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We report for the first time an implementable method to identify and suppress the driving force misalignment angle for a MEMS gyroscope working either in amplitude modulated (AM) or Lissajous frequency modulated (LFM) mode using parametric excitation. By introducing driving force misalignment angle into gyroscope dynamic equations, we illustrate that gyroscope angular rate output is affected by driving force misalignment angle and cross-axis damping jointly. We propose parametric excitation as a way to both identify and calculate the driving force misalignment angle. The identification results for a gyroscope working in both AM and LFM mode are similar, which indicates the effectiveness of the proposed identification method. Instead of using traditional amplitude control loop by adjusting the driving force, we do the automatic gain control by adjusting the parametric pump voltage so that a fixed drive voltage can be used, which also indicates fixed force coupling. Experimental results show that after suppression, the bias instability (BI) of AM mode is improved from 4.7° h−1 to 2.3° h−1 and the BI of LFM mode is improved from 1.4° h−1 to 0.9° h−1 which is the lowest result reported for LFM gyroscope. [ABSTRACT FROM AUTHOR]

This article provides a novel method to analyze and calculate the effect of laser frequency noise on a resonant fiber optic gyroscope (RFOG). The output signal of the fiber ring resonator is expressed as the sum of various harmonic responses. It is found that the laser frequency noise at certain noise frequency would be demodulated together with the rotation-induced frequency signal, and thus deteriorating the gyro output stability. A theoretical model is then setup. The effect of laser frequency noise on the RFOG based on the separate modulation-demodulation technique is numerically evaluated and the effectiveness of the reciprocal modulation-demodulation technique is verified both theoretically and experimentally. The measured angular random walk of the reciprocal RFOG improves as the detected light power at the photodetector increases, which indicates that the measured angular random walk reaches the theoretical shot-noise limited sensitivity in the RFOG. The best value is 0.0021 °/√h when the light power arrived at the photodetector is 69 μW. [ABSTRACT FROM AUTHOR]

We propose a MEMS gyroscope system working with a fixed resonance frequency which combines resonant constant-frequency (RCF) driving and real-time automatic mode-matching technique with the help of linear tuning triangular capacitors. The special tuning capacitors are implemented in both the gyroscope drive mode and sense mode as drive-mode frequency-tuning (DFT) and sense-mode frequency-tuning (SFT), respectively. RCF assures that the drive-mode equivalent resonance frequency after tuned can keep with the given constant excitation frequency, while real-time automatic mode-matching further eliminates mismatches between the drive-mode and sense-mode equivalent resonance frequencies. As a result, the gyroscope system achieves constancy and equality of the excitation frequency and two modal resonance frequencies. Performance evaluations show that the gyroscope with the sense mode quality factor of 26.7k reaches bias instability of 0.09°/h and angle random walk of 0.0087°/ $\surd \text{h}$ under room temperature without any compensation, and is capable of detecting an angular rate as low as 0.001°/s. [ABSTRACT FROM AUTHOR]

This work analyses circuit phase delay for carrier-modulation MEMS capacitive gyroscopes. The temperature-dependent circuit phase delay is a major source of gyroscope output drift, which deteriorates the gyroscope bias instability (BI) and angle random walk (ARW). Effects of both drive-mode and sense-mode circuit phase delay on gyroscope performance when using different signal extraction architectures are analyzed in detail. The online suppression method which combines the so-called modified double sideband (MDSB) extraction architecture in the gyroscope drive mode and closed-loop force-rebalance loop in the sense mode can eliminate the impact of residual fluctuation error of circuit phase delay in real time. When drive-mode circuit phase delay equivalently varies from −20° to 20°, using MDSB decreases the fluctuation of the open-loop zero-rate output (ZRO) by 70% compared to using double sideband (DSB) and by 99.7% with respect to using single sideband (SSB). Meanwhile, improvement for the closed-loop ZRO using MDSB is 92.48% and 94% compared to cases using DSB and SSB, respectively. Furthermore, when the equivalent circuit phase delay of the sense-mode alters from −20° to 20°, ZRO variation for the gyroscope with force rebalanced sense loop and quadrature stiffness nulling loop decreases by 80% in contrast to the case with open loop, which demonstrates the effectiveness of online suppression for circuit phase delay of both the drive-mode and sense-mode. Using the online suppression method, the gyroscope has achieved a BI of 0.16° h−1 and ARW of 0.011° (√h)−1. Furthermore, using the MDSB in the drive mode obtains the best stability compared to using the DSB and SSB as the temperature changes. [ABSTRACT FROM AUTHOR]

This paper presents the linear parametric resonance for MEMS vibratory gyroscopes using triangular area-varying capacitors. Compared to parametric resonance using gap-varying capacitors, the electrostatic stiffness using triangular capacitors is completely linear and independent of the motion displacement. A pump voltage in the square-rooted form consisting of both DC tuning voltage and AC signal with twice the drive resonance frequency is applied to the triangular capacitors in gyroscope sense mode for both mode matching and parametric amplification of Coriolis signal simultaneously. Parametric amplification or attenuation is realized by choosing specific phase and amplitude of the pump voltage. Experimental results show a maximum parametric gain of 13 times in gyroscope sense mode and the open-loop scale factor amplification of 4.8 times compared with the case where no pump voltage is applied. For one-hour zero-rate-output data, an improvement factor of 5.74 is achieved for angle random walk from 0.1745 ° √h−1 to 0.0304 ° √h−1. Meanwhile, an improvement factor of 9.73 for bias instability is achieved from 3.609 ° h−1 (occurring at integration time 40 s) to 0.371 ° h−1 (at 52 s). The quadrature error due to stiffness coupling is reduced from 9 ° s−1 to 1 ° s−1 which agrees well with our analysis that Coriolis force is mechanically amplified while quadrature error is dampened. [ABSTRACT FROM AUTHOR]

In this paper, the development and evaluation of passive optical ring resonator gyroscopes (OPRGs) are critical reviewed. Attention has been paid to the countermeasures against the parasitic noise sources which are encountered in the OPRG including backscattering, backreflection, polarization error, nonlinear Kerr effect, and laser frequency noise. The new progress in a feasible OPRG is shown. In addition, the advanced and complex digital signal processing in the OPRGs is also addressed. [ABSTRACT FROM PUBLISHER]

This paper proposed a novel slot-structure z-axis gyroscope with a positive or negative electrostatic spring. The slot-structure gyroscope has in-plane drive and sense modes. Different from conventional comb finger structure, variable-area fixed out-of-plane electrodes under the proof-mass are used to excite the in-plane vibratory modes. To overcome the disadvantage that the resonant frequencies are unable to be adjusted through variable-area capacitors in the conventional slot-structure gyroscope, a variable-area capacitor with triangular shape fixed electrodes is designed to introduce the electrostatic tuning of the in-plane vibratory modes. A voltage difference Vt across the triangular fixed electrodes and movable electrodes produces a positive or negative electrostatic spring. The induced electrostatic spring constant is proportional to Vt^{2}. A prototype with a positive electrostatic spring is fabricated and tested. The difference of the nature frequencies of the drive mode and sense mode is about 13.5 Hz. A 15 V Vt makes the gyroscope perfect mode matching. The scale factor of the prototype is about 72 mV/^\circ/s when Vt is 0 V and increases with Vt. It presents a scale factor of 320.6 mV/^\circ/s and noise density of 11.63^\circ/h/vHz when mode matched. Interestingly, the bandwidth of the gyroscope only slightly decreased from the initial value of 7 Hz to 4.6 Hz when mode matched, possible reasons are discussed in this paper. [2011-0297] [ABSTRACT FROM PUBLISHER]

Abstract: This paper proposes a new oscillation control algorithm for vibratory micro-machined gyroscope system. The control algorithm tunes the resonant frequency of the gyroscope to the specified resonant frequency and maintains the specified amplitude of oscillation by altering the gyroscope dynamics. Feedback control is designed to achieve frequency tuning in the presence of time-delay. The stability of the control system is analyzed using the averaging method. Based on the real system, simulation models were set up to evaluate the control algorithm. Further, the algorithm mainly implemented using a field-programmable-gate-array (FPGA) is tested on a capacitive vibrational gyroscope operating at atmospheric pressure. First measurement results of the novel digital prototype show the phase variance of the detected signal of drive axis is 13ppm in an hour while the amplitude variance is 22ppm. A bias instability value of 6°/h is achieved using this new oscillation control loop. [Copyright &y& Elsevier]

Abstract: Experiments on resonator micro-optic gyro (RMOG) with a digital proportional integral (PI) feedback scheme are performed. In this experimental setup, the key rotation sensing element is a polarization maintaining silica waveguide ring resonator (WRR) with a ring length of 7.9cm and a diameter of 2.5cm. A good linearity of 0.0015% over a wide range of ±2×104 °/s can be achieved for the RMOG theoretically. The optimal digital PI feedback scheme is adopted in the frequency servo loop to reduce the reciprocal frequency fluctuations due to the WRR resonance frequency and laser frequency drifts. Residual equivalent input fluctuation can be reduced as low as 0.03°/s/√Hz based on the optimal digital PI feedback scheme, which is close to the shot noise limited spectral density 0.02°/s/√Hz of the RMOG with the input optical power of 0.2mW. Relationship between RMOG output signal and angular rate is obtained from ±0.1°/s to ±5°/s. The standard deviation of the residuals between RMOG output results and linear fit curve is 0.066°/s. For an integration of the processing circuit, all the processing circuit is implemented by a field programmable gate array (FPGA) instead of instruments. The output of this digitalized RMOG is obtained over a range of ±550°/s. The linearity of this digitalized RMOG is 0.0169%. [Copyright &y& Elsevier]

This study investigated the effects of structural dimension variation arising from fabrication imperfections or active structural design on the vibration characteristics of a (100) single crystal silicon (SCS) ring-based Coriolis vibratory gyroscope. A mathematical model considering the geometrical irregularities and the anisotropy of Young's modulus was developed via Lagrange's equations for simulating the dynamical behavior of an imperfect ring-based gyroscope. The dynamical analyses are focused on the effects on the frequency split between two vibration modes of interest as well as the rotation of the principal axis of the 2θ mode pair, leading to modal coupling and the degradation of gyroscopic sensitivity. While both anisotropic Young's modulus and nonideal deep trench verticality affect the frequency difference between two vibration modes, they have little contribution to deflecting the principal axis of the 2θ mode pair. However, the 4θ variations in the width of both the ring and the supporting beams cause modal coupling to occur and the degenerate 2θ mode pair to split in frequency. To aid the optimal design of MEMS ring-based gyroscopic sensors that has relatively high robustness to fabrication tolerance, a geometrical compensation based on the developed model is demonstrated to identify the geometries of the ring and the suspension. [ABSTRACT FROM AUTHOR]

This paper presents for the first time an improved algorithm for vibration amplitude-phase information extraction of capacitive microelectromechanical systems (MEMS) gyroscopes. Amplitude and phase information resulting from the improved algorithm is insensitive to the phase variation of an interface capacitance-voltage (CV) circuit, thus both long time drift of the gyroscope and bias instability have been improved. Experimental results show that both the phase and amplitude information extracted using this improved algorithm is insensitive to phase variation of CV circuit which is in accordance with theory. Bias instability using this improved configuration is 0.64°/h, which is improved two times more than the configuration using traditional double-side-band (DSB) demodulation configuration, and 4.3 times more than the configuration using single-side-band (SSB) demodulation, respectively. Allan deviation analysis shows that the slow varying drift term using D&S configuration is effectively reduced due to its robustness to CV phase variation compared to test results using DSB or SSB configuration. [ABSTRACT FROM AUTHOR]

Abstract A resonant fiber optic gyro (RFOG) is a high-accuracy inertial rotation sensor based on the Sagnac effect. Knowledge of the laser frequency noise, especially the study of its transfer characteristics is critical to optimize the resonant frequency servo loop parameters in the RFOG. In this paper, a Mach–Zehnder interferometer (MZI) is used to measure the changes of the power spectral density (PSD) of the laser frequency noise. Three different observation points are set to investigate the transfer characteristics of the laser beam along the transmission loop of the RFOG. Through real-time observation and analysis of the PSDs of the laser frequency noise, we found that the effects of the laser frequency noise on the RFOG can be clearly determined, and the resonant frequency servo loop parameters can be optimized according to the required gyro bandwidth. We also demonstrate the significance of reducing the residual error at the lock-in frequency while ensuring a sufficient gyro bandwidth. [ABSTRACT FROM AUTHOR]

This paper reports a novel capacitive sensing method, enabling accurate and self-calibrated measurements for both the amplitude and phase information in sinusoidal motion. The approach constructively utilizes the inherent nonlinearity of a triangular-electrode based (TEB) variable-area sense capacitor. In the case of TEB detection signal, two harmonics exist and each carries information about the motional amplitude and phase. The TEB method robustly extracts the motional amplitude from the ratio of two sideband amplitudes and extracts the motional phase from the subtraction of two sideband phases. This technique is especially valuable for capacitive detection of periodic motion in MEMS resonant devices, such as the resonant accelerometer and Coriolis vibratory gyroscope. The paper presents detailed theoretical analysis and proposes a real-time measurement algorithm implemented in an FPGA device. Experimental results manifest that, compared with the traditional linear method, the sensitivity of the measured amplitude and phase to system parameter variations is highly suppressed up to 95%. Furthermore, an oscillation control system with TEB capacitive detection is introduced for micro-machined vibratory gyroscopes. First measurement results show the amplitude variance of the drive displacement is 120 ppm in an hour while the phase variance is 80 ppm. Allan variance analysis indicates a bias instability of 6.5°/h for the gyroscope output. [ABSTRACT FROM AUTHOR]

A universal expression is proposed for evaluating the residual amplitude modulation (RAM) in a phase modulator. The different effects of the interference and linear terms of the RAM on the resonant micro-optic gyroscope (RMOG) are analyzed. It is found that the effect of RAM depends on the magnitude of RAM itself and the phase component. A theoretical model is then developed to calculate the RAM induced bias error in the RMOG. Finally, a technique for suppression of RAM is proposed and demonstrated, and the bias error of the separate-phase-modulation RMOG is successfully eliminated. [ABSTRACT FROM AUTHOR]

A miniaturized compact open-loop resonator fiber optic gyro (RFOG) prototype with main body size of about 10.4 cm×10.4 cm×5.2 cm is reported, and a demodulation signal compensation technique is proposed, aiming to suppress the drift arising from accompanying intensity modulation induced by semiconductor laser diode (LD). The scheme of how to establish this miniaturized RFOG prototype is specifically stated. The linear relationship between the first-harmonic and second-harmonic demodulated signals respectively for the two counter propagating beams in the resonator is verified by theory and experiment, and based on this relationship, the demodulation signal compensation technique by monitoring the second-harmonic demodulated signal is described in detail. With this compensation technique, the gyro output stability under 1°/s rotation rate is effectively improved from 0.12°/s to 0.03°/s, and especially, an about 0.36°/s peak-to-peak fluctuation due to tuning current reset is significantly suppressed. A long term bias stability of about 4.5°/h in 1 h for such a small-sized RFOG prototype is demonstrated, which is of the same magnitude as that of currently reported large-sized RFOG systems utilizing LD as the laser source as well. [ABSTRACT FROM AUTHOR]

Waveguide ring resonator (WRR) is beneficial to the miniaturization and integration of the resonant micro optic gyroscope (RMOG). The shot-noise-limited sensitivity of the RMOG equipped with the multi-turn WRR is derived. The simulation results show that when the crossing loss or the waveguide propagation loss is higher than 0.07 dB/crossing or 1.2 dB/m, the WRR of multi-turn structure does no good to the sensitivity of the RMOG. Two configurations of the WRR are introduced and tested. According to the measured waveguide propagation loss and crossing loss, the optimal angular random walk (ARW) is obtained when the RMOG equipped with a WRR of 2 or 3 turns. The ARW of the RMOG equipped with a 3-turn WRR is measured at different laser output power which agrees well with the theoretical value. • The turns of the transmission-type WRR are optimized and the optimal angular random walk (ARW) is obtained when the RMOG equipped with a WRR of 2 or 3 turns. • The ARW of the RMOG equipped with a 3-turn WRR is measured at different laser output power which agrees well with the theoretical value. [ABSTRACT FROM AUTHOR]