Vibratory Rate Research Articles

Design and optimization of a resonant output frequency gyroscope for robust sensitivity and bandwidth performance

This paper presents the architecture and optimization verification of a designed mode-mismatching gyroscope prototype made with fused silica in atmospheric pressure. The gyroscope prototype uses the decoupling frame and double-ended tuning fork (DETF) to achieve high sensitivity and quality factor. This structure can suppress residual quadrature error due to fabrication errors and imperfections. The angle rate-sensitive elements of the proposed gyroscope prototype with quasi-digital FM output are two DETF resonators resulting in differential implementation. We describe the principle of operation characterization of our micromechanical vibratory rate gyroscope based on resonant sensing of the Coriolis force and establish mathematical model called multi-parameters excitation system dynamics of Mathieu equation based on our previous work. We specify and quantify the impact functions of mechanical parameters on the properties of gyroscopes and identify sensitivity and limitation of sensitivity and bandwidth each other. A sample-based stochastic model is established to investigate the influence of different uncertain structure size on gyroscope performance. According to the uncertainty analysis, we modify the previous gyroscope structure, and then the parameters and structure of the improved third version gyroscope are obtained. This research can provide a reference for design and optimization of the structure size to improve robustness and performance of resonant angle rate sensor.

Drive-mode control for an underactuated MEMS vibratory rate gyroscope

It has been shown that the underactuated rate gyroscopes (URGs) hold appealing robust operational performance against the fluctuations of temperature, pressure and structure parameters. In order to further improve the performance of the URGs, the dynamics and the closed-loop control issues of the URGs are investigated in this paper. For a three-DOFs gyroscope with two drive-modes, single sense mode, and single actuator, it is shown that the dynamics of the drive subsystem of the URG can be described as a second-order nonholonomic constraint system, and the dynamics of the drive subsystem of the URG can be transformed into a fourth-order linear system with the Brunovsky's canonical forms by properly selecting the controlled output. Then a robust controller is presented to stabilize the underactuated system by solving a set of linear matrix inequalities. Additionally, the stability of the presented controller is analyzed and demonstrated by some simulations.

Foucault pendulum on a chip: Rate integrating silicon MEMS gyroscope

We report detailed characterization of a vacuum sealed rate integrating silicon MEMS gyroscope. The new gyroscope utilizes geometrically symmetric, dynamically balanced quadruple mass architecture, which provides a combination of maximized quality (Q) factors and isotropy of both the resonant frequency and damping. The vacuum sealed SOI prototype with a 2kHz operational frequency demonstrated virtually identical X- and Y-mode Q-factors of 1.2 million. Due to the stiffness and damping symmetry, and low energy dissipation, the gyroscope can be instrumented for direct angle measurements with fundamentally unlimited rotation range and bandwidth. Experimental characterization of the mode-matched gyroscope operated in whole-angle mode confirmed linear response in a ±450°/s range and 100Hz bandwidth (limited by the experimental setup), eliminating both bandwidth and range constraints of conventional open-loop Coriolis vibratory rate gyroscopes.

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.

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.

Fuzzy Adaptive Sliding Mode Controller for MEMS Vibratory Rate Gyroscope

AbstractUsing a proportional-integral sliding surface, a fuzzy adaptive sliding mode controller (SMC) is proposed to control micro-electromechanical systems (MEMS) gyroscopes and estimating the angular rate, damping ratios and stiffness coefficients in real time. The tracking performance of pure adaptive SMC is affected by high range chattering due to modeling uncertainties and exogenous inputs. Therefore, the discontinuous term of SMC is replaced by a fuzzy system which results in chattering free tracking and improved estimation accuracy. Therefore, the simple and intelligent Mamdani-type controller is resulted with high robustness against parametric uncertainties and exogenous disturbances. The performance of the proposed methods is evaluated through simulations.

Quadrature Compensation for Gyroscopes in Electro- Mechanical Bandpass ΣΔ-Modulators beyond Full-Scale Limits using Pattern Recognition

This paper presents a novel quadrature compensation scheme for vibratory rate gyroscopes in closed-loop electro- mechanical sigma-delta-modulators (ΣΔM). The proposed technique is able to detect and compensate quadrature errors beyond the full-scale limits of the ΣΔM with a minimal analog hardware effort. The quadrature detection is based on a pure digital pattern recognition algorithm, the quadrature compensation is done using DC bias voltages. An appropriate quadrature compensation is reached within a few iterations of the proposed algorithm.

Effect of Axial Force on the Performance of Micromachined Vibratory Rate Gyroscopes

It is reported in the published literature that the resonant frequency of a silicon micromachined gyroscope decreases linearly with increasing temperature. However, when the axial force is considerable, the resonant frequency might increase as the temperature increases. The axial force is mainly induced by thermal stress due to the mismatch between the thermal expansion coefficients of the structure and substrate. In this paper, two types of micromachined suspended vibratory gyroscopes with slanted beams were proposed to evaluate the effect of the axial force. One type was suspended with a clamped-free (C-F) beam and the other one was suspended with a clamped-clamped (C-C) beam. Their drive modes are the bending of the slanted beam, and their sense modes are the torsion of the slanted beam. The relationships between the resonant frequencies of the two types were developed. The prototypes were packaged by vacuum under 0.1 mbar and an analytical solution for the axial force effect on the resonant frequency was obtained. The temperature dependent performances of the operated mode responses of the micromachined gyroscopes were measured. The experimental values of the temperature coefficients of resonant frequencies (TCF) due to axial force were 101.5 ppm/°C for the drive mode and 21.6 ppm/°C for the sense mode. The axial force has a great influence on the modal frequency of the micromachined gyroscopes suspended with a C-C beam, especially for the flexure mode. The quality factors of the operated modes decreased with increasing temperature, and changed drastically when the micromachined gyroscopes worked at higher temperatures.

A novel control loop design and its application to the force balance of vibratory rate sensor

This paper investigates a new loop design approach of force balance control for the vibratory rate sensor application. The proposed force balance control design takes advantages of the modified automatic gain control configuration in controlling the system’s oscillating dynamics at the sense mode. The adapted automatic gain control scheme and force balance strategy, which maintains a constant oscillation magnitude in the sense mode, have several advantages. First it is possible to analyze a complicated nonlinear feedback system using a linear control theory, which resulted in straightforward prediction of closed loop performance. Moreover the control system to achieve the design goals can be implemented using a relatively simple feedback configuration. An application to the vibratory rate sensor using the proposed automatic gain control configuration witnessed that the force balance control can be validated in a practical design process. Experiments using an actual micromachined rate sensor verified the feasibility of the proposed control scheme with demonstration of enhanced performance.

Performance characterization of a new temperature-robust gain-bandwidth improved MEMS gyroscope operated in air

This paper reports a new MEMS vibratory rate gyroscope designed with increased robustness to fabrication imperfections and variations in environmental conditions. The proposed architecture utilizes a single degree-of-freedom (DOF) drive-mode and a fully coupled 2-DOF sense-mode. The drive-mode operational frequency and the sense-mode bandwidth can be set independently, relaxing the tradeoff between the gain, die size, and detection capacitance inherent to the previously reported robust gyroscopes with dynamic vibration absorber (DVA) architecture of the 2-DOF sense-mode. Prototypes with 2.5 kHz operational frequency were extensively characterized in air and demonstrated sense-mode 3 dB bandwidth of 250 Hz. The uncompensated temperature coefficients of bias and scale factor were 313 ( ° /h)/ ° C and 351 ppm ° C, respectively. Using off-chip detection electronics, the rate sensitivity was 28 μ V/( ° /s), ARW – 0.09 ( ° /s)/ Hz , bias instability – 0.08 ( ° /s), and ARRW – 0.03 ( ° /s) Hz . Detailed time domain, Allan variance, and probability density function analysis revealed that both ARW and ARRW are of Gaussian type and Coriolis-uncorrelated, showing stable in-operational noise performance of the reported gyroscope.

A disturbance rejection-based control system design for Z-axis vibratory rate gyroscopes

The current paper presents a new control strategy known as active disturbance rejection control (ADRC) for controlling the sense axis of a vibrational microelectromechanical system (MEMS) gyroscope and detecting time-varying rotation rates. In the ADRC framework, the generalized disturbance, which is referred to as the combination of the internal dynamics and external disturbances, is estimated and compensated for in real time. It is assumed that the drive axis outputs an ideal sinusoidal signal. A force-to-rebalance mode of operation is applied to the sense axis of the gyroscope. Under this mode, the output of the sense axis is continuously monitored and driven to zero by ADRC and the rotation rate is estimated by employing the demodulation technique. Simulation results and performance analysis demonstrate the effectiveness and robustness of the ADRC against parameter variations and noises.

Dynamic Stability of Beam-type Vibratory Angular Rate Sensors Subjected to Rate Fluctuations

Dynamic stability behavior of a beam-type vibratory structure, for applications in a class of vibratory angular rate sensors is investigated. A suitable mathematical model for a rotating beam perturbed by periodic velocity fluctuations is developed. The natural frequency variations due to the gyroscopic coupling present in the system are characterized. When the system is considered to be under an influence of periodic perturbations in the input angular speed, the dynamic stability is investigated. The method of averaging is employed for this purpose, and closed-form stability conditions are obtained. The analytical results are verified by direct numerical integration of the system equations.

Dynamic response-based characterization of ring-based vibratory angular rate sensors

Dynamic response behaviour of a rotating ring is investigated in order to better understand the achievable performance improvements as well as system limitations. For this purpose, the governing equations that represent the transverse as well as the tangential in-plane motion of a rotating ring are derived via the Hamilton’s principle. These equations are then discretized to represent a two-degree-of-freedom time-varying gyroscopic system. The asymmetry effects are considered important and are included by considering mass mismatch in the system mass matrix. In order to predict dynamic behaviour of a ring system subjected to external excitation and body rotation, time and frequency response analyses are performed. The natural frequency variations due to the gyroscopic coupling presented in the system are first characterized for varying input angular rates. The effects of system parameters such as damping and mass mismatch on the sensor sensitivity and operating range are quantified via suitable time and frequency response analyses.

Micromachined Vibratory Gyroscopes Controlled by a High-Order Bandpass Sigma-Delta Modulator

This work reports on the design of novel closed-loop control systems for the sense mode of a vibratory-rate gyroscope based on a high-order sigma-delta modulator (SigmaDeltaM). A low-pass and two distinctive bandpass topologies are derived, and their advantages discussed. So far, most closed-loop force-feedback control systems for these sensors were based on low-pass SigmaDeltaM's. Usually, the sensing element of a vibratory gyroscope is designed with a high quality factor Q to increase the sensitivity and, hence, can be treated as a mechanical resonator. Furthermore, the output characteristic of vibratory rate gyroscopes is narrowband amplitude-modulated signal. Therefore, a bandpass SigmaDeltaM is a more appropriate control strategy for a vibratory gyroscope than a low-pass SigmaDeltaM. Using a high-order bandpass SigmaDeltaM, the control system can adopt a much lower sampling frequency compared with a low-pass SigmaDeltaM while achieving a similar noise floor for a given oversampling ratio (OSR). In addition, a control system based on a high-order bandpass SigmaDeltaM is superior as it not only greatly shapes the quantization noise, but also alleviates tonal behavior, as is often seen in low-order SigmaDeltaM control systems, and has good immunities to fabrication tolerances and parameter mismatch. These properties are investigated in this study at system level

Modal Coupling in Micromechanical Vibratory Rate Gyroscopes

The authors present modeling approaches to describe the coupling of modes in a resonant vibratory rate gyroscope. Modal coupling due to off-diagonal stiffness and damping terms is considered. Three analytical modeling approaches are presented in the context of a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$z$</tex> -axis micromechanical vibratory rate gyroscope fabricated in an integrated polysilicon surface-micromachining process. The first approach is based on frequency-response analysis of the gyroscope output. The second approach takes the route of state-space-based system identification to identify the modal-coupling parameters. A third approach based on measured vibration data identifies the coupling parameters due to stiffness and damping. These three methods are then applied to predict the extent of displacement and force coupling between the drive and the sense axes of an existing device as a function of varying degrees of matching between the resonant frequencies associated with the drive and the sense modes. Experimental data show that as the resonant frequencies of the drive and sense modes are brought closer together, an improvement in overall resolution and scale factor of the device is obtained at the expense of an enhanced coupling of forces to displacements between the two axes and the onset of instability for an open-loop sensing implementation.

Device and procedure to treat cardiac atrial arrhythmias

A non-invasive vagal stimulation device (10) comprises a body having a vibration member (14). The stimulation is created by the vibration member (14) which has a vibratory rate that can be adjusted from being off to a preferred operating range. The non-invasive stimulation method consists of placing the non-invasive stimulation device (10) in the vicinity of the carotid artery bifrication where arises a carotid sinus and body which contain afferent sensory nerves that travel to medulla oblongata of brain, and either applying pressure in place, or moving the device (10) along the target arm. The method can be accomplished either with the vibration feature of the device turned on or off.

Experiment of Antenna Pointing Control for Satellite Communications Tracking Systems on Vehicles. Experiment of Acquisition and Tracking for BS Satellite.

Satellite communications are utilized widely fields -navigations, broadcast and scientific. Recently mobile communications and satellite broadcast are developing remarkably. And the active antenna pointing sysem is required so that we may communicate with satellite in transportation, such as sail boat, truck and car. In this case, we can assume that the antenna base receives perturbation of a high frequency, and we must construct a compact antenna control system with high response. In this research, we use an existing antenna system consisting of a 2-axis gimbal structure driven by stepping motor and a 3-axis vibratory rate gyroscope to control the base attitude. The antenna system is used to track a Japanese broadcast satellite in geostationary orbit. We propose intellectual satellite position search system with feedback control using AGC level and feedforward control using gyro sensor to correct various errors. This papers discusses the 2-axis gimbal structure, sensor system, control algorithm, and experimental result.

Modelling and design of an electrostatically levitated disc forinertial sensing applications

In this paper the design of a micromachined disc is described. Thedisc is encaged by electrodes at its top, bottom and periphery. Electrostaticforces are used to levitate the disc at the centre position. Such a device hasapplications for inertial sensors such as accelerometers and gyroscopes. Ithas considerable advantages over existing approaches, including increasedindependence of fabrication tolerances, online characteristics adjustmentand in particular, compared to vibratory rate gyroscopes, inherently rulesout quadrature error and the need for modal frequency tuning. A system levelmodel of such a device is presented and the fabrication process relying onthick-film resist and electroplating is described.

Vibration Characteristics of Twin Resonance Tuning-Fork Type Gyro. 2nd Report. Improvement of Dynamic Characteristics with Magnetic Damper.

Twin resonance tuning-fork type gyro that is one of Vibratory Rate Gyroscopes has a number of advantages. On the other hand, its output signal is very small on the structure of the vibratory body as a fault. Therefore, the rate gyro of this type is supported by an elastic mechanism and is required high gain in the resonance between the excitation system and the detection system by fine tuning(7). However, the quick response and the stabilization of gyro vibration system worsen by high mechanical Q value. They are problems which do not coexist easily, and conflict. Then, it is necessary to give moderate damping to both of the twin resonance tuning-fork and the gyro support part for improvement of dynamic characteristics and stabilization. Therefore, this paper discribes an experimental study concerning the quick response and the stabilization of twin resonance tuning-fork type gyro made a high gain by the method of the first report, and reports on a method of obtaining moderate damping as the means.

System Identification of a MEMS Gyroscope

This paper reports the experimental system identification of the Jet Propulsion Laboratory MEMS vibratory rate gyroscope. A primary objective is to estimate the orientation of the stiffness matrix principal axes for important sensor dynamic modes with respect to the electrode pick-offs in the sensor. An adaptive lattice filter is initially used to identify a high-order two-input/two-output transfer function describing the input/output dynamics of the sensor. A three-mode model is then developed from the identified input/output model to determine the axes’ orientation. The identified model, which is extracted from only two seconds of input/output data, also yields the frequency split between the sensor’s modes that are exploited in detecting the rotation rate. The principal axes’ orientation and frequency split give direct insight into the source of quadrature measurement error that corrupts detection of the sensor’s angular rate.