratory micromachined gyroscopes for high-volume applications have proven to be extremely challenging, primarily due to the high sensitivity of the dynamical system response to fabrication and environmental variations. This paper reports a novel micromachined gyroscope with 2 degrees-of-freedom (DOF) sense-mode oscillator, that provides inherent robustness against structural parameter variations. The 2-DOF sense-mode oscillator provides a sense-mode frequency response with two resonant peaks and a flat region between the peaks, where the amplitude and phase of the response are insensitive to parameter fluctuations. Furthermore, the sensitivity is improved by utilizing dynamical amplification of oscillations in the 2-DOF sense-mode oscillator. Prototype gyroscopes were fabricated using a bulk-micromachining process, and the performance and robustness of the devices have been experimentally evaluated. With a 5.8mum drive-mode amplitude, the tested unit exhibited a measured noise-floor of 0.64deg/s/radic(Hz) at 50Hz bandwidth in atmospheric pressure. The sense-mode response in the flat operating region was also experimentally demonstrated to be inherently insensitive to pressure, temperature and DC bias variations

An approach for increasing drive-mode bandwidth of MEMS vibratory gyroscopes

The limitations of the photolithography-based micromachining technologies defines the upper-bound on the performance and robustness of micromachined gyroscopes. Conventional gyroscope designs based on matching (or near-matching) the drive and sense modes are extremely sensitive to variations in oscillatory system parameters that shift the natural frequencies and introduce quadrature errors. Nonconventional design concepts have been reported that increase bandwidth to improve robustness, but with the expense of response gain reduction. This paper presents a new approach that may yield robust vibratory MEMS gyroscopes with better gain characteristics while retaining the wide bandwidth. The approach is based on utilizing multiple drive-mode oscillators with incrementally spaced resonance frequencies to achieve wide-bandwidth response in the drive-mode, leading to improved robustness to structural and thermal parameter fluctuations. Enhanced mode-decoupling is achieved by distributing the linear drive-mode oscillators radially and symmetrically, to form a multidirectional linear drive-mode and a torsional sense-mode; minimizing quadrature error and zero-rate output. The approach has been implemented on bulk-micromachined prototypes fabricated in a silicon-on-insulator (SOI)-based process, and experimentally demonstrated.

MEMS Vibratory Gyroscopes

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Environmentally Robust MEMS Vibratory Gyroscopes for Automotive Applications

price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria. Prices indicated with ** include VAT for electronic products; 19% for Germany, 20% for Austria. All prices exclusive of carriage charges. Prices and other details are subject to change without notice. All errors and omissions excepted. C. Acar, A. Shkel MEMS Vibratory Gyroscopes

Glass Blowing on a Wafer Level

Automotive applications are known to impose quite harsh environmental conditions such as vibration, shock, temperature, and thermal cycling on inertial sensors. Micromachined gyroscopes are known to be especially challenging to develop and commercialize due to high sensitivity of their dynamic response to fabrication and environmental variations. Meeting performance specifications in the demanding automotive environment with low-cost and high-yield devices requires a very robust microelectromechanical systems (MEMS) sensing element. This paper reviews the design trend in structural implementations that provides inherent robustness against structural and environmental parameter variations at the sensing element level. The fundamental approach is based on obtaining a gain and phase stable region in the frequency response of the sense-mode dynamical system in order to achieve overall system robustness. Operating in the stable sense frequency region provides improved bias stability, temperature stability, and immunity to environmental and fabrication variations.

Structural design and experimental characterization of torsional micromachined gyroscopes with non-resonant drive mode

A fabrication process for the simultaneous shaping of arrays of glass shells on a wafer level is introduced in this paper. The process is based on etching cavities in silicon, followed by anodic bonding of a thin glass wafer to the etched silicon wafer. The bonded wafers are then heated inside a furnace at a temperature above the softening point of the glass, and due to the expansion of the trapped gas in the silicon cavities the glass is blown into three-dimensional spherical shells. An analytical model which can be used to predict the shape of the glass shells is described and demonstrated to match the experimental data. The ability to blow glass on a wafer level may enable novel capabilities including mass-production of microscopic spherical gas confinement chambers, microlenses, and complex microfluidic networks