Digital Tri-Axis Accelerometer with X/Y-Axial Resonators and Z-Axial Capacitive Seesaw.

A tri-axis accelerometer with a digital readout circuit and communication system is introduced. It is composed of two resonant accelerometers in the x and y-axis, and a seesaw capacitive one in the z-axis. The device is encapsulated in air to ensure that the z-axis works in an over-damped state. Moreover, the closed-loop drive circuit establishes the x-axis and y-axis in resonant mode, and the z-axis in force balance mode. A miniaturized measurement based on FPGA is designed to collect these output signals. The phase noise of the resonance part and the amplitude noise of the seesaw part are studied by simulation. The model can predict the contribution of each part to the measurement error and Allan variance. Multiplied clock and Kalman filter in sliding window are used to reduce the frequency error. The test results show that the accelerometer has low bias instability (<30 µg), low cross-coupling error (<0.5%), and low nonlinearity (<0.1%). The tri-axis digital accelerometer with serial ports is more valuable than the previous works with large commercial instruments.

Theoretical study of extremely narrow plasmonic surface lattice resonances observed by MIM nanogratings under normal incidence in asymmetric environments.

Nanoarray structures can support plasmonic surface lattice resonances (SLRs) with extremely narrow linewidths and huge electric field enhancement features, which are attractive applications in nanolasers, biochemical sensors, and nonlinear optics. However, current nanoarray structures located in an asymmetric dielectric environment with a refractive index contrast of 1.00/1.52 of the superstrate/substrate excite much poorer SLRs under normal incidence, which largely limits their application range. In this work, we report extremely narrow SLRs supported by one-dimensional metal-insulator-metal nanograting in asymmetric dielectric environments. The simulation results show that an SLRs with linewidth of 3.26 nm and quality factor of 233.2 can be excited under normal incidence. This high-quality SLRs is attributed to the interference formation between the out-of-plane dipole resonance mode and the out-of-plane quadrupole resonance mode. We also show that the resonance wavelength and quality factor can be tuned by changing the structure geometry and period, and we calculate the normal incidence SLRs quality factor to be up to 248 in 1.33/1.52 and 250 in 1.45/1.52. We expect the SLRs of this work to find potential applications in asymmetric dielectric environments.

Optimization and Fabrication of an MOEMS Gyroscope Based on a WGM Resonator.

In this paper, the characterization of a whispering gallery mode (WGM) resonator applied in a novel micro-opto-electro-mechanical system (MOEMS) gyroscope was investigated. The WGM optical transmission coupling model was analyzed and compared by adjusting key parameters, such as the cavity radius, the waveguide width, and the gap between them for silicon and silicon nitride materials in simulations, which will greatly affect the quality factor (Q) of the WGM resonator. Furthermore, the structural parameters of the disk resonant gyroscope were also optimized. Then, the fabrication process was optimized to overcome the difficulties in the realization of micro-optical devices. Finally, a gyroscope prototype with the integrated WGM resonator was verified experimentally. The scale factor and bias instability performance of the MOEMS gyroscope was 2.63 mv/°/s and 4.0339°/h, respectively.

A New Design of an MOEMS Gyroscope Based on a WGM Microdisk Resonator.

In this paper, we present a new design for a micro-opto-electro-mechanical (MOEMS) gyroscope based on a whispering-gallery mode (WGM) microdisk resonator and MEMS resonator. The mechanical characteristics, frequency split, and quality factor (Q) of the MEMS resonator; the optical characteristics, Q value, and coupling regimes of the WGM resonator; and the coupling between the two resonators were analyzed. Its operation principle-the transformation process from angular velocity to the resonance wavelength of the WGM resonator-is presented at same time. Next, the analysis conclusions were validated with the help of simulations in ANSYS and FDTD (Finite-Difference Time-Domain) Solutions. Afterwards, some key specifications were estimated based on the results of simulations. Lastly, the fabrication process is detailed.

Correction: Shen, X. et al. Research on the Disc Sensitive Structure of a Micro Optoelectromechanical System (MOEMS) Resonator Gyroscope. Micromachines, 2019, 10, 264.

In the published paper [...].

Research on the Disc Sensitive Structure of a Micro Optoelectromechanical System (MOEMS) Resonator Gyroscope.

A micro optoelectromechanical system (MOEMS) resonator gyroscope based on a waveguide micro-ring resonator was proposed. This sensor was operated by measuring the shift of the transmission spectrum. Modal analysis was carried out for the disc sensitive structure of the MOEMS resonator gyroscope (MOEMS-RG). We deduced the equations between the equivalent stiffness and voltage of each tuning electrode and the modal parameters. A comprehensive investigation of the influences of the structure parameters on the sensitivity noise of the MOEMS-RG is presented in this paper. The mechanical sensitivity and transducer sensitivities of the MOEMS-RG, with varying structural parameters, are calculated based on the finite-element method. Frequency response test and the fiber optic spectrometer displacement test were implemented to verify the reliability of the model. Research results indicate that the resonant frequencies of the operating modes are tested to be 5768.407 Hz and 5771.116 Hz and the resonant wavelength change ΔX was 0.08 nm for 45° rotation angle. The resonant wavelength, which has a good linear response in working range, changes from -0.071 nm to 0.080 µm. The MOEMS-RG, with an optimized disc sensitive structure, can detect the deformation of the sensitive membrane effectively, and has a high sensitivity. This resonator shows very large meff, low f 0 , and very high Q. Therefore, this resonator can provide a small A R W B ( 0.09 ° / h ), which makes it a promising candidate for a low-cost, batch-fabricated, small size inertial-grade MOEMS gyroscope. The multi-objective optimization method could be expanded to include other objectives, constraints, or variables relevant to all kinds of gyroscopes or other microelectromechanical systems devices.

A Robust Inner and Outer Loop Control Method for Trajectory Tracking of a Quadrotor.

In order to achieve the complicated trajectory tracking of quadrotor, a geometric inner and outer loop control scheme is presented. The outer loop generates the desired rotation matrix for the inner loop. To improve the response speed and robustness, a geometric SMC controller is designed for the inner loop. The outer loop is also designed via sliding mode control (SMC). By Lyapunov theory and cascade theory, the closed-loop system stability is guaranteed. Next, the tracking performance is validated by tracking three representative trajectories. Then, the robustness of the proposed control method is illustrated by trajectory tracking in presence of model uncertainty and disturbances. Subsequently, experiments are carried out to verify the method. In the experiment, ultra wideband (UWB) is used for indoor positioning. Extended Kalman Filter (EKF) is used for fusing inertial measurement unit (IMU) and UWB measurements. The experimental results show the feasibility of the designed controller in practice. The comparative experiments with PD and PD loop demonstrate the robustness of the proposed control method.

Indoor Autonomous Control of a Two-Wheeled Inverted Pendulum Vehicle Using Ultra Wide Band Technology.

In this paper, we aimed to achieve the indoor tracking control of a two-wheeled inverted pendulum (TWIP) vehicle. The attitude data are acquired from a low cost micro inertial measurement unit (IMU), and the ultra-wideband (UWB) technology is utilized to obtain an accurate estimation of the TWIP's position. We propose a dual-loop control method to realize the simultaneous balance and trajectory tracking control for the TWIP vehicle. A robust adaptive second-order sliding mode control (2-RASMC) method based on an improved super-twisting (STW) algorithm is investigated to obtain the control laws, followed by several simulations to verify its robustness. The outer loop controller is designed using the idea of backstepping. Moreover, three typical trajectories, including a circle, a trifolium and a hexagon, have been designed to prove the adaptability of the control combinations. Six different combinations of inner and outer loop control algorithms have been compared, and the characteristics of inner and outer loop algorithm combinations have been analyzed. Simulation results demonstrate its tracking performance and thus verify the validity of the proposed control methods. Trajectory tracking experiments in a real indoor environment have been performed using our experimental vehicle to further validate the feasibility of the proposed algorithm in practice.

Structural Analysis of Disk Resonance Gyroscope.

In this paper, we present two design methods to improve the performance of disk resonator gyroscope (DRG), including decreasing the frequency split and increasing the quality factor (Q). The structure parameters, which can affect the frequency split and Q value were concluded with the help of the FEM software. Meanwhile, devices with different parameters were designed, fabricated, and tested, and the experimental result was in accordance with the simulation. With the proposed methods, the DRG was selected with a high Q value and a low frequency split to satisfy the demand of high performance. The weakness and future works were pointed at last.

Coupling Mechanism Analysis and Fabrication of Triaxial Gyroscopes in Monolithic MIMU.

A novel fully decoupled micro inertial measurement unit (MIMU) is presented in this paper. The proposed MIMU structure, mostly focusing on the gyroscope unit, is highly symmetrical and can be limited to an area of 10,000 µm × 10,000 µm. Both the tri-axis gyroscope and tri-axis accelerometer structures are fabricated on the same single silicon chip, which can differentially detect three axes' angular velocities and linear accelerated velocities at the same time. By elaborately arranging different decoupling beams, anchors and sensing frames, the drive and sense modes of the tri-axis gyroscope are fully decoupled from each other. Several dynamic models, including decoupling beams with fabrication imperfections, are established for theoretical analysis. The numerical simulation made by MATLAB shows the structural decoupling of three sense modes, and indicates that the key decoupling beams, which affect the quadrature error, can be improved in design. The whole fabrication process, including silicon on glass (SOG) process, dry/wet etching as well as the methods for improving the fabrication quality, is then shown. Experiments for mode frequency and quality factors of four modes (drive, yaw, pitch and roll) have been performed, and are found to be 455 (6950.2 Hz), 66 (7054.4 Hz), 109 (7034.2 Hz) and 107 (7040.5 Hz) respectively. The analysis and experiment both prove that this novel MIMU has the potential value of further intensive investigation.

A Digitalized Gyroscope System Based on a Modified Adaptive Control Method.

In this work we investigate the possibility of applying the adaptive control algorithm to Micro-Electro-Mechanical System (MEMS) gyroscopes. Through comparing the gyroscope working conditions with the reference model, the adaptive control method can provide online estimation of the key parameters and the proper control strategy for the system. The digital second-order oscillators in the reference model are substituted for two phase locked loops (PLLs) to achieve a more steady amplitude and frequency control. The adaptive law is modified to satisfy the condition of unequal coupling stiffness and coupling damping coefficient. The rotation mode of the gyroscope system is considered in our work and a rotation elimination section is added to the digitalized system. Before implementing the algorithm in the hardware platform, different simulations are conducted to ensure the algorithm can meet the requirement of the angular rate sensor, and some of the key adaptive law coefficients are optimized. The coupling components are detected and suppressed respectively and Lyapunov criterion is applied to prove the stability of the system. The modified adaptive control algorithm is verified in a set of digitalized gyroscope system, the control system is realized in digital domain, with the application of Field Programmable Gate Array (FPGA). Key structure parameters are measured and compared with the estimation results, which validated that the algorithm is feasible in the setup. Extra gyroscopes are used in repeated experiments to prove the commonality of the algorithm.

A Mode Matched Triaxial Vibratory Wheel Gyroscope with Fully Decoupled Structure.

To avoid the oscillation of four unequal masses seen in previous triaxial linear gyroscopes, a modified silicon triaxial gyroscope with a rotary wheel is presented in this paper. To maintain a large sensitivity and suppress the coupling of different modes, this novel gyroscope structure is designed be perfectly symmetrical with a relatively large size of about 9.8 mm × 9.8 mm. It is available for differentially detecting three-axis angular rates simultaneously. To overcome the coupling between drive and sense modes, numerous necessary frames, beams, and anchors are delicately figured out and properly arranged. Besides, some frequency tuning and feedback mechanisms are addressed in the case of post processing after fabrication. To facilitate mode matched function, a new artificial fish swarm algorithm (AFSA) performed faster than particle swarm optimization (PSO) with a frequency split of 108 Hz. Then, by entrusting the post adjustment of the springs dimensions to the finite element method (FEM) software ANSYS, the final frequency splits can be below 3 Hz. The simulation results demonstrate that the modal frequencies in drive and different sense modes are respectively 8001.1, 8002.6, 8002.8 and 8003.3 Hz. Subsequently, different axis cross coupling effects and scale factors are also analyzed. The simulation results effectively validate the feasibility of the design and relevant theoretical calculation.

Design and Analysis of a Novel Fully Decoupled Tri-axis Linear Vibratory Gyroscope with Matched Modes.

We present in this paper a novel fully decoupled silicon micromachined tri-axis linear vibratory gyroscope. The proposed gyroscope structure is highly symmetrical and can be limited to an area of about 8.5 mm × 8.5 mm. It can differentially detect three axes' angular velocities at the same time. By elaborately arranging different beams, anchors and sensing frames, the drive and sense modes are fully decoupled from each other. Moreover, the quadrature error correction and frequency tuning functions are taken into consideration in the structure design for all the sense modes. Since there exists an unwanted in-plane rotational mode, theoretical analysis is implemented to eliminate it. To accelerate the mode matching process, the particle swam optimization (PSO) algorithm is adopted and a frequency split of 149 Hz is first achieved by this method. Then, after two steps of manual adjustment of the springs' dimensions, the frequency gap is further decreased to 3 Hz. With the help of the finite element method (FEM) software ANSYS, the natural frequencies of drive, yaw, and pitch/roll modes are found to be 14,017 Hz, 14,018 Hz and 14,020 Hz, respectively. The cross-axis effect and scale factor of each mode are also simulated. All the simulation results are in good accordance with the theoretical analysis, which means the design is effective and worthy of further investigation on the integration of tri-axis accelerometers on the same single chip to form an inertial measurement unit.

The development of micromachined gyroscope structure and circuitry technology.

This review surveys micromachined gyroscope structure and circuitry technology. The principle of micromachined gyroscopes is first introduced. Then, different kinds of MEMS gyroscope structures, materials and fabrication technologies are illustrated. Micromachined gyroscopes are mainly categorized into micromachined vibrating gyroscopes (MVGs), piezoelectric vibrating gyroscopes (PVGs), surface acoustic wave (SAW) gyroscopes, bulk acoustic wave (BAW) gyroscopes, micromachined electrostatically suspended gyroscopes (MESGs), magnetically suspended gyroscopes (MSGs), micro fiber optic gyroscopes (MFOGs), micro fluid gyroscopes (MFGs), micro atom gyroscopes (MAGs), and special micromachined gyroscopes. Next, the control electronics of micromachined gyroscopes are analyzed. The control circuits are categorized into typical circuitry and special circuitry technologies. The typical circuitry technologies include typical analog circuitry and digital circuitry, while the special circuitry consists of sigma delta, mode matching, temperature/quadrature compensation and novel special technologies. Finally, the characteristics of various typical gyroscopes and their development tendency are discussed and investigated in detail.

A micro dynamically tuned gyroscope with adjustable static capacitance.

This paper presents a novel micro dynamically tuned gyroscope (MDTG) with adjustable static capacitance. First, the principle of MDTG is theoretically analyzed. Next, some simulations under the optimized structure parameters are given as a reference for the mask design of the rotor wafer and electrode plates. As two key components, the process flows of the rotor wafer and electrode plates are described in detail. All the scanning electron microscopy (SEM) photos show that the fabrication process is effective and optimized. Then, an assembly model is designed for the static capacitance adjustable MDTG, whose static capacitance can be changed by rotating the lower electrode plate support and substituting gasket rings of different thicknesses. Thus, the scale factor is easily changeable. Afterwards, the digitalized closed-loop measurement circuit is simulated. The discrete correction and decoupling modules are designed to make the closed-loop stable and cross-coupling effect small. The dual axis closed-loop system bandwidths can reach more than 60 Hz and the dual axis scale factors are completely symmetrical. All the simulation results demonstrate the proposed fabrication of the MDTG can meet the application requirements. Finally, the paper presents the test results of static and dynamic capacitance values which are consistent with the simulation values.

A digitalized silicon microgyroscope based on embedded FPGA.

This paper presents a novel digital miniaturization method for a prototype silicon micro-gyroscope (SMG) with the symmetrical and decoupled structure. The schematic blocks of the overall system consist of high precision analog front-end interface, high-speed 18-bit analog to digital convertor, a high-performance core Field Programmable Gate Array (FPGA) chip and other peripherals such as high-speed serial ports for transmitting data. In drive mode, the closed-loop drive circuit are implemented by automatic gain control (AGC) loop and software phase-locked loop (SPLL) based on the Coordinated Rotation Digital Computer (CORDIC) algorithm. Meanwhile, the sense demodulation module based on varying step least mean square demodulation (LMSD) are addressed in detail. All kinds of algorithms are simulated by Simulink and DSPbuilder tools, which is in good agreement with the theoretical design. The experimental results have fully demonstrated the stability and flexibility of the system.

Temperature effects and compensation-control methods.

In the analysis of the effects of temperature on the performance of microgyroscopes, it is found that the resonant frequency of the microgyroscope decreases linearly as the temperature increases, and the quality factor changes drastically at low temperatures. Moreover, the zero bias changes greatly with temperature variations. To reduce the temperature effects on the microgyroscope, temperature compensation-control methods are proposed. In the first place, a BP (Back Propagation) neural network and polynomial fitting are utilized for building the temperature model of the microgyroscope. Considering the simplicity and real-time requirements, piecewise polynomial fitting is applied in the temperature compensation system. Then, an integral-separated PID (Proportion Integration Differentiation) control algorithm is adopted in the temperature control system, which can stabilize the temperature inside the microgyrocope in pursuing its optimal performance. Experimental results reveal that the combination of microgyroscope temperature compensation and control methods is both realizable and effective in a miniaturized microgyroscope prototype.

Development of a prototype miniature silicon microgyroscope.

A miniature vacuum-packaged silicon microgyroscope (SMG) with symmetrical and decoupled structure was designed to prevent unintended coupling between drive and sense modes. To ensure high resonant stability and strong disturbance resisting capacity, a self-oscillating closed-loop circuit including an automatic gain control (AGC) loop based on electrostatic force feedback is adopted in drive mode, while, dual-channel decomposition and reconstruction closed loops are applied in sense mode. Moreover, the temperature effect on its zero bias was characterized experimentally and a practical compensation method is given. The testing results demonstrate that the useful signal and quadrature signal will not interact with each other because their phases are decoupled. Under a scale factor condition of 9.6 mV/(°)/s, in full measurement range of ± 300 deg/s, the zero bias stability reaches 15(°)/h with worse-case nonlinearity of 400 ppm, and the temperature variation trend of the SMG bias is thus largely eliminated, so that the maximum bias value is reduced to one tenth of the original after compensation from -40 (°)C to 80 (°)C.