Scale Factor Nonlinearity Research Articles

Impact of interference fringe visibility changes on closed-loop IFOGs operating across multiple fringes

This study investigates the impact of interference fringe visibility changes on closed-loop interferometric fiber optic gyroscopes (IFOGs) operating across multiple fringes. We introduce a model that addresses the challenges posed by spectral asymmetry and limited temporal coherence, which can induce scale factor non-linearity. By analyzing high-order fringes and employing suitable experimental setups with large fiber coil geometries, we demonstrate the effectiveness of our compensation model. Experimental results indicate significant reductions in scale factor non-linearity, with improvements of up to 9.3 times in one setup. This work highlights the importance of considering fringe visibility changes to enhance the dynamic range of IFOGs while ensuring measurement accuracy.

Real-time correction of gain nonlinearity in electrostatic actuation for whole-angle micro-shell resonator gyroscope

MEMS gyroscopes are well known for their outstanding advantages in Cost Size Weight and Power (CSWaP), which have inspired great research attention in recent years. A higher signal-to-noise ratio (SNR) for MEMS gyroscopes operating at larger vibrating amplitudes provides improved measuring resolution and ARW performance. However, the increment of amplitude causes strong nonlinear effects of MEMS gyroscopes due to their micron size, which has negative influences on the performance. This paper carries out detailed research on a general nonlinear mechanism on the sensors using parallel-plate capacitive transducers, which is called the gain nonlinearity in electrostatic actuation. The theoretical model established in this paper demonstrates the actuation gain nonlinearity causes the control-force coupling and brings extra angle-dependent bias with the 4th component for the whole-angle gyroscopes, which are verified by the experiments carried out on a micro-shell resonator gyroscope (MSRG). Furthermore, a real-time correction method is proposed to restore a linear response of the electrostatic actuation, which is realized by the gain modification with an online parameter estimation based on the harmonic-component relationship of capacitive detection. This real-time correction method could reduce the 4th component of the angle-dependent bias by over 95% from 0.003°/s to less than 0.0001°/s even under different temperatures. After the correction of actuation gain nonlinearity, the bias instability (BI) of whole-angle MSRG is improved by about 3.5 times from 0.101°/h to 0.029°/h and the scale factor nonlinearity (SFN) is reduced by almost one order of magnitude from 2.02 ppm to 0.21 ppm.

High-precision identification and compensation of nonlinear error in hemispherical resonator gyro

This paper presents a novel nonlinear error identification and compensation method for the Hemispherical Resonator Gyro (HRG) from the signal processing perspective. Firstly, the paper establishes an HRG nonlinear error model that reveals the quantitative correlation between angle measurement error and the amplitude-gap ratio. Subsequently, a dynamic analysis model for gyro drift is developed using nonlinear motion equations. Based on this, a scalar factor nonlinear identification model encompassing assembly and nonlinear errors is proposed. Nonlinear optimization is then used to identify error parameters accurately. Finally, a joint compensation method is devised to mitigate assembly and nonlinear error issues. Empirical findings provide concrete validation for the precision of the identification and compensation method. The experimental results demonstrate that reductions of 97%, 89%, and 40% after the joint compensation are achieved in the fourth harmonic component, scale factor nonlinearity, and bias instability of the gyro, respectively.

A rate hemispherical resonator gyroscope with bias stability of 0.0056°/h with compensation of phase delay

This paper demonstrated a high accuracy rate hemispherical resonator gyroscope (HRG) with compensation of the phase delay induced by the front-end amplifier and the digital control circuit. Due to the existence of the phase delay, the output of the gyroscope is affected not only by the damping mismatch, but also by the frequency split of the resonator gyroscope, which is the main cause of the bias drift and the scale factor nonlinearity of rate resonator gyroscopes. Based on the results of theoretical analysis, a novel calibration method for the phase delay was proposed by monitoring the scale factor of the quadrature control loop. Detailed experimental results show that with phase delay compensation, the bias instability (BI) was improved from 0.0089°/h to 0.0027°/h, the angle random walk (ARW) was improved from 0.0047°/√h to 0.003°/√h, and the scale factor nonlinearity was decreased by 93.8 % from 734.8 ppm to 45.1 ppm. Measurement of one rate HRG after phase compensation at room temperature with duration of 7 hours shows a bias stability of better than 0.00658°/h and a bias repeatability of 0.0053°/h. The results show that the rate HRG with accurate phase delay compensation can achieve excellent accuracy and repeatability in long-time operation.

The Influence and Suppression of Spectral Width on Scale Factor Nonlinearity in Fiber Optic Gyroscopes with Broadband Sources

The Influence and Suppression of Spectral Width on Scale Factor Nonlinearity in Fiber Optic Gyroscopes with Broadband Sources

Interactive Errors Analysis and Scale Factor Nonlinearity Reduction Methods for Lissajous Frequency Modulated MEMS Gyroscope.

Although the Lissajous frequency modulated (LFM) mode can improve the long-term and temperature stability of the scale factor (SF) for mode mismatch MEMS gyroscopes, its SF nonlinearity poses a significant limitation for full-scale accuracy maintenance. This paper examines the interaction effects among stiffness coupling, system phase delay, readout demodulation phase shift, and velocity amplitude mismatch within the control process. Based on the completion of frequency difference control and demodulation phase matching, we clarify that the remaining stiffness coupling and residual system phase error are the primary factors influencing SF nonlinearity. Furthermore, SF nonlinearity is reduced through error compensation. On one hand, this paper suppresses stiffness coupling through the observation of the instantaneous frequency difference and the application of the quadrature voltage. On the other hand, system phase error is compensated by observing the amplitude control force and tuning the reference in the Phase-Locked Loops (PLLs). Subsequent simulations of these methods demonstrated a remarkable 97% reduction in SF nonlinearity within the measurement range of ±500°/s. In addition, an observed rule dictates that maintaining a sufficiently large frequency split effectively constrains the SF nonlinearity.

Closed-Loop Resonant Fiber-Optic Gyroscope With a Broadband Light Source

The resonant fiber-optic gyroscope (RFOG) with a broadband light source has recently emerged as an attractive new type optical gyroscope. However, the use of a broadband source limits the linear dynamic range and worsens the scale factor accuracy. In this paper, the closed-loop scheme of the broadband source-driven RFOG is proposed and demonstrated. First, a novel method called the period-stacking method is presented. Then the closed-loop mechanism of the broadband source system is revealed. Although the rotation-induced frequency difference is wavelength-dependent in the broadband source scheme, we are pleased to find that the frequency shift generated by the serrodyne modulation is wavelength-independent and can be used to compensate for the rotation information. Finally, a closed-loop broadband source-driven RFOG with a 100 m-long and 7.6 cm-diameter fiber-optic ring resnator is experimentally demonstrated. The measured result shows that the long-term bias stability of the closed-loop broadband source-driven RFOG is 0.0063 °/h over a test time of up to 500 minutes. The temperature dependence drops from 2.8 (°/h)/℃ in the open-loop system to 0.54 (°/h)/℃. It is improved by a factor of 5.2. The open-loop linear detection range of ± 50 °/s is improved to ± 350 °/s. It is improved by a factor of 7. The open-loop scale factor nonlinearity of 8% is decreased to 0.0281% (281 ppm), which is improved by a factor of 285.

Real-Time Phase Compensation for Scale Factor Nonlinearity Improvement Over Temperature Variations for MEMS Gyroscope

Real-Time Phase Compensation for Scale Factor Nonlinearity Improvement Over Temperature Variations for MEMS Gyroscope

Calibration of Coupling Errors for Scale Factor Nonlinearity Improvement in Navigation-Grade Honeycomb Disk Resonator Gyroscope

With the performance of micromechanical gyroscopes approaching navigation grade, the scale factor nonlinearity is gradually becoming the limitation for high-performance applications such as the satellite attitude measurement. Coupling errors caused by parasitic capacitance are the major sources of scale factor nonlinearity but are usually neglected. In this paper, the parasitic-capacitance coupling errors are introduced into the traditional gyroscope model and the scale factor nonlinearity induced by the coupling errors has been analyzed theoretically. The analysis indicates that two parasitic-capacitance couples from sense excitation signal to drive or sense detection signal are the dominant causes of scale factor nonlinearity. Two measurements (i.e. the amplitude of driving excitation signal and axis tuning voltage) are used to realize the calibration of coupling errors with the least square method. The experiment is also carried out to verify this novel calibration method on a navigation-grade honeycomb disk resonator gyroscope. The experimental results demonstrate that the coupling errors has decreased by 87.5 and 44.5 times respectively after the error compensation and that the scale factor nonlinearity has been improved from 244.8ppm to 29.00ppm. Furthermore, this calibration method can be applied to other resonator gyroscopes with the similar structure and control scheme.

Rate Integrating Hemispherical Resonator Gyroscope Detection Error Analysis and Compensation

Compensation for the hemispherical resonator gyroscope (HRG) detection error significantly improves gyroscope performance as well as provides a basis for the implementation of high-precision control algorithms. In this article, an identification method is proposed in which the precession factor and the detection error parameters, including gain error, nonorthogonal angle error, and phase error, can be identified simultaneously in a single test. First, we analyze the detection error caused by gyroscope manufacturing as well as the inconsistency in circuit device parameters. Second, the detection error is modeled, and the impact of the error on the standing wave azimuth detection and the control system is discussed. Third, a method is presented for identifying the error parameters based on the nonlinear least squares. Finally, experiments are conducted to verify the effectiveness of the identification and compensation method. As a result of compensation, the bias instability decreases by 33 times from 5.08°/h to 0.15°/h, and the scale factor nonlinearity decreases by four times from 50.26 to 10.23 ppm.

Compensation of scale factor nonlinear error introduced by harmonic distortion for open-loop fiber optic gyroscopes.

The scale factor (SF) of a gyroscope is the ratio of the detection output rotational rate and the input, and is expected to be a constant. However, for open-loop interferometric fiber optic gyroscopes (IFOGs) with sinusoidal modulation, harmonic amplitudes are inevitably affected by detection defects, such as nonuniform frequency response of the photodetector or unequal gain of amplification circuits. As a result, harmonic distortion leads to SF nonlinearity, which seriously hinders the accuracy of high-precision gyroscopes. In this Letter, the theoretical form of the SF error introduced by harmonic distortion of open-loop gyroscopes is analyzed, and an effective and simple compensation method is proposed. Instead of traversing the whole dynamic range, the proposed method simplifies the calibration pretest, where only a section of the dynamic range needs to be tested. Experimental results on an open-loop IFOG prototype show that, with our proposed method, the SF nonlinear error is suppressed to 2.5 ppm within the range -300 to +300∘/s, which is 33 times less than that before compensation.

Continuous Mode-Reversal FM Accelerometer With 60-g FSR, 10-μg/K Drift, and VRE Rejection

This work advances the research on continuous mode-reversal frequency modulated accelerometers by characterizing in depth some of their nonidealities, proposing methods for their compensation, and exploiting a renovated sensor design that enables closed-loop compensation of shock and vibrations. The scale factor nonlinearity is first investigated and compensated through a cubic calibration term, yielding a 50% larger range for a 2.5-fold larger scale factor than in former implementations. Additionally, temperature effects on the zero-g offset are compensated by exploiting the value of the low-pass filtered resonance frequency, which yields a valuable information of the silicon sensor temperature. This enables reducing the zero-g-offset temperature dependence by a factor 5 over previous works on similar structures. Finally, a closed-loop compensation of the quality factor, implemented through additional driving electrodes in the structure, guarantees a 25-fold reduction on effects of shocks and vibrations exciting the acceleration-sensitive mode. [2022-0117]

Research on improving the north-seeking precision of MEMS gyroscope

In order to improve the north-seeking precision of the micro-electro-mechanical system (MEMS) gyroscope, it is necessary to measure the earth’s rotation angular velocity accurately. The output precision of the MEMS gyroscope is affected by zero bias, installation error, scale factor error, etc. Aiming at the problem of the low output precision of the MEMS gyroscope, this paper mainly studies the test method of the MEMS gyroscope scale factor. In this study, the north-seeking principle of the MEMS gyroscope is analyzed, and the equivalent relationship between scale factor error and angular rate error is investigated. A Multi-Position ground velocity method is proposed for testing the scale factor of the MEMS gyroscope. In this method, the Earth’s rotation angular velocity component is used as the input of the MEMS gyroscope, and the scale factor is calculated by dual exponential fitting. The feasibility of the test method is verified by experiments on the rate turntable. The experimental results show that when the input angular velocity is between −0.0036° s−1 and 0.0036° s−1, compared with the traditional angular rate test method, the nonlinearity of the MEMS gyroscope scale factor tested by the proposed method is reduced from 227.45 ppm to 68.19 ppm, the asymmetry is reduced from 253.61 ppm to 73.65 ppm, and the north-seeking accuracy is improved 4.17 times, which verifies the effectiveness and superiority of the proposed method.

A Digital Control Structure for Lissajous Frequency-Modulated Mode MEMS Gyroscope

This article proposes a digital control structure for a doubly decoupled gyroscope working in the Lissajous frequency-modulated (LFM) mode based on digital phase-locked loops (PLLs), which demodulates the angular rate signal directly from the readable digital gyroscope resonance frequency, eliminating the need for specific frequency readout circuits. The resonance frequencies of the LFM gyroscope working modes contain a mode mismatch frequency modulated by input angular rate, respectively, which are tracked by two digital PLLs followed by subsequent digital demodulation and filtering. A linearized model of the digital PLL is built to analyze noise and control characteristics for different PI parameters. The impact of different amplitude–phase extraction architectures on the extracted phase signal is also addressed in this article. Contrast experiments are carried out using the same gyroscope with large internal thermal stress due to the silicon-glass bonding process and no stress relief structure around the sensing element, working in the traditional amplitude-modulated (AM) mode and the LFM mode. Overall, the LFM working mode maintains its low-temperature sensitivity and high stability in spite of the large internal thermal stress in the gyroscope compared to AM working modes. The maximum scale factor variation over the temperature range from 10 °C to 50 °C is 1000 ppm for the LFM mode compared to 51 900 ppm for the AM closed mode. The maximum zero rate output drift over the same temperature range is 0.1248 °/s for the LFM mode and 10.7139 °/s for the AM closed mode. The scale factor nonlinearity is 329 ppm with an angular rate input range of ±50 °/s for the LFM mode compared to 1902 ppm for the AM closed mode. The LFM mode zero-bias fluctuation for ten days is less than 0.12 °/s. The angle random walk (ARW) and the bias instability (BI) of the LFM gyroscope are 0.316 °/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd \text{h}$ </tex-math></inline-formula> and 2 °/h, respectively.

Identification and Correction of Phase Error for Whole-Angle Micro-Shell Resonator Gyroscope

The phase error is inevitable in the whole-angle control system and has a great impact on the gyroscope’s performance. In this article, the identification and correction of phase errors are carried out to eliminate the effects of phase errors under the whole-angle mode. The sources of phase errors are analyzed at first from the phase delay of the whole-angle control system. Furthermore, the effects of phase errors are also investigated from the theoretical and experimental analyses. It demonstrates that the phase error would produce coupling effects between the pattern angle and quadrature control loops and produce additional angle drift (AAD) affecting the performance of the whole-angle gyroscope. Therefore, the identification method of phase errors is presented on the basis of the observation of the AAD and the correction of phase errors can also be carried out by the phase shift module. After the correction of phase errors, the performance of bias instability and scale-factor nonlinearity improves by five and nine times, respectively.

Study of nonlinear vibration of resonant gyroscope based on uncertainty analysis method

To study the nonlinear vibration characteristics of resonant gyroscope, the vibration model of the resonant beam is established primarily, aiming for the analytical formulas of the nonlinear stiffness coefficients and linear intrinsic frequencies of the gyroscope. With that foundation, the influence of the structural parameters of the resonant beam on the frequency tracking error caused by nonlinear vibration is analyzed thoroughly at first. Secondly, by random sampling, an uncertainty analysis model is established to evaluate the impact of each structural parameter of the resonant beam on the critical performance indexes of the gyroscope such as linear intrinsic frequency, nonlinear frequency offset and scale factor of the resonant beam. Finally, an equivalent circuit is constructed corresponding to the nonlinear vibration equations of the resonant gyroscope based on the electromechanical analogy method. By studying the nonlinearity of the circuit for equivalence, it turns out that the vibration characteristics of the equivalent circuit are consistent with that of the resonant gyroscope obtained by using the uncertainty analysis method. It effectively verifies the feasibility of the nonlinear vibration research method for the resonant gyroscope based on uncertainty analysis method.

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To study the nonlinear vibration characteristics of resonant gyroscope, the vibration model of the resonant beam is established primarily, aiming for the analytical formulas of the nonlinear stiffness coefficients and linear intrinsic frequencies of the gyroscope. With that foundation, the influence of the structural parameters of the resonant beam on the frequency tracking error caused by nonlinear vibration is analyzed thoroughly at first. Secondly, by random sampling, an uncertainty analysis model is established to evaluate the impact of each structural parameter of the resonant beam on the critical performance indexes of the gyroscope such as linear intrinsic frequency, nonlinear frequency offset and scale factor of the resonant beam. Finally, an equivalent circuit is constructed corresponding to the nonlinear vibration equations of the resonant gyroscope based on the electromechanical analogy method. By studying the nonlinearity of the circuit for equivalence, it turns out that the vibration characteristics of the equivalent circuit are consistent with that of the resonant gyroscope obtained by using the uncertainty analysis method. It effectively verifies the feasibility of the nonlinear vibration research method for the resonant gyroscope based on uncertainty analysis method.

Automatic Rate and Rate-Integrating Mode-Switchable Axisymmetric Gyroscope.

This paper describes a novel rate and rate-integrating mode-switchable axisymmetric gyroscope. A precession angle tracking algorithm is developed to enable the gyro to switch automatically between rate and rate-integrating modes at preset rate points through a digital control system within the gyro. We also propose a vibrating amplitude control method for the rate-integrating mode that directly extracts the angular rate output to ensure switching stability. In rate mode, the bias instability and angle random walk of the gyro reach 0.106°/h and 0.011°/√h, respectively. Additionally, an input range of over ±5000°/s is measured in rate-integrating mode. The scale factor nonlinearity reaches approximately 116 ppm over the full-scale range. The control system implements effective steering control of the gyroscope, with a switching delay of 10 ms from rate mode to rate-integrating mode and 100 ms from rate-integrating to rate mode. The proposed system actualizes a new type of gyroscope with high accuracy and a wide input range, which combines the benefits of rate and rate-integrating modes.

Analysis of the Scale Factor Nonlinearity of MEMS Differential Silicon Resonant Accelerometer Caused by the DETF’s Force-Frequency Nonlinear Characteristic

The scale factor nonlinearity of MEMS differential silicon resonant accelerometer(DSRA) structure is mainly due to the force-frequency nonlinear characteristic of DETF. This paper presents a detailed analysis of the relationship between the structural parameters, measurement range and the scale factor nonlinearity, which will provide a reference for the parameter design of DETF and overall structure. The inherent force-frequency nonlinearity of DETFs is analyzed, and the effects of structural parameters of DETF and axial force on nonlinearity of frequency variation are revealed. Combining the working principle of MEMS DSRA introduced first, the scale factor nonlinearity is studied. The results show that the structural parameters of the proof mass (determines the conversion between acceleration and inertial force), the support mechanism and the lever mechanism (determines the transfer coefficient of inertial force), and the DETF (determines the inherent force-frequency nonlinearity and affect the transfer coefficient of inertial force), as well as the measurement range, can all affect the scale factor nonlinearity. Moreover, the scale factor nonlinearity is directly proportional to the square of the measurement range and the square of the nominal scale factor, and inversely proportional to the square of the natural frequency of DETF. The finite element simulation is carried out, and the simulation results are in good agreement with the theoretical analysis values. Finally, the experiment on the scale factor nonlinearity of a prototype is carried out. The measured scale factor nonlinearity of the prototype is 1994.09ppm, which is consistent with the theoretical analysis value of 1737.30ppm.

Investigation of Angle Drift Induced by Actuation Electrode Errors for Whole-Angle Micro-Shell Resonator Gyroscope

The symmetry of the actuation electrode is of great importance for the whole-angle gyroscope. In this paper, the angle drift induced by actuation electrode errors of micro-shell resonator gyroscope is investigated. The actuation electrode errors due to the assembly of the micro-shell resonator and substrate electrode would result in interference effects between the energy and pattern-angle control loops and produce the additional angle drift which has great influences on the performance. The additional angle drift is investigated from experimental and simulation analysis under various actuation gain and angle errors. Furthermore, the characterization and compensation methods of actuation electrode errors are also proposed to eliminate the interference effects of control loops and the additional angle drift. After compensation, the scale-factor nonlinearity and bias instability has been improved by 3 and 2 times to 5.79ppm and 0.064 °/h.