Hemispherical Resonator Gyro Research Articles

Imperfection Parameter Observer and Drift Compensation Controller Design of Hemispherical Resonator Gyros

The hemispherical resonator gyroscope is a type of vibratory gyroscope, which can measure angle or angular rate, based on its operating mode. This paper deals with the case when the hemispherical resonator gyroscope is operated in angle measurement mode. In angle measurement mode, the resonator pattern angle precesses, with respect to the external rotation input, by the principle of the Coriolis effect, so that the external rotation can be estimated, by measuring the amount of precession angle. However, this pattern angle drifts, due to the manufacturing error of the resonator. Since the drift effect causes degradation of the angle estimation performance of the resonator, the corresponding drift compensation control should be performed, to enhance the estimation performance. In this paper, a mathematical model of the hemispherical resonator gyro is first introduced. By using the mathematical model, a nonlinear observer for imperfection parameter estimation, and the corresponding compensation controller are designed to operate hemispherical resonator gyros, as angle measurement sensors.

A MEMS diamond hemispherical resonator

In this paper we report the fabrication of hemispherical polycrystalline diamond resonators fabricated on a novel high-temperature glass substrate. The hemispherical resonator gyroscope is one of the most accurate and rugged of the mechanical gyroscopes, and can be operated in either rate or whole-angle mode due to its high degree of symmetry. A fabrication sequence for creating extremely symmetric 3D MEMS hemispheres is presented. Mode shapes and frequencies obtained with a laser vibrometer are shown, as well as curves of Q versus pressure, and the dependence of frequency on anchor size. Fundamental mode frequency matching to <0.1% in as-fabricated devices has been achieved, which is essential to gyroscope operation in whole-angle mode.

반구형 공진 자이로의 동작모델과 기초 제어특성 실험

This article focuses on a hemispherical resonator gyro driven by the Coriolis effect. The operational principle of resonator gyros and mathematical models are introduced. These models are useful to explain the behavior of a resonator and to design controllers. Several control tests of a resonator have been done. A resonator has been excited by electromagnets controlled by a computer. Its amplitude has been adjusted by a PI control. The transient response is matched with a simulation result based on a mathematical model. A vibrating pattern may drift due to non-uniform factors of a resonator. The drift of the vibrating pattern is controlled and aligned to a reference direction by a PI control. These results are very useful to understand the behavior of resonator gyros and to design advanced control algorithm for better performance.

반구형공진기 실험장치 개발과 진동패턴 제어

본 논문에서는 반구형 공진자이로에 대한 연구를 위해 NI FPGA 장비를 기반으로 한 실험 장치를 개발하였고 공진유도, 진폭제어 및 회전실험을 통해 실험 장치에 대한 적합성을 판별하고 시스템에 대한 파라미터를 추정하였다. 또한 공진기의 형상 불 균일로 인해 진동패턴이 표류하는 현상을 확인하고, 이를 정렬시킴으로써 구동모드중 하나인 FTR 모드 구현에 대한 선행연구를 수행하였다. The authors have developed a test system for a hemispherical resonator gyroscope by using NI FPGA equipment. We have verified its suitability for the research of resonator gyroscopes through several tests: deriving resonance, controlling amplitudes, and estimating resonator parameters. The authors have adjusted a vibrating pattern to be aligned with the driving axis (or electromagnets). This pattern alignment is a basic and important operation of the FTR mode, which is one of operating modes for resonant gyroscopes.

Research on Bell-Shaped Vibratory Angular Rate Gyro’s Character of Resonator

Bell-shaped vibratory angular rate gyro (abbreviated as BVG) is a new type Coriolis vibratory gyro that was inspired by Chinese traditional clocks. The resonator fuses based on a variable thickness axisymmetric multicurved surface shell. Its characteristics can directly influence the performance of BVG. The BVG structure not only has capabilities of bearing high overload, high impact and, compared with the tuning fork, vibrating beam, shell and a comb structure, but also a higher frequency to overcome the influence of the disturbance of the exterior environment than the same sized hemispherical resonator gyroscope (HRG) and the traditional cylinder vibratory gyroscope. It can be widely applied in high dynamic low precision angular rate measurement occasions. The main work is as follows: the issue mainly analyzes the structure and basic principle, and investigates the bell-shaped resonator's mathematical model. The reasonable structural parameters are obtained from finite element analysis and an intelligent platform. Using the current solid vibration gyro theory analyzes the structural characteristics and principles of BVG. The bell-shaped resonator is simplified as a paraboloid of the revolution mechanical model, which has a fixed closed end and a free opened end. It obtains the natural frequency and vibration modes based on the theory of elasticity. The structural parameters are obtained from the orthogonal method by the research on the structural parameters of the resonator analysis. It obtains the modal analysis, stress analysis and impact analysis with the chosen parameters. Finally, using the turntable experiment verifies the gyro effect of the BVG.

High and Moderate-Level Vacuum Packaging of Vibratory MEMS

We report vacuum packaging procedures for low-stress die attachment and versatile hermetic sealing of resonant MEMS. The developed in-house infrastructure allows for both high and moderate-level vacuum packaging addressing the requirements of various applications. Prototypes of 100 μm silicon-on-insulator Quadruple Mass Gyroscopes (QMGs) were packaged using the developed process with and without getters. Characterization of stand-alone packaged devices with no getters resulted in stable quality factors (Q-factors) of 1000 (corresponding to 0.5 Torr vacuum level), while devices sealed with activated getters demonstrated Q-factors of 1.2 million (below 0.1 mTorr level inside the package). Due to the high Q-factors achieved in this work, we project that the QMG used in this work can potentially reach the navigation-grade performance, potentially bridging the gap between the inertial silicon MEMS and the state-of-the-art fused quartz hemispherical resonator gyroscopes.

Vibration Character Analysis and Calculation for Hemispherical Resonator Gyro

Hemispherical Resonator Gyro is rotation-sensing instrument and has the merits of reliability and longevity etc. The precision of HRG is depended on the vibration character of hemispherical shells. Using the semi-analytic method, this paper discussed vibration character of hemispherical shell resonator and derived an algorithm of semi-analytic spherical elements. The method applies displacement function with toroidal analysis and axial discrete, so original two dimension problem is reduced to one dimension problem. The new method is very much simplified and can efficiently calculate the correlative physical character of hemispherical shell resonator, so it has high practical value for engineering application.

Milli-HRG inertial navigation system

The Hemispherical Resonator Gyro (HRG) has proven itself to be an ultra-reliable technology for space application with over 18 million operation hours and 100% mission success. Northrop Grumman Navigation Systems Division is developing a terrestrial inertial navigation system (INS) based on the proven space technology that can be used for precision pointing applications. The Precision Pointing System (PPS) design yields a small size and lightweight system and will require only a few watts of power to operate. To achieve this small sized INS, the PPS utilizes a new golf-ball sized milli-HRG (mHRG) that is based on the current HRG 130P production gyro design used in extremely accurate space pointing systems. The power reduction is derived from a new electronics design based around low power elements. The new mHRG gyro design has demonstrated bias stability performance better than the navigation grade gyros and will quickly attain this accuracy due to the extremely low noise characteristics of the HRG. Instrumental in the success of the mHRG performance has been the implementation of a calibration mechanization that eliminates the requirement for thermal control or modeling. This implementation will allow the INS to align quickly and will be advantageous for applications that have a quick response time requirement. Additionally, due to the stability of the mHRG the system can operate without GPS aiding for greater than an hour, while maintaining the attitude accuracy required for precision pointing, before an internal re-alignment is needed. The simplified design of mHRG has reduced the parts count by roughly 90% when compared to the current space qualified HRG production unit. With the major parts reduction it is projected that the mHRG can be produced efficiently and at a cost making it a viable choice for terrestrial applications.

반구형 공진 자이로스코프의 신호 검출 및 제어

In this paper, signal detection and control circuits for hemispherical resonator gyroscope(HRG) are designed, simulated and tested. HRG is one of the coriolis vibratory gyroscope(CVG) which has very stable quartz hemispherical resonator and shows very precise performance. HRG signals are usually modulated at the several kHz of resonant frequency. So the general control scheme cannot be applied directly because general control schemes mainly focused at low frequency range. Using demodulated and modulated PI control scheme with the signal detection which is presented in this paper, performance of manufactured HRG has tested.

Temperature Drift Compensation for Hemispherical Resonator Gyro Based on Natural Frequency

Temperature changes have a strong effect on Hemispherical Resonator Gyro (HRG) output; therefore, it is of vital importance to observe their influence and then make necessary compensations. In this paper, a temperature compensation model for HRG based on the natural frequency of the resonator is established and then temperature drift compensations are accomplished. To begin with, a math model of the relationship between the temperature and the natural frequency of HRG is set up. Then, the math model is written into a Taylor expansion expression and the expansion coefficients are calibrated through temperature experiments. The experimental results show that the frequency changes correspond to temperature changes and each temperature only corresponds to one natural frequency, so the output of HRG can be compensated through the natural frequency of the resonator instead of the temperature itself. As a result, compensations are made for the output drift of HRG based on natural frequency through a stepwise linear regression method. The compensation results show that temperature-frequency method is valid and suitable for the gyroscope drift compensation, which would ensure HRG's application in a larger temperature range in the future.

Force to Rebalance Control of HRG and Suppression of Its Errors on the Basis of FPGA

A novel design of force to rebalance control for a hemispherical resonator gyro (HRG) based on FPGA is demonstrated in this paper. The proposed design takes advantage of the automatic gain control loop and phase lock loop configuration in the drive mode while making full use of the quadrature control loop and rebalance control loop in controlling the oscillating dynamics in the sense mode. First, the math model of HRG with inhomogeneous damping and frequency split is theoretically analyzed. In addition, the major drift mechanisms in the HRG are described and the methods that can suppress the gyro drift are mentioned. Based on the math model and drift mechanisms suppression method, four control loops are employed to realize the manipulation of the HRG by using a FPGA circuit. The reference-phase loop and amplitude control loop are used to maintain the vibration of primary mode at its natural frequency with constant amplitude. The frequency split is readily eliminated by the quadrature loop with a DC voltage feedback from the quadrature component of the node. The secondary mode response to the angle rate input is nullified by the rebalance control loop. In order to validate the effect of the digital control of HRG, experiments are carried out with a turntable. The experimental results show that the design is suitable for the control of HRG which has good linearity scale factor and bias stability.

Low-Dissipation Silicon Tuning Fork Gyroscopes for Rate and Whole Angle Measurements

We report a new family of ultra high- Q silicon microelectromechanical systems (MEMS) tuning fork gyroscopes demonstrating angular rate and, for the first time, rate integrating (whole angle) operation. The novel mechanical architecture maximizes the Q-factor and minimizes frequency and damping mismatches. We demonstrated the vacuum packaged SOI dual and quadruple mass gyroscopes with Q-factors of 0.64 and 0.86 million at 2 kHz operational frequency, respectively. Due to the stiffness and damping symmetry, the quadruple mass gyroscope was instrumented to measure the angle of rotation directly, eliminating the bandwidth and dynamic range limitations of conventional MEMS vibratory rate gyroscopes. The technology may enable silicon micromachined devices for inertial guidance applications previously limited to precision-machined quartz hemispherical resonator gyroscopes.

A new control mode greatly improving performance of axisymmetrical vibrating gyroscopes

Coriolis vibrating gyroscopes using axisymmetrical or near-axisymmetrical resonators, such as Sagem Quapason™, hemispherical resonator gyros, cylindrical vibrating gyros, and axisymmetrical MEMS gyros, may work in whole-angle (WA) or in force-to-rebalance (FTR) (angle-rate) mode. Although a specific industrial process is implemented, including defect identification and correction, ageing effects cannot be compensated and affect drift and scale factor stability. This paper shows how the equations governing the relations between defects, commands, and errors can be used to define a new control mode, which combines FTR and WA modes in order to greatly improve performance. The implementation of those principles to the Quapason™ gyro leads to the GVNG gyro (French acronym for Gyro Vibrant Nouvelle Generation — New Generation Vibrating Gyro), a new digitally controlled coriolis vibrating gyroscope. Its experimental results are presented in this paper. The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) for the Clean Sky Joint Technology Initiative under grant agreement no. CSJU-GAM-SFWA-2008-001.

Dynamics of rotating and vibrating thin hemispherical shell with mass and damping imperfections and parametrically driven by discrete electrodes

A parametric electrode is normally used in hemispherical resonator gyroscopes, operating in the whole angle regime, for maintaining the amplitudes of vibratory patterns. It is well known that, due to variation of the gap between the resonator and parametric electrode, a drift of the vibrating pattern is obtained. This drift is similar to the gyro drift stipulated by the Q-factor imperfections and substantially deteriorates the quality of the hemispherical resonator gyroscope. In the present paper, we consider the methods of compensation of these drifts by means of special control of the vibrating pattern by a sectioned parametric electrode. Compensation of the drifts is achieved through amplitudes of voltage and phase manipulations at the sectioned parametric electrodes. The side effect of this control consisting of spurious splitting of frequencies of the vibrating pattern is discussed.

Influence of the resonator angular displacements in a hemispherical resonator gyro on the coupling between the working and beam-type vibrations

In [1], we have studied how the coupling between the working and beam type vibrations of the resonator affects the hemispherical resonator gyro operation. We show that such a coupling arises if the resonator is unbalanced. The beam type vibrations are considered as translational displacements of the resonator hemisphere in the plane orthogonal to the symmetry axis. In the present paper, we take into account the fact that the hemisphere translational displacement is accompanied by its rotation about the axis perpendicular to the displacement line. We show that in this case a more accurate balancing of the resonator is required to eliminate the coupling between the two vibration modes.

Amplitude control contour in a hemispherical resonator gyro with automatic compensation for difference in Q-factors

For the normal operation of a hemispherical resonator gyro, its circuit must contain a control contour maintaining the resonator vibrations in the form of a standing wave with a prescribed amplitude. A turn of the basement leads to a turn of the standing wave, which permits using the resonator as a gyro. A turn of the standing wave may arise without a turn of the basement if the resonator has difference in Q-factors, i.e., if the damping constant of the standing wave depends on its orientation. This is one important source of device errors. Some information about the difference in Q-factors can be obtained by analyzing how the control signal maintaining the prescribed amplitude depends on the wave orientation. The larger the damping constant, the larger control signal is required to maintain the wave with the largest amplitude. In the present paper, we consider a version of the amplitude control contour in which the control signal maintaining the amplitude is supplemented with signal compensating for difference in Q-factors of the resonator. The compensating signals are produced by time integration of the control signal multiplied by certain trigonometric functions of the wave orientation angle. In this case, we decrease the level of dynamic errors of the amplitude maintenance contour, which arise in the usual circuit with each change of the wave orientation in the resonator, and simultaneously eliminate the drift caused by difference in Q-factors.

Effect of movability of the resonator center on the operation of a hemispherical resonator gyro

It was established in [2] that resonator deformation according to the second mode shape of a thin hemispherical shell results in a displacement of the center of mass if the resonator is unbalanced, i.e., if the distribution of mass over the surface of the hemisphere deviates from axial symmetry. In the same paper, it was shown that this displacement of the center of mass makes the instrument sensitive to linear vibrations. The present paper deals with linear vibration caused in the presence of unbalance by the working vibrations themselves and by the forces used to maintain the latter. The linear vibration is considered in the form of beam vibrations of the resonator stem. The study is aimed at determining the influence of the coupling between the working and beam vibrations on the instrument readings. We obtain a formula relating the hemispherical resonator gyro drift to the unbalance and the eccentricity, which, in particular, can be caused by the gravity component normal to the sensitivity axis. The drift considered here is essentially caused by the fact that deformation of the resonator supports also results in deformation of the electric control field in the gap between the electrodes. The resulting additional forces cause the effect studied in this paper. The drift magnitude depends on how the control of the phase state of the resonator is chosen. In what follows, to be definite, we consider the control in fast-time mode, i.e., at the natural vibration frequency. A similar effect takes place for any other type of control of waves in the resonator.

Vibration of a hemispherical shell gyro excited by an electrostatic field

In this paper the stability and precession phenomenon of the modal pattern of a rotating hemispherical shell gyro excited parametrically by electrostatic forces is investigated. Nonlinear modal equations of the rotating shell under small strain and moderate rotation are derived by following Niordson's thin shell theory. The method of multiple time scales is used to determine quantitatively the vibration displacement of the shell from which the precession rate of the modal vibration pattern can be extracted. Floquet theory is employed to study the stability of the analytical solution. Numerical simulation verifies the analytical results. Recent work by Matthews and Rybak (1), and Chou and Chang (2,3) showed that the hemispherical shell gyroscope becomes attractive and competitive in comparison with other types of gyros. The work- ing principle is that the modal vibration pattern of the shell moves when the shell is rotated about its axis and this movement provides a measure of the applied rate of turn. An important design feature of the hemispherical resonator gyroscope is that one is able to excite the shell without having a direct mechan- ical coupling between the shell and its supporting frame. In order to maintain the precessing vibration modal pattern, an electrostatic excitation is employed. Linear analysis (3) of a rotating hemispherical shell gyro excited parametrically by electrostatic forces showed that the vibration amplitude is decayed to zero in the stable region and becomes divergent in the unstable region under excitation. Therefore the geometrically nonlinear (4) effects of the shell under small strain and moderate rotation (5) are studied. Reissner (6) derived the geometrical nonlinear shell equations with Kirchhoff-Love assumption. Since that, many people continuously improved the nonlinear shell theories (7). In this paper, the nonlinear modal equations of the rotating shell under small strain and moderate rotation are derived by following Niordson's (8) thin shell theory. The method of multiple time scales (9) is used to determine quantitatively the vibration amplitude of the shell from which the precessional rate of the modal vibration pattern can be extracted. Floquet (10) theory is employed to study the stability of the analytical solution. Numerical simulation verifies the analytical results.

Comparison of hemispherical resonator gyro and optical gyros

The basic design of the small hemispherical resonator gyro inertial and tactical grade sensors and associated electronics is described. To reduce the cost of the electronics and maintain part per million accuracy, emphasis has been placed on digital control and processing techniques. A comparison of the ring laser gyro, fiber optic gyro, and hemispherical resonator gyro sensors shows that the latter offer lower cost, smaller size, and higher reliability than their optical counterparts.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On flexural vibration of hemispherical shell

This paper makes detailed analyses for the flexural vibration (frequency) of the hemispherical shell and presents the varying laws of frequency with the varying boundary angles and the wall thickness of the above shell. It is an important value to develop the instrument, such as hemispherical resonator gyro (HRG), whose sensing component is a hemispherical shell.