Angular Rate Signal Research Articles

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.

Civil Aircraft Fault Tolerant Attitude Tracking based on Extended State Observers and Nonlinear Dynamic Inversion

For the problem of sensor faults and actuator faults in aircraft attitude control, this paper proposes a fault tolerant control (FTC) scheme based on extended state observer (ESO) and nonlinear dynamic inversion (NDI). First, two ESOs are designed to estimate sensor faults and actuator faults respectively. Second, the angular rate signal is reconstructed according to the estimation of sensor faults. Third, in angular rate loop, NDI is designed based on reconstruction of angular rate signals and estimation of actuator faults. The FTC scheme proposed in this paper is testified through numerical simulations. The results show that it is feasible and has good fault tolerant ability.

A New Compressed-Structure-Based Coning Algorithm for Fiber Optic Strapdown Inertial Navigation Systems

For strapdown inertial navigation systems (SINSs) equipped with high-precision fiber optic gyroscope whose outputs are angular rate signals, the attitude calculation accuracies of traditional angular-rate-based rotation vector algorithms are limited when the vehicle is in a highly dynamic environment due to the fact that only the compensation of the second-order noncommutativity error is considered. Although the attitude algorithms based on polynomial iteration have higher accuracy, the computational complexity is too large. In order to fully tap the accuracy of the inertial measurement unit (IMU) to reduce the attitude errors, the third-, fourth-, and fifth-order Picard solutions for the equivalent rotation vector differential equation are derived in this article. A new method with a compressed structure to calculate the rotation vector for real-time processing systems is proposed to further reduce the noncommutativity error. In a classical coning motion environment, the frequency-series-based Taylor expansions are utilized for error analysis and design of the new algorithm’s coefficients. The effectiveness of the proposed coning algorithm with eighth-order accuracy is validated by digital simulation and initial alignment experiments in the turntable. In comparison with the traditional algorithms, the proposed algorithm improves the yaw alignment accuracy by 78.5%, the pitch alignment accuracy by 73.8%, and the roll alignment accuracy by 66.9% on average.

Integrated control of attitude maneuver and vibration suppression of flexible spacecraft based on magnetically suspended control moment gyros

This paper adopts magnetically suspended control moment gyro (MSCMG) to realize the integration of attitude control and wideband micro-vibration suppression of spacecraft without adding extra hardware resources. The coupling between central rigid body and flexible attachment has been effectively retained in the controller design. First, an open-loop modal observer is constructed in advantage of the inherent physical characteristics of flexible modes, and then an adaptive backstepping controller involving flexible modal estimation, spacecraft attitude quaternion, and angular velocity is designed. Next, the band-pass filters are employed to separate the low-frequency gimbal command angular rate signal and medium–high-frequency rotor command angular rate signal, respectively, so that MSCMG can accurately track the command signal output by the integrated controller. Taking advantage of MSCMG’s ability to output high bandwidth micro-gimbal moment, the proposed method can not only meet the requirement of spacecraft rapid maneuver but also effectively suppress the broadband micro-vibration, including low-frequency flexible vibration and medium–high-frequency micro-vibration caused by spacecraft rotating parts. Numerical simulations and frequency domain analysis demonstrate the correctness and effectiveness of the proposed method.

A Nonlinear Rate Microsensor utilising Internal Resonance

Micro- and nano-resonators have been studied extensively both for the scientific viewpoint to understand basic interactions at small scales as well as for applied research to build sensors and mechanical signal processors. Majority of the resonant microsystems, particularly those manufactured at a large scale, have employed simple mechanical structures with one dominant resonant mode, such as in timing resonators, or linearly coupled resonant modes, as in vibratory gyroscopes. There is an increasing interest in the development of models and methods to better understand the nonlinear interactions at micro- and nano-scales and also to potentially improve the performance of the existing devices in the market beyond limits permissible by the linear effects. Internal resonance is a phenomenon that allows for nonlinear coupling and energy transfer between different vibration modes of a properly designed system. Herein, for the first time, we describe and experimentally demonstrate the potential for employing internal resonance for detection of angular rate signals, where the Coriolis effect modifies the energy coupling between the distinct drive and sense vibration modes. In doing so, in addition to providing a robust method of exciting the desired mode, the proposed approach further alleviates the mode-matching requirements and reduces instabilities due to the cross-coupling between the modes in current linear vibratory gyroscopes.

Analysis of Correlation in MEMS Gyroscope Array and its Influence on Accuracy Improvement for the Combined Angular Rate Signal.

Obtaining a correlation factor is a prerequisite for fusing multiple outputs of a mircoelectromechanical system (MEMS) gyroscope array and evaluating accuracy improvement. In this paper, a mathematical statistics method is established to analyze and obtain the practical correlation factor of a MEMS gyroscope array, which solves the problem of determining the Kalman filter (KF) covariance matrix Q and fusing the multiple gyroscope signals. The working principle and mathematical model of the sensor array fusion is briefly described, and then an optimal estimate of input rate signal is achieved by using of a steady-state KF gain in an off-line estimation approach. Both theoretical analysis and simulation show that the negative correlation factor has a favorable influence on accuracy improvement. Additionally, a four-gyro array system composed of four discrete individual gyroscopes was developed to test the correlation factor and its influence on KF accuracy improvement. The result showed that correlation factors have both positive and negative values; in particular, there exist differences for correlation factor between the different units in the array. The test results also indicated that the Angular Random Walk (ARW) of 1.57°/h0.5 and bias drift of 224.2°/h for a single gyroscope were reduced to 0.33°/h0.5 and 47.8°/h with some negative correlation factors existing in the gyroscope array, making a noise reduction factor of about 4.7, which is higher than that of a uncorrelated four-gyro array. The overall accuracy of the combined angular rate signal can be further improved if the negative correlation factors in the gyroscope array become larger.

Study on solving method for output signal of frequency resonant gyroscope

This paper proposed a kind of real-time online solving method based on the analog circuit for the output signal solution of frequency resonant gyroscope. This method firstly established the vibration differential equation of frequency resonant gyroscope, deduced the output signal solving model under some constraints, and used the digital simulation technology for the principle verification of solving equation. Then the verification results showed that the solving equation was feasible. Subsequently, the corresponding circuit design scheme and specific analog circuit design were given, the differential equation of this solving circuit was deduced, and the equivalent relation between the theoretically solving model and circuit differential equation was built. The experimental results showed that there existed a higher linearity between input signal and output signal of angular rate as well as that adj. R2 reached 0.99978. Hence, these experimental results verified the effectiveness of this method. Simultaneously, the analog circuit of the whole solving process was likely to provide the integrated and small solving unit in future. This solving method provided a new way to solve the efficient and real-time angular rate signal for the frequency resonant gyroscope.

Multimodal fusion for functional rehabilitation at home

Conventional musculoskeletal rehabilitation consists of a therapy consultancy, an exercise assignment, and an execution task with or without assistance of the therapist. This classical approach consumes plenty of the patient's time, money and effort, and especially those of medical staff. Serious games have been studied as an aided tool for clinical and home-based rehabilitation, with patient autonomy in the exercise execution but monitored by the therapist staff. In order to estimate joint angles, most of these systems used a Kinect camera for musculoskeletal rehabilitation motion but the estimation accuracy represents the principal drawback. Therefore, in this work, which is under development, we have proposed a data fusion system based on accelerometers devices (Shimmer) and Kinect camera. Figure 1 shows that wearable sensors can be used to closely monitor Parkinson's disease motor fluctuations and predict clinical scores with high accuracy. Exploiting a quaternion representation of orientation, we propose to estimate joint angle from Shimmer sensors using a gradient descent algorithm, which is based on accelerometer and magnetometer signals (magnetic distortion has been taken into account). The estimated orientation will be fused with the calculated orientation using angular rate signal. The weighted sum fusion algorithm is used. The output of the fusion algorithm is used to continuously correct Kinect camera output. Below, in Figure 1 , we describe the general workflow of the proposed system. The system will be able to inform the user in real time the successful completion of the rehabilitation exercises.

Temporal fluctuations of tremor signals from inertial sensor: a preliminary study in differentiating Parkinson's disease from essential tremor.

BackgroundParkinson’s disease (PD) and essential tremor (ET) are the two most common movement disorders but the rate of misdiagnosis rate in these disorders is high due to similar characteristics of tremor. The purpose of the study is to present: (a) a solution to identify PD and ET patients by using the novel measurement of tremor signal variations while performing the resting task, (b) the improvement of the differentiation of PD from ET patients can be obtained by using the ratio of the novel measurement while performing two specific tasks.Methods35 PD and 22 ET patients were asked to participate in the study. They were asked to wear a 6-axis inertial sensor on his/her index finger of the tremor dominant hand and perform three tasks including kinetic, postural and resting tasks. Each task required 10 s to complete. The angular rate signal measured during the performance of these tasks was band-pass filtered and transformed into a two-dimensional representation. The ratio of the ellipse area covering 95 % of this two-dimensional representation of different tasks was investigated and the two best tasks were selected for the purpose of differentiation.ResultsThe ellipse area of two-dimensional representation of the resting task of PD and ET subjects are statistically significantly different (p < 0.05). Furthermore, the fluctuation ratio, defined as a ratio of the ellipse area of two-dimensional representation of resting to kinetic tremor, of PD subjects were statistically significantly higher than ET subjects in all axes (p = 0.0014, 0.0011 and 0.0001 for x, y and z-axis, respectively). The validation shows that the proposed method provides 100 % sensitivity, specificity and accuracy of the discrimination in the 5 subjects in the validation group. While the method would have to be validated with a larger number of subjects, these preliminary results show the feasibility of the approach.ConclusionsThis study provides the novel measurement of tremor variation in time domain termed ‘temporal fluctuation’. The temporal fluctuation of the resting task can be used to discriminate PD from ET subjects. The ratio of the temporal fluctuation of the resting task to the kinetic task improves the reliability of the discrimination. While the method is powerful, it is also simple so it could be applied on low resource platforms such as smart phones and watches which are commonly equipped with inertial sensors.

Noise Reduction of MEMS Gyroscope Based on Direct Modeling for an Angular Rate Signal

In this paper, a novel approach for processing the outputs signal of the microelectromechanical systems (MEMS) gyroscopes was presented to reduce the bias drift and noise. The principle for the noise reduction was presented, and an optimal Kalman filter (KF) was designed by a steady-state filter gain obtained from the analysis of KF observability. In particular, the true angular rate signal was directly modeled to obtain an optimal estimate and make a self-compensation for the gyroscope without needing other sensor’s information, whether in static or dynamic condition. A linear fit equation that describes the relationship between the KF bandwidth and modeling parameter of true angular rate was derived from the analysis of KF frequency response. The test results indicated that the MEMS gyroscope having an ARW noise of 4.87°/h0.5 and a bias instability of 44.41°/h were reduced to 0.4°/h0.5 and 4.13°/h by the KF under a given bandwidth (10 Hz), respectively. The 1σ estimated error was reduced from 1.9°/s to 0.14°/s and 1.7°/s to 0.5°/s in the constant rate test and swing rate test, respectively. It also showed that the filtered angular rate signal could well reflect the dynamic characteristic of the input rate signal in dynamic conditions. The presented algorithm is proved to be effective at improving the measurement precision of the MEMS gyroscope.

Analysis of Dynamic Performance of a Kalman Filter for Combining Multiple MEMS Gyroscopes

In this paper, the dynamic performance of a Kalman filter (KF) was analyzed, which is used to combine multiple measurements of a gyroscopes array to reduce the noise and improve the accuracy of the individual sensors. A principle for accuracy improvement by the KF was briefly presented to obtain an optimal estimate of input rate signal. In particular, the influences of some crucial factors on the KF dynamic performance were analyzed by simulations such as the factors input signal frequency, signal sampling, and KF filtering rate. Finally, a system that was comprised of a six-gyroscope array was designed and implemented to test the dynamic performance. Experimental results indicated that the 1σ error for the combined rate signal was reduced to about 0.2°/s in the constant rate test, which was a reduction by a factor of more than eight compared to the single gyroscope. The 1σ error was also reduced from 1.6°/s to 0.48°/s in the swing test. It showed that the estimated angular rate signal could well reflect the dynamic characteristic of the input signal in dynamic conditions.

The Use of an Orientation Kalman Filter for the Static Postural Sway Analysis

The paper presents a quaternion-based extended Kalman filter for postural instability evaluation during stance. It uses low-cost MEMS inertial sensors attached on the lower back of the person at a known height in order to instrumenting the static balancing test. Generally, patients with Parkinson's disease or vestibular-loss are at greater risk for having this problem. The objective of this study was to assess the feasibility of using Kalman filter to characterize the postural steadiness. The Kalman filter is used here as a data fusion algorithm to estimate the orientation of the body based on acceleration and angular rate signals. In order to get the coordinate of the body's centre of mass (CoM), the height of the sensor is projected on the horizontal plane by using the estimated orientation. Many parameters such as the mean velocity of sway, lateral/anterior-posterior range and others are then obtained from the sway path, which help the clinicians to assess the postural instability. The method was tested on 9 healthy individuals (21-31 years). Three different test conditions, namely feet comfortable stance with eyes-open, feet together stance with closed eyes and one-leg stance with eyes-open were evaluated here. The proposed algorithm showed successful estimation of the time-domain parameter for the postural sway analysis.

Research on Vibration Angle of Six Degree-of-Freedom

Based on fiber optic gyroscope technique new method of rotation angle testing in three-axis vibration is proposed in this paper, and the theory of fiber optic gyroscope is introduced as well. According to the measurement accuracy requirement, the angle testing system of FOG is designed by analyzing the environment of three-axis vibration. It was applied in experimental investigation of rotation angle in three-axis vibration with the FOG testing system and the real-time angular rate signal was processed by frequency analysis. The results of practical application show that it is feasibility and validity of angle testing method by means of FOG technique.

Feasibility Study and Performance Analysis of a Gyroless Orientation Tracker

Inertial orientation tracking systems commonly use three types of sensors: accelerometers, magnetometers, and gyroscopes. The angular rate signal is used to obtain a dead reckoning estimate, whereas the gravitational and local magnetic field measures allow us to apply a correction and to obtain a drift-free result. Considering the present market of inertial MEMS sensors, the current consumption of gyroscopes represents a major part of the power budget of wireless inertial sensor nodes, which should be minimized given the mobility of the application. This paper introduces an orientation tracking algorithm, based on an unscented Kalman filter, that does not require angular rate data for tracking human movements up to 450 °/s , which is a reasonable value for many applications. Since accelerometers measure other accelerations beside gravity and magnetometers are prone to magnetic disturbances, adaptive techniques are applied in order to reduce the influence on the estimations. The performance of the system is quantitatively analyzed and compared to an estimator that includes angular rate information.

Research on Nozzle Array Structure Fluidic Gyroscope Signal Extraction Circuit

The nozzle array structure fluidic gyroscope signal extraction circuit was researched. To acquire output voltage signal from the gyroscope angular rate sensitive element, which had enough sensitivity to detect, the signal extraction circuit was designed. Then, the circuit function and principle for each module was analyzed. The signal extraction circuit is composed up bridge circuit, voltage regulator circuit, amplifying circuit and filter circuit. The experiment results show that using the signal extraction circuit, the sensitive element output sensitivity is 10mV/°/s and linearity is 4.8% from the first stage. Therefore, the signal extraction circuit realizes the transformation from angular rate signal to the voltage signal and eliminates effectively noise jamming from the external environment, which provides the foundation for the fluidic gyroscope compensation circuit.

Detection of (In)activity Periods in Human Body Motion Using Inertial Sensors: A Comparative Study

Determination of (in)activity periods when monitoring human body motion is a mandatory preprocessing step in all human inertial navigation and position analysis applications. Distinction of (in)activity needs to be established in order to allow the system to recompute the calibration parameters of the inertial sensors as well as the Zero Velocity Updates (ZUPT) of inertial navigation. The periodical recomputation of these parameters allows the application to maintain a constant degree of precision. This work presents a comparative study among different well known inertial magnitude-based detectors and proposes a new approach by applying spectrum-based detectors and memory-based detectors. A robust statistical comparison is carried out by the use of an accelerometer and angular rate signal synthesizer that mimics the output of accelerometers and gyroscopes when subjects are performing basic activities of daily life. Theoretical results are verified by testing the algorithms over signals gathered using an Inertial Measurement Unit (IMU). Detection accuracy rates of up to 97% are achieved.

Active suspension control design for unmanned ground vehicles

This paper presents the design of an active suspension control system for an unmanned ground vehicle (UGV). The purpose is to design an active suspension control for a low-speed (less than 1 m/s) off-road UGV in order to be able to move through rugged terrain with the least pitch and roll motion. Classical active suspension design methods cannot be used for minimizing pitch and roll angles, therefore a new approach is applied. The control design is based on the LQG method. The control system uses only pitch and roll angular rate signals, which ensures a simple and cheap control system, but any bias error on the gyro signals cause some problems in reconstructing angles. The control algorithm consists of an optimal state-feedback fed by an augmented observer for estimating the states and the bias error of the gyro sensors. The appropriate tuning of the observer is introduced, which eliminates the bias error problem and ensures the fast reconstruction of the states for the optimal state-feedback. In simulations, the active suspension control system shows high performance at minimizing pitch and roll angles.

Model-based control concepts for vibratory MEMS gyroscopes

In this contribution, a systematic method for the design of open- and closed-loop controllers for vibratory MEMS gyroscopes based on so-called envelope models will be presented. The methodology will be exemplarily carried out for a gyroscope with electrostatic actuation and read-out elements. The specifically designed capacitive actuators of the gyroscope are capable of compensating the system’s inherent mechanical unbalance (quadrature compensation) as well as the system’s response to an external angular rate (force feedback). The utilized envelope model solely captures the relevant system dynamics of the gyroscope while at the same time describing the actuation and read-out mechanisms simplified to a suitable level of detail thus providing the basis for an efficient and systematic control design.In order to demonstrate the proposed methodology, an optimized start-up strategy for the control of the primary oscillation is designed. Furthermore, the approach is utilized for the deviation of a basic quadrature controller for the secondary oscillation. In order to account for the typically weakly damped open-loop dynamics of the gyroscope and the transient coupling between the quadrature and the angular rate signal a more sophisticated combined concept of closed-loop quadrature and force feedback control is introduced. Both simulation and measurement results obtained for a prototype gyroscope validate the mathematical models and prove the feasibility of the proposed concepts.

Temperature Modeling and Compensation of Double h Quartz Tuning Fork Gyroscope

The double-H quartz tuning fork has a (zyω)5° cut shape[1], its structure and vibration mode are different with H quartz tuning fork clearly, and we have applied for a patent for the structure of the double-H quartz tuning fork gyroscope. It is desired that the driving signal has very high frequency stability and amplitude stability on the operation of the quartz tuning fork. But, the quartz tuning fork resonant frequency of the reference mode may change with temperature, and if the driving signal frequency can’t automatically track the resonant frequency of the reference mode, the error signal will appear in the output angular rate signal. Based on the severe nonlinearity drift error induced by temperature change, a practical and precise composite model was proposed to compensate the error caused by temperature change. The double-H quartz tuning fork gyroscope temperature modeling was set up by test experiment and data processing at full temperature range, the accuracy of the double-H quartz tuning fork gyroscope was improved greatly by utilizing temperature compensation, and the experiment results indicate that the method is useful and feasible.

Optimization approach to adapt Kalman filters for the real-time application of accelerometer and gyroscope signals' filtering

A problem of accelerometer and gyroscope signals' filtering is discussed in the paper. Triple-axis accelerometer and three single-axis gyroscopes are the elements of strapdown system measuring head. Effective noise filtration impacts on measured signal reliability and the computation precision of moving object position and orientation. The investigations were carried out to apply Kalman filter in a real-time application of acceleration and angular rate signals filtering. The filter parameter adjusting is the most important task of the investigation, because of unknown accuracy of the measuring head and unavailability of precisely known model of the system and the measurement. Results of calculations presented in the paper describe relation between filter parameters and two assumed criterions of filtering quality: output signal noise level and filter response rate. The aim of investigation was to achieve and find values of the parameters which make Kalman filter useful in the real-time application of acceleration and angular rate signals filtering.