Gyroscopic Systems Research Articles

High Temperature Inertial Navigation Sensors, Electronics and Packaging for reliable 300°C Operation

Conventional oil and gas drilling measurement while drilling (MWD) systems are typically designed to operate at temperatures <200°C. To increase the efficiency of drilling unconventional geothermal wells, downhole MWD tools are needed that can operate in the unique thermal challenges encountered in enhanced geothermal systems (EGS). GE demonstrated a 300°C downhole navigation system. The system utilizes GE’s internally developed state-of-the-art MEMS multiple ring Gyroscope (MRG), and a high temperature gyroscope control and readout application specific integrated circuit (ASIC). The MRG, ASIC and associated high temperature, high reliability packaging were integrated to demonstrate the performance and functionality of the gyroscope across the temperature range from room temperature to 300°C. Specialized long-term capable high temperature test platforms were developed to enable the characterization and testing of the gyroscope system and utilized to validate application-relevant lifetime capability.

Adaptive Fractional Prescribed Performance Control for Micro-Electromechanical System Gyros Using a Modified Neural Estimator

In this paper, a neural fractional order prescribed performance control is proposed for micro-electromechanical system (MEMS) gyros. Gyros tend to become smaller in size and more precise in structure with the development of micro-manufacturing technology. The operational security for MEMS gyros in cases of disturbances and parameter uncertainties becomes a challenging problem that has attracted much attention. The proposed method incorporates a prescribed performance technique to accomplish a bounded (within 10% of the vibration amplitude) gyro trajectory tracking error dynamic to secure the gyro’s operation. Meanwhile, fractional calculus is integrated into the controller’s design to provide precise adjustments to the gyro’s motion and thus further improve gyro control performance (shortening error convergence time by 20%). Furthermore, to enlarge the application scope and to improve gyro system robustness, a modified neural network estimator with a constrained input mapping mechanism is proposed to approximate unknown time-varying angular-velocity-related gyro dynamics. Notably, the constrained input mapping mechanism can help guide neural parameter initialization to avoid a time-consuming parameter adjustment process. The stability of the closed-loop gyro control system is proved in the framework of Lyapunov stability theory, and comparisons of simulation results are presented to demonstrate the effectiveness of the proposed method.

A method for compensating random errors in MEMS gyroscopes based on interval empirical mode decomposition and ARMA

The random error in micro-electro-mechanical systems (MEMS) gyroscopes is one of the major aspects that limit measurement accuracy. In order to address the inaccurate extraction of noise and trend during the signal preprocessing, as well as the subjectivity in autoregressive moving average (ARMA) model ordering, this paper proposes a method based on interval empirical mode decomposition and ARMA model. In the proposed method, the original signal is decomposed into a series of intrinsic mode functions (IMFs) and a residual through empirical mode decomposition (EMD). Based on the Hellinger distance and autocorrelation function, IMFs are then classified into noise IMFs, hybrid IMFs, and signal IMFs. The improved sand cat swarm optimization is utilized to optimize the ordering process of the ARMA model. The improved adaptive filter is adopted to compensate the random error, and the compensated signal is reconstructed with the signal IMFs and residual to obtain the final output. Experiments show that under static conditions, the proposed method could reduce the root mean square error (RMSE) by 52.6% and 33.3%, respectively, compared with the traditional EMD and ARMA methods. Under dynamic conditions, the proposed method could reduce the RMSE by 51.1% and 37.1%, respectively, compared with the traditional EMD and ARMA methods. The proposed method could effectively compensate the random error and improve the measurement accuracy of MEMS gyroscopes.

Stabilizing unstable periodic orbit of unknown fractional-order systems via adaptive delayed feedback control

This article presents an adaptive nonlinear delayed feedback control scheme for stabilizing the unstable periodic orbit of unknown fractional-order chaotic systems. The proposed control framework uses the Lyapunov approach and sliding mode control technique to guarantee that the closed-loop system is asymptotically stable on a periodic trajectory sufficiently close to the unstable periodic orbit of the system. The proposed method has two significant advantages. First, it employs a direct adaptive control method, making it easy to implement this method on systems with unknown parameters. Second, the framework requires only the period of the unstable periodic orbit. The robustness of the closed-loop system against system uncertainties and external disturbances with unknown bounds is guaranteed. Simulations on fractional-order duffing and gyro systems are used to illustrate the effectiveness of the theoretical results. The simulation results demonstrate that our approach outperforms the previously developed linear feedback control method for stabilizing unstable periodic orbits in fractional-order chaotic systems, particularly in reducing steady-state error and achieving faster convergence of tracking error.

Analysis and design of a fourth-order ΣΔ ADC for MEMS digital gyroscope sensors

This paper presents a fourth-order sigma-delta (ΣΔ) ADC applied to a micro-electro-mechanical system (MEMS) gyroscope system. First, a system-level model of ΣΔ modulator containing non-ideal factors is established, and the optimal system performance of the ΣΔ modulator is determined by optimizing the feedforward path and the feedback coefficient of the feedback path. Then, the operational transconductance amplifier (OTA) with chopping technique and clock timing to control bias current in the first stage integrator of the circuit design is able to reduce not only the flicker noise of the modulator, but also reduce the system power consumption. Third, the design of other essential circuit modules is presented, and the circuit performance meets the requirements and low-power consumption is achieved. The designed ΣΔ ADC uses a 0.18 μm CMOS BCD process, with a ΣΔ modulator area of 0.64 mm2 and a digital filter area of 2.03 mm2. When the sampling frequency is 2 MHz and the signal bandwidth is 7.8 kHz, the experimental measurement results show that the proposed ΣΔ modulator with the fourth-order CIFF structure can achieve a signal-to-noise ratio (SNR) of 66.3 dB and an effective number of bits (ENOB) of 10.07 bits, with a dynamic range (DR) of 89 dB and a power consumption of 9 mW. The SNR of ΣΔ ADC after filtering is 63 dB, which meets the requirements of high DR and low-power consumption of MEMS digital gyroscope sensors.

Sparse structure preserving finite element model updating problem for gyroscopic systems

An important yet difficult aspect of the finite element model updating problem is to preserve the original inherent structures in the updated model. The analytical matrices resulting from the discretization of distributed parameter systems using finite element techniques are often symmetric and sparse. In this paper, an iterative method is proposed for solving the constrained optimization problem (COP) of gyroscopic systems, that is, finding the optimal updated matrices M̂,Ĝ and K̂ that satisfy the constraints of the characteristic equation, symmetry (or skew-symmetry) and sparsity. The proposed method is proved to be convergent and numerical examples verify the effectiveness of the method.

Embedded adaptive fractional-order sliding mode control based on TSK fuzzy system for nonlinear fractional-order systems

An adaptive fractional-order sliding mode control (AFOSMC) is proposed to control a nonlinear fractional-order system. This scheme combines the features of sliding mode control and fractional control for improving the response of nonlinear systems. The structure of AFOSMC includes two units: fractional-order sliding mode control (FOSMC) and the tuning unit that employs a certain Takagi–Sugeno–Kang fuzzy logic system for online adjusting the parameters of FOSMC. Tuning the parameters of the FOSMC improves its performance with various control problems. Moreover, stability analysis of the proposed controller is studied using Lyapunov theorem. Finally, the developed control scheme is introduced for controlling a fractional-order gyroscope system. The proposed AFOSMC is implemented practically using a microcontroller where the test is carried out using the hardware-in-the-loop simulation. The practical results indicate the improvements and enhancements introduced by the developed controller under external disturbance, uncertainties and random noise effects.

Design and Experiment of MEMS Solid-State Wave Gyroscope Quadrature Error Correction System

A novel gyroscope quadrature error correction system based on quadrature force correction is introduced in this paper. The source of quadrature error of MEMS solid-state wave gyroscope is analyzed. The main source of quadrature error is the inevitable machining error. The gyroscope system model is established, the quadrature error correction method is proposed, and the quadrature error correction system is simulated. Through the comparative test, the gyroscope with quadrature error correction system has better performance. With the addition of quadrature error correction system, the scale factor of the gyroscope changes from 1.13 mV/°/s to 1.02 mV/°/s, the nonlinearity is increased from 1382.7ppm to 795.4 ppm, and the asymmetry is improved from 1532.4ppm to 945.1ppm, the angle random walk (ARW) from 269.1 °/h/√Hz to 39.45 °/h/√Hz, and the bias stability from 46.62 °/h to 6.785 °/h.

Design of MEMS gyroscope interface ASIC with on-chip temperature compensation

Zero bias and scale factor are important overall performance indicators for micromechanical gyroscopes and are commonly used to describe the temperature stability of MEMS gyroscope. This article presents a mode-matched MEMS gyroscope interface Application Specific Integrated Circuit (ASIC) with on-chip temperature compensation, which improves the temperature adaptability of the gyroscope by means of temperature compensation. By establishing a mathematical model between the equivalent integration constant of the driving loop and the temperature, the relationship between the phase margin of driving loop and temperature is analyzed. The effect of sense loop control parameters on the bandwidth of the gyroscope system is investigated, and the influence law between bandwidth and loop gain of the sense circuit is verified. A temperature compensation method based on an on-chip virtual temperature sensor is presented, and the design principle with an on-chip temperature compensation interface ASIC is described. The experimental results show that the standard deviation of scale factor in the temperature range of −40 to 60 °C is reduced to 11.2% of that before compensation, and the standard deviation of the zero bias is reduced to 2.5%. The zero bias instability of the gyroscope is reduced from 4.6 to 1.9°/h of that before compensation.

Jump and Pull-in Instability of a MEMS Gyroscope Vibrating System.

Jump and pull-in instability are common nonlinear dynamic behaviors leading to the loss of the performance reliability and structural safety of electrostatic micro gyroscopes. To achieve a better understanding of these initial-sensitive phenomena, the dynamics of a micro gyroscope system considering the nonlinearities of the stiffness and electrostatic forces are explored from a global perspective. Static and dynamic analyses of the system are performed to estimate the threshold of the detecting voltage for static pull-in, and dynamic responses are analyzed in the driving and detecting modes for the case of primary resonance and 1:1 internal resonance. The results show that, when the driving voltage frequency is a bit higher than the natural frequency, a high amplitude of the driving AC voltage may induce the coexistence of bistable periodic responses due to saddle-node bifurcation of the periodic solution. Basins of attraction of bistable attractors provide evidence that disturbance of the initial conditions can trigger a jump between bistable attractors. Moreover, the Melnikov method is applied to discuss the condition for pull-in instability, which can be ascribed to heteroclinic bifurcation. The validity of the prediction is verified using the sequences of safe basins and unsafe zones for dynamic pull-in. It follows that pull-in instability can be caused and aggravated by the increase in the amplitude of the driving AC voltage.

Modeling and Analysis of an Inertia Wave Energy Converter and Its Optimal Design

A novel structural design of a wave energy converter (WEC) is proposed, utilizing a gyroscope as the main component for energy absorption. A vacuum-sealed, high-speed flywheel is implemented within the gyroscope to convert energy and reduce energy loss from air resistance. A dynamic model that considers the response of the floater, gyroscope, and power take-off (PTO) system with multi-degree-of-freedom (DoF) wave excitations is created. The primary parameters such as flywheel speed, damping, and stiffness of the WEC system that affect the gyroscope and PTO on energy absorption are analyzed through numerical simulations. The simulation results demonstrate that changes to these parameters can significantly impact the energy-absorption peak value. Furthermore, an improved multi-objective evolutionary algorithm based on the decomposition (MOEA/D) algorithm is applied to optimize key parameters, such as the power conversion and gyro precession of the WEC system, using a hybrid constraint handling strategy for enhanced diversity and the HV value as the evaluation criterion. The optimal design solution is selected from the Pareto solution set using a technique for order preference by similarity to the ideal solution (TOPSIS) method based on entropy weighting so that technical guidance can be provided for the design and control of the WEC system.

A Method to Identify Different Comb Gaps for MEMS Gyroscope at the Wafer Level Based on Negative Electrostatic Stiffness

For high-accurate micro-electro-mechanical systems (MEMS) gyroscopes, comb gap errors influence the mechanical coupling errors and limit performance. In this study, an in situ method was proposed to identify the gaps of drive combs, drive-sense combs, and sense combs in MEMS gyroscopes that can be applied at the wafer level. Negative electrostatic stiffness of combs was considered in the model construction of the sense mode and the Y-axis in-phase mode, and the frequency change caused by this was applied to characterize the comb gaps. Eight chips in different positions of a wafer were selected for verification of this method. The results shows that errors of drive comb gaps, drive-sense comb gaps, and sense comb gaps in the chip near the wafer center were 0.67 μm, 0.60 μm, and 0.53 μm, respectively, and those in the chip at the wafer edge were 0.96 μm, 0.95 μm, and 0.71 μm, respectively. The variation of comb gaps was 0.08 μm in a single chip near the wafer center, and 0.03 μm in a single chip at the wafer edge. This work provides a method for the fabless designers to explore the effect of wafer process on the structures and reduce it through careful design.

The Effects of Vibro-Tactile Biofeedback Balance Training on Balance Control and Dizziness in Patients with Persistent Postural-Perceptual Dizziness (PPPD).

Patients with persistent postural-perceptual dizziness (PPPD) frequently report having problems with balance control. Artificial systems providing vibro-tactile feedback (VTfb) of trunk sway to the patient could aid recalibration of "falsely" programmed natural sensory signal gains underlying unstable balance control and dizziness. Thus, the question we examine, retrospectively, is whether such artificial systems improve balance control in PPPD patients and simultaneously reduce the effects of dizziness on their living circumstances. Therefore, we assessed in PPPD patients the effects of VTfb of trunk sway on balance control during stance and gait tests, and on their perceived dizziness. Balance control was assessed in 23 PPPD patients (11 of primary PPPD origin) using peak-to-peak amplitudes of trunk sway measured in the pitch and roll planes with a gyroscope system (SwayStar™) during 14 stance and gait tests. The tests included standing eyes closed on foam, walking tandem steps, and walking over low barriers. The measures of trunk sway were combined into a Balance Control Index (BCI) and used to determine whether the patient had a quantified balance deficit (QBD) or dizziness only (DO). The Dizziness Handicap Inventory (DHI) was used to assess perceived dizziness. The subjects first underwent a standard balance assessment from which the VTfb thresholds in eight directions, separated by 45 deg, were calculated for each assessment test based on the 90% range of the trunk sway angles in the pitch and roll directions for the test. A headband-mounted VTfb system, connected to the SwayStar™, was active in one of the eight directions when the threshold for that direction was exceeded. The subjects trained for 11 of the 14 balance tests with VTfb twice per week for 30 min over a total of 2 consecutive weeks. The BCI and DHI were reassessed each week and the thresholds were reset after the first week of training. On average, the patients showed an improved balance control in the BCI values after 2 weeks of VTfb training (24% p = 0.0001). The improvement was greater for the QBD patients than for the DO patients (26 vs. 21%), and greater for the gait tests than the stance tests. After 2 weeks, the mean BCI values of the DO patients, but not the QBD patients, were significantly less (p = 0.0008) than the upper 95% limit of normal age-matched reference values. A subjective benefit in balance control was spontaneously reported by 11 patients. Lower (36%), but less significant DHI values were also achieved after VTfb training (p = 0.006). The DHI changes were identical for the QBD and DO patients and approximately equal to the minimum clinical important difference. These initial results show, as far as we are aware for the first time, that providing VTfb of trunk sway to PPPD subjects yields a significant improvement in balance control, but a far less significant change in DHI-assessed dizziness. The intervention benefitted the gait trials more than the stance trials and benefited the QBD group of PPPD patients more than the DO group. This study increases our understanding of the pathophysiologic processes underlying PPPD and provides a basis for future interventions.

Fault‐tolerant fixed‐time prescribed performance control of MEMS gyroscope

AbstractThis paper investigates a fault‐tolerant fixed‐time prescribed performance microelectromechanical system gyroscope using the adaptive backstepping method. The control protocol is designed such that not only is the system robust to even extremely harsh conditions of disturbance and actuator faults but also the performance and its settling time are user‐adjustable. Also, the system itself along with the external disturbances and actuator faults are assumed to be uncertain. Two case studies have been analyzed; the controller performance in the presence of very severe while uncertain disturbance and actuator faults, and a comparison between fixed‐time and finite‐time in this model in terms of their performance and convergence rate. First, the dynamics of the system are derived, and the prescribed performance error is defined for the analysis. Then, using the backstepping method, and adaptive estimations for the uncertainties, the algorithm is designed to converge the errors to a small set near zero with a fixed‐time convergence rate after which the stability of the system is verified via Lyapunov theory. In the end, a simulation example is presented in each case study to represent the efficacy of the proposed control scheme.

A 0.82 μVrms ultralow 1/f noise bandgap reference for a MEMS gyroscope

High-precision microelectromechanical system (MEMS) gyroscopes are significant in many applications. Bias instability (BI) is an important parameter that indicates the performance of a MEMS gyroscope and is affected by the 1/f noise of the MEMS resonator and readout circuit. Since the bandgap reference (BGR) is an important block in the readout circuit, reducing its 1/f noise is key to improving a gyroscope’s BI. In a traditional BGR, the error amplifier is applied to provide a virtual short-circuit point, but it introduces the main low-frequency noise sources. This paper proposes an ultralow 1/f noise BGR by removing the error amplifier and applying an optimized circuit topology. In addition, a simplified but accurate noise model of the proposed BGR is obtained to optimize the BGR’s output noise performance. To verify this design, the proposed BGR has been implemented in a 180 nm CMOS process with a chip area of 545 × 423 μm. The experimental results show that the BGR’s output integrated noise from 0.1 to 10 Hz is 0.82 μV and the thermal noise is 35 nV/√Hz. Furthermore, bias stability tests of the MEMS gyroscope fabricated in our laboratory with the proposed BGR and some commercial BGRs are carried out. Statistical results show that reducing the BGR’s 1/f noise can nearly linearly improve the gyroscope’s BI.

An Ultra-Low-Loss Waveguide Based on BIC Used for an On-Chip Integrated Optical Gyroscope

The development of integrated optical technology and the continuous emergence of various low-loss optical waveguide materials have promoted the development of low-cost, size, weight, and power optical gyroscopes. However, the losses in conventional optical waveguide materials are much greater than those in optical fibers, and different waveguide materials often require completely different etching processes, resulting in severely limited gyroscope performance, which is not conducive to the monolithic integration of gyroscope systems. In this paper, an ultra-low-loss Archimedean spiral waveguide structure is designed for an on-chip integrated optical gyroscope by using the high Q value and low-loss optical characteristics of the bound state in the continuum (BIC). The structure does not require the etching of high-refractive-index optical functional materials, avoiding the etching problem that has been difficult to solve for a long time. In addition, the optical properties of the BIC straight and the BIC bent waveguide are simulated using the finite element method (FEM) to find the waveguide structural parameters corresponding to the BIC mode, which is used to design the integrated sensing coil and analyze the gyroscope performance. The simulation results show that the gyroscope’s sensitivity can reach 0.6699°/s. This research is the first time a BIC optical waveguide has been used for an integrated optical gyroscope, providing a novel idea for the monolithic integration of optical gyroscopes.

Position Self-Correction of Resolver Based on a Composite Method in Gimbal System

This article explores a composite self-correction method for the angular position of the resolver in the gimbal system of the control moment gyroscope (CMG). The nonideal signals of the resolver in the gimbal resolver-to-digital conversion (RDC) system result in a systematic error, which can decrease the performance of the output torque of the CMG. However, it is impractical to adopt additional high-precision sensors to correct the angular position of the resolver in the installed gimbal system on account of the limitation of the structure and space. Therefore, a novel self-correction composite method based on a discrete extended state observer (DESO) and a harmonic observer method (HOM) is put forward to calibrate the angular position of the resolver. First, the sine and cosine signals with harmonics can be directly obtained. Then, the composite proposed method is performed to get the accurate angular position of the resolver, and the position error can also be acquired. Based on the position error, the compensation table can be established, and finally, the high-precision position can be acquired. The proposed self-correction method is verified by simulation and experiments, and the results show that the angular position accuracy is significantly improved.

Calibration Method of MEMS Gyroscopes Using a Robot Manipulator

Inertial measurement units composed of microelectromechanical systems (MEMS) gyroscopes are widely used sensors for small spacecraft and nanosatellite attitude estimation, control, and orientation. This is due to the fact that when developing nanosatellites, it is convenient to use devices of small dimensions and low energy consumption, which are advantages of MEMS sensors. However, one of the significant disadvantages of these measuring devices is their relatively low accuracy, which is related to systematic and random errors. For this reason, this article proposes a method for calibrating MEMS-based angular rate sensors using a robot manipulator for partial elimination of these errors. There are high-precision rotary calibration stands on the market that are designed to set angular rates and orientations when testing products of various types and accuracy classes. Similarly, a robot manipulator represents a possible option for performing this task. As a result, a modified six-position method as a sequence for performing laboratory calibration using a robot joint for high-precision rotation is proposed. The features of the results of processing experimental measurement data of tests have been validated on MEMS angular rate sensors. After calibration, the quality of MEMS gyroscope output data using this calibration approach was significantly improved.

Approximately Optimal Stabilization of a Gyroscopic System with Many Degrees of Freedom and Slowly Varying Parameters

Approximately Optimal Stabilization of a Gyroscopic System with Many Degrees of Freedom and Slowly Varying Parameters

An Interface ASIC Design of MEMS Gyroscope with Analog Closed Loop Driving.

This paper introduces a digital interface application-specific integrated circuit (ASIC) for a micro-electromechanical systems (MEMS) vibratory gyroscope. The driving circuit of the interface ASIC uses an automatic gain circuit (AGC) module instead of a phase-locked loop to realize a self-excited vibration, which gives the gyroscope system good robustness. In order to realize the co-simulation of the mechanically sensitive structure and interface circuit of the gyroscope, the equivalent electrical model analysis and modeling of the mechanically sensitive structure of the gyro are carried out by Verilog-A. According to the design scheme of the MEMS gyroscope interface circuit, a system-level simulation model including mechanically sensitive structure and measurement and control circuit is established by SIMULINK. A digital-to-analog converter (ADC) is designed for the digital processing and temperature compensation of the angular velocity in the MEMS gyroscope digital circuit system. Using the positive and negative diode temperature characteristics, the function of the on-chip temperature sensor is realized, and the temperature compensation and zero bias correction are carried out simultaneously. The MEMS interface ASIC is designed using a standard 0.18 μM CMOS BCD process. The experimental results show that the signal-to-noise ratio (SNR) of sigma-delta (ΣΔ) ADC is 111.56 dB. The nonlinearity of the MEMS gyroscope system is 0.03% over the full-scale range.