Rate-integrating Gyroscope Research Articles

Angular Velocity Estimation Using Rate-Integrating Gyro Measurements

Rate integrating gyroscopes (RIGs) measure integrated angular rates or angular displacement, requiring an observer or filter to provide full state feedback to the attitude controller. A nonlinear observer is presented, which estimates the angular velocity of a rotating rigid body using continuous-time measurements from an RIG. Torque applied to the system is assumed to be accurately known. When the inertia matrix is accurately known, the provided observer achieves exponential convergence, while an asymptotically converging adaptive observer is designed for cases when the inertia is unknown. The nonadaptive observer is shown to be robust to bounded inaccuracies in the knowledge of inertia and external torque acting upon the system. For the adaptive observer, conventional certainty equivalence methods require the angular rate states that are unavailable. To overcome this problem a novel update rule with additional control knobs is proposed, which uses just the attitude states for inertia parameter adaptation. The observer is tested in simulation to demonstrate its effectiveness.

Nonlinear Dynamics of the Hemispherical Resonator of a Rate-Integrating Gyroscope under Parametric Excitation of the Free Precession Mode

Nonlinear Dynamics of the Hemispherical Resonator of a Rate-Integrating Gyroscope under Parametric Excitation of the Free Precession Mode

A MEMS Rate-Integrating Gyroscope (RIG) With In-Run Automatic Mode-Matching

Toward the objective of eliminating the angle error and rate threshold of the rate integrating gyroscope (RIG) caused by stiffness asymmetry, a novel in-run automatic mode-matching method is presented in this paper. Although other manual mode-matching methods can reduce the stiffness asymmetry temporarily, the environmental factors will interfere the manual calibration. Combined with virtual rotation, the processing circuits obtain the resonant frequencies of RIG operation modes and a controller is used to reduce the frequency difference. Meanwhile, an innovative method is proposed for RIG angle error analysis, avoiding the drawbacks of the traditional analysis methods. An FPGA based platform using a MEMS disk resonator is tested and the angle error is reduced to 1 degree compared with the manual calibration result 6.1 degrees.

A Rate-Integrating Honeycomb Disk Resonator Gyroscope With 0.038°/h Bias Instability and °7000°/s Measurement Range

This letter presents a high performance rate-integrating honeycomb disk resonator gyroscope (HDRG). High Q factor resonator and symmetric vibration detection gain are the key to high performance rate-integrating gyroscope. By stiffness-mass decoupling design, HDRG can achieve high Q factor of about 600k and decay time of over 44s. A compensation method is applied to suppress the rate-dependent angular drift caused by the asymmetry circular distribution of detection gains. Finally, the rate-integrating HDRG shows an excellent bias instability of 0.038°/h, 1.05ppm scale factor nonlinearity, wide measurement range of over ±7000°/s and a threshold value of about ±0.0001°/s, which is the best performance in the reported rate-integrating MEMS gyroscopes.

High sensitivity rate-integrating hemispherical resonator gyroscope with dead area compensation for damping asymmetry

The rate-integrating gyroscope (RIG) operation is considered as the next generation architecture for hemispherical resonator gyroscopes (HRGs) with advantages of direct angle measurement and unlimited dynamic range. However, this RIG operation requires high symmetry for the HRG device and the damping mismatch of the two gyroscopic modes will result in a dead area problem. This work analyzes the error mechanism of the damping asymmetry induced dead area and proposed a novel virtual procession compensation method for HRG RIG. The simulation proves the existence of the dead area as the theory predicted. More importantly, the experimental HRG RIG platform with the proposed compensation method can significantly expand the dynamic range with accurate angle measurement and overcome the problem of dead area. The earth rotation is accurate measured which is the first time that captured by a RIG scheme as a state-of-the-art result.

Rate Integrating Gyroscope Using Independently Controlled CW and CCW Modes on Single Resonator

This paper reports a rate integrating gyroscope (RIG) using independently controlled clockwise (CW) and counter clockwise (CCW) modes on a single MEMS resonator. The rotation angle is read out by the phase difference between these modes. A CW/CCW mode separator was used to independently control these modes superposed on the resonator. The frequency and Q-factor mismatches were compensated by the phases and amplitudes of driving signals. A control system including the mode separator, feedback controllers, signal generators, mismatch compensators were implemented in a field programmable gate array (FPGA). Using the proposed mismatch compensation technique, the equivalent aniso-damping term became 1/100. As a result, the scale factor became constant and the non-linearity became less than 0.2% even when the slow angular rate region around 5°/s. In addition, the temperature coefficient of scale factor as small as -1.84 ± 0.62 ppm/K was achieved without any temperature correction.

Micromachined Rate-Integrating Gyroscopes: Concept, Asymmetry Error Sources and Phenomena

Rate-integrating gyroscope (RIG) operation is an attractive operation scheme for micro gyroscopes, because it can provide direct angle measurement and a high dynamic range. However, its zero rate output (ZRO) has a severe drift issue. This work compared the difference between rate and rate-integrating gyroscope operations, and further modeled the gyroscope with asymmetric error terms. Then the influences of these non-ideal factors were analyzed to abridge the ZRO drift phenomena and the sources. The numerical verification proved the theory that such an oscillation pattern is caused by the stiffness mismatch, and decaying to X/Y axis manner resulted from the damping errors. The conclusions can contribute to aiding engineers to rapidly locate the bottlenecks of RIG operations.

A Novel Compensation Method for Eliminating Precession Angular-Rate Bias in MEMS Rate-Integrating Gyroscopes

The structural asymmetry of the MEMS rate-integrating gyro (RIG) mode produces a threshold and an angle-dependent bias (ADB) that cause gyroscopes operating in this mode to stop working at input rates below the threshold and degrade the linearity of the output angle. This defect in the RIG output angle is actually caused by a precession angular-rate bias that results from both damping asymmetry (anisodamping) and stiffness asymmetry (anisostiffness). This paper describes a novel compensation method based on Fourier series fitting combined with a multiple iteration technique. The proposed compensation method can significantly reduce both the input rate threshold and ADB. Simulations indicate that the threshold and ADB caused by anisodamping and anisostiffness can be reduced by three orders of magnitude. An experimental application of this method produced a MEMS RIG threshold as low as 0.05° per second, representing an improvement of two orders of magnitude and lower than has previously been reported.

Effects of Nonlinearity on the Angular Drift Error of an Electrostatic MEMS Rate Integrating Gyroscope

Electrostatic MEMS coriolis vibratory gyroscopes (CVG) are essentially nonlinear because of the capacitive transducers employed for the excitation and detection of resonance vibration. This paper investigates the influence of nonlinearity on the precession angle dependent bias error of a MEMS rate integrating gyroscope (RIG) and proposes a novel correction to minimize this effect. A linear model of CVGs is commonly used in the dynamic analysis and control of MEMS RIGs. The linear model predicts a 2nd harmonic angular drift error due mainly to non-proportional damping. However, experimental results from previous work demonstrate the existence of an additional 4th harmonic component in the precession rate, and in the resonant frequency and quadrature control. The analysis and removal of this high-order error term will further improve the accuracy of the RIG. Here, it is shown that high-order angularly modulated drift error is the result of nonlinear damping, and the stiffness nonlinearity is responsible for the 4th harmonics present in the fluctuation of the operating frequency and in the control for quadrature nulling. It is understood that nonlinear damping may be introduced electrically by the energy sustain state feedback control that uses nonlinear capacitive measurements. Nonlinearity correction is proposed to the capacitive displacement detection that significantly reduces the high-order drift error. Simulation and experimental results are provided to validate the analysis. A DSP controlled MEMS RIG with nonlinearity correction exhibits an angular drift error of less than 0.2 deg/s.

MEMS Gyroscope With Concentrated Springs Suspensions Demonstrating Single Digit Frequency Split and Temperature Robustness

We report on a new design approach for X-Y symmetric resonator, emphasizing the increase in symmetry by localization of the device anchors. The resonator is mechanized as a z-axis rate gyroscope (RG), and the concept is compatible with the rate-integrating gyroscope mechanization. Our approach is based on strategically placing the critical mechanical elements at the center of the resonator structure, to mitigate the effect of fabrication imperfections across the device. We experimentally demonstrated that the design yields a sub-Hz frequency separation between operational modes, which is attributed to the introduced design approach. The high symmetry of the device led to a temperature stability of 50 mHz over 130 °C temperature range. A ring down test demonstrated the Q -factor greater than 330 K. The thermal stability and preliminary characterization results of the gyro in-run stability are presented. [2017-0177]

Micromechanical Rate Integrating Gyroscope With Angle-Dependent Bias Compensation Using a Self-Precession Method

Toward the objective of direct angle measurement using a rate integrating gyroscope (RIG) without a minimum rate threshold and with performance limited only by electrical and mechanical thermal noise, in this paper, we present the implementation of a generalized electronic feedback method for the compensation of MEMS gyroscope damping asymmetry (anisodamping) and stiffness asymmetry (anisoelasticity) on a stand-alone digital signal processing platform. Using the new method, the precession angle-dependent bias error and minimum rate threshold, two issues identified by Lynch for a MEMS RIG [1] due to anisodamping are overcome. To minimize angledependent bias, we augment the electronic feedback force of the amplitude regulator with a non-unity gain output distribution matrix selected to correct for anisodamping. Using this method, we have decreased the angle-dependent bias error by a factor of 12, resulting in a minimum rate threshold of ~3 °/s. To further improve RIG performance, an electronically induced self-precession rate is incorporated and successfully demonstrated to lower the rate threshold.

Countering the Effects of Nonlinearity in Rate-Integrating Gyroscopes

This paper addresses the impact of cubic nonlinearity on the operation of a rate-integrating gyroscope (RIG). It is demonstrated that below the bifurcation threshold, cubic nonlinearity results in angle-dependent frequency split between the two resonant modes of the gyroscope, which impacts angle-dependent bias, quadrature error, and controller efficacy in addition to distorting the scale factor due to off-resonant excitation. These errors are experimentally demonstrated using a high- $Q$ disk resonator gyroscope, which are shown to be in close agreement with theory. A method of compensating for angle-dependent frequency error is proposed and experimentally validated. It is demonstrated that mode mismatch can be experimentally reduced to the level of thermal noise, effectively cancelling the effects of nonlinearity and eliminating the distortion of readout angle.

Three-Axis Attitude Estimation Using Rate-Integrating Gyroscopes

Traditionally, attitude estimation has been performed using a combination of external attitude sensors and internal three-axis gyroscopes. There are many studies of three-axis attitude estimation using gyroscopes that read angular rates. Rate-integrating gyroscopes measure integrated rates or angular displacements, but three-axis attitude estimation using these types of gyroscopes has not been as fully investigated. This paper derives a Kalman filtering framework for attitude estimation using attitude sensors coupled with rate-integrating gyroscopes. To account for correlations introduced by using these gyroscopes, the state vector must be augmented, compared with filters using traditional gyroscopes that read angular rates. Two filters are derived in this paper. The first uses an augmented state-vector form that estimates attitude, gyroscope biases, and gyroscope angular displacements. The second ignores correlations, leading to a filter that estimates attitude and gyroscope biases only. Simulation comparisons are shown for both filters. The work presented in this paper focuses only on attitude estimation using rate-integrating gyroscopes, but it can easily be extended to other applications such as inertial navigation, which estimates attitude and position.

Single-crystal diamond micro-cupped resonators made by laser ablation

This paper presents a novel three-dimensional fabrication process of micro-scale shell resonator made of single-crystal diamond (SCD) called micro-cupped resonator (MCR). The key feature of the process is the application of laser ablation, which can contribute to the shaping process of SCD with higher accuracy, better structural symmetry, greater speed, and lower breakage rate. UV laser high precision processing machine has been employed for the ablation of SCD in the present investigation. This paper describes the principle of laser ablation of SCD and analyses the effects of beam parameters on ablation quality. Then MCR with better structural symmetry and less structural imperfection has been successfully fabricated based on optimum parameters by laser ablation. The MCR is promising for emerging applications such as micro rate-integrating gyroscope.

An Evaluation Of Survey Accuracy At Cold Lake

Abstract Directional survey accuracy has become increasingly important in many development drilling projects. Recently, Esso Resources Canada Limited conducted a three-part survey evaluation program in Cold Lake to de/ermine the most cost-effective method of surveying. The first part of the program consisted of surveying 21 wells with a rate-integrating gyroscope. These wells had been drilled using magnetic single shot surveys. The gyroscope indicated that many of the high-angle wells oriented in an east-west direction were outside of acceptable target limits. A more accurate method of surveying these wells while drilling was required. The second part of the evaluation program consisted of drilling 43 wells using alternate survey methods including: Measurement While Drilling (MWD) on 26 wells: gyroscopes on 5 wells: and eleclronic single shot instruments on 12 wells. Electronic multi-shot tools were run in 16 wells prior to running casing providing multiple survey runs on some wells. A rate-integrating gyroscope was run in 18 cased wells to provide a comparison to the wells surveyed during the first part of the evaluation program. The third part of the program was the implementation of the use of a survey system based on recommendations from the second part of the program. Introduction Description of Cold Lake Production Project Esso Resources Canada Limited started commercial development of the Cold Lake Held in October 1983. Each phase of the Cold Lake Production Project (CLPP) consists of 10 twenty well pads for a total of approximately 200 wells in each phase. The directional wells are designed to kick off at 25 m and build angle at a rate of 2.5 degrees per 30 m to an inclination of 9.5 degrees at 140 m measured depth (MD). Additional angle, if required, is built at rates of up to 4.5 degrees per 30 m. Maximum inclinations vary from 15 to 55 degrees with approximately 60% of the wells having inclinations greater than 35 degrees. Horizontal displacements vary from 55 m to 310 m with wells being drilled in all directions as shown in the pad layout in Figure 1. The average drilling time in Cold Lake is less than 2 days per well. Importance of Accurate Surveys Cold lake targets are defined by an 8 m by 13 m rectangle with the major axis oriented along the preferential steam path direction N30 °E ("on-trend "). If the target is missed, inefficient sweep of the reservoir caused by early communication between wells, results in some heavy oil being left in the reservoir. The amount of oil left in place is estimated using a reservoir analysis model and is referred to as "lost recovery ". Figure 2 shows the value of lost recovery versus the distance between the well and target centre. Two lines are shown, one for the off-trend direction and the other for the on trend direction. With the development of the lost recovery model, and the subsequent increase in concern for hitting small targets, the need to evaluate survey accuracy and the cost of accurate surveying was identified.

Design of a single-axis platform for balloon-borne remote sensing

We describe the design of two telescope pointing systems for remote optical sensing of the stratosphere from a balloon-borne gondola. The telescope pointing accuracy is ±0.02° in elevation, from a gondola which has static and dynamic tilts up to ±3°. Each system consists of a telescope, an elevation control subsystem, and a pitch-stabilized single-axis reference platform. The Mark I unit has performed successfully on each of its two balloon flights, for a total of over 16 h in the stratosphere; the Mark II unit is currently under construction. The single-axis platform is referenced to a rate-integrating gyroscope and an inclinometer for high- and low-frequency pitch-angle variations, respectively. The Mark I platform is supported by ball bearings, driven by a brush-contact torque motor, and is subject to a small, permanent pitch angle error which depends directly on the gyro drift rate. The Mark II platform uses flex-pivot supports, a brushless motor, and for even a relatively large gyro drift rate, is designed to asymptotically approach zero angular offset error.

OBSERVATIONS WITH PIM

Abstract The performance of gyro-theodolites is not widely known amongst land surveyors because the use of these costly instruments is mainly confined to mining and artillery surveyors. The instruments themselves have been well described: accounts of the pendulous type in which the spinner hangs by means of a thin filament aligned in the vertical axis of the theodolite are given by Strasser & Schwendener [1] and Schwendener & Ward [2]; whilst the floated rate-integrating gyroscope manufactured by the British Aircraft Corporation and known as the Precision Indicator of the Meridian, or PIM for short, is the subject of lucid papers by Sutton & Thomas [3] and Thomas [4, 5]. The results of PIM observations taken under Thomas' direction are given in his papers, but the only protracted series quoted are those for the determination of azimuth inside the Sperry factory [5; p. 58] and these results are briefly summarized.

Temperature control of the inertial-grade floated rate-integrating gyroscope

The performance of the inertial-grade floated rate-integrating gyroscope is critically dependent on the instrument surface temperature distribution. During operation, the instrument is degraded by distributed surface heat-flux disturbances, and it is desired to control the surface temperature distribution in a closed-loop feedback configuration such that the instrument degradation is minimized. This is achieved via optimal control theory, where a distributed feedback controller is determined such that the square of thermally induced drift rate is minimized. The structure of the resulting controller is examined, and various configurations for implementation are suggested.

Temperature control of the inertial-grade floated rate-integrating gyroscope

Temperature control of the inertial-grade floated rate-integrating gyroscope

The Rate-integrating Gyro as an Aircraft Heading Reference

A description is given of a floated rate-integrating gyroscope and of the way in which it may be used to provide a high-accuracy aircraft heading reference. The sources of error of the system are examined and the overall heading accuracy is estimated as being comparable with the distance accuracy of a doppler system. This paper was presented, on 15 January, at the same Ordinary Meeting of the Institute as the preceding paper by Green and Glenny.The advent of the high-accuracy single-axis floated gyroscopes which have been developed so rapidly over recent years, primarily for inertial navigation use, has raised the question of whether the accuracy of these instruments can be made use of in other applications. Can systems which have been employing the older established types of gyroscope benefit from the greater stability of the new type? If a direct change of instrument with no modification of the method of use is considered, the answer will in many cases be no. For example, an improvement in the accuracy of the north-seeking marine gyro compass may not be found rewarding with existing marine navigation techniques, as other factors such as the accuracy with which a ship can be steered would become limiting, defeating the advantage of improved compass accuracy. The introduction of the doppler system has created a different situation in the field of aircraft navigation. Doppler navigation equipment enables an aircraft's drift angle to be measured accurately. That is, the aircraft's track can be defined with an accuracy dependent on the accuracy with which its heading can be measured. In this new situation the overall navigation accuracy is limited by the accuracy of aircraft compasses. These have in general been magnetic compasses, given improved dynamic performance in later years by the incorporation of a gyroscope or use of an associated directional gyro but still dependent on the magnetic element for long-term accuracy. Such a direction reference, though simple and reliable, is at no time precise by modern standards, and as the region of the magnetic pole is approached it becomes practically of very little value. For this reason in recent years the technique of using a free gyro alone as a long-term memory, to store direction information, has been developed, particularly by the airlines operating transpolar services. It is a system such as this that can reap most benefit from use of the new gyroscopes.