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

NASA Tech Briefs, October 2003

Topics covered include: Cryogenic Temperature-Gradient Foam/Substrate Tensile Tester; Flight Test of an Intelligent Flight-Control System; Slat Heater Boxes for Thermal Vacuum Testing; System for Testing Thermal Insulation of Pipes; Electrical-Impedance-Based Ice-Thickness Gauges; Simulation System for Training in Laparoscopic Surgery; Flasher Powered by Photovoltaic Cells and Ultracapacitors; Improved Autoassociative Neural Networks; Toroidal-Core Microinductors Biased by Permanent Magnets; Using Correlated Photons to Suppress Background Noise; Atmospheric-Fade-Tolerant Tracking and Pointing in Wireless Optical Communication; Curved Focal-Plane Arrays Using Back-Illuminated High-Purity Photodetectors; Software for Displaying Data from Planetary Rovers; Software for Refining or Coarsening Computational Grids; Software for Diagnosis of Multiple Coordinated Spacecraft; Software Helps Retrieve Information Relevant to the User; Software for Simulating a Complex Robot; Software for Planning Scientific Activities on Mars; Software for Training in Pre-College Mathematics; Switching and Rectification in Carbon-Nanotube Junctions; Scandia-and-Yttria-Stabilized Zirconia for Thermal Barriers; Environmentally Safer, Less Toxic Fire-Extinguishing Agents; Multiaxial Temperature- and Time-Dependent Failure Model; Cloverleaf Vibratory Microgyroscope with Integrated Post; Single-Vector Calibration of Wind-Tunnel Force Balances; Microgyroscope with Vibrating Post as Rotation Transducer; Continuous Tuning and Calibration of Vibratory Gyroscopes; Compact, Pneumatically Actuated Filter Shuttle; Improved Bearingless Switched-Reluctance Motor; Fluorescent Quantum Dots for Biological Labeling; Growing Three-Dimensional Corneal Tissue in a Bioreactor; Scanning Tunneling Optical Resonance Microscopy; The Micro-Arcsecond Metrology Testbed; Detecting Moving Targets by Use of Soliton Resonances; and Finite-Element Methods for Real-Time Simulation of Surgery

Fabrication of high aspect ratio vibrating cylinder microgyroscope structures by use of the LIGA process

Inertial grade microgyroscopes are of great importance to improve and augment inertial navigation systems based on GPS for industrial, automotive, and military applications. The efforts by various research groups worldwide to develop inertial grade microgyroscopes have not been successful to date. In 1994, the Department of Mechanical Engineering at Louisiana State University and SatCon Technology Corporation (Boston, Massachusetts) proposed a series of shock tolerant micromachined vibrating cylinder rate gyroscopes with aspect ratios of up to 250:1 to meet the needs of inertial navigation systems based on existing conventional vibrating cylinder gyroscopes. Each microgyroscope consisted of a tall thin shell metallic cylinder attached to a substrate at one end and surrounded by four drive- and four sense-electrodes. The proposed drive- and sense-mechanisms were capacitive-force and capacitance-change, respectively. Since the high aspect ratio metallic microgyroscope structures could not be fabricated by using traditional silicon-based MEMS processes, a LIGA-based two layer fabrication process was developed. A wiring layer was constructed by using a combination of thick film photolithography and electroplating (nickel and gold) on a silicon substrate covered with silicon nitride and a tri-layer plating base; aligned X-ray lithography and nickel electroplating were used to build the high aspect ratio cylinders and electrodes. Deficiencies in the LIGA process were also addressed in this research. Three types of X-ray mask fabrication processes for multi-level LIGA were developed on graphite, borosilicate glass and silicon nitride substrates. Stable and reliable gold electroplating methods for X-ray masks were also established. The plating rate and internal stress of deposits were thoroughly characterized for two brands of commercially available sulfite-based gold electroplating solutions, Techni Gold 25E and NEUTRONEX 309. The gaps between the cylinders and electrodes, which are defined by thin PMMA walls during electroplating, were found to be smaller than designed and deformed in many of the microgyroscope structures. The lateral dimensional loss (LDL) and deformation were identified to be related to the overall thickness and lateral aspect ratio (LAR) of the thin PMMA walls

System and circuit design for a capacitive MEMS gyroscope

In this thesis, issues related to the design and implementation of a micro-electro-mechanicalangular velocity sensor are studied. The work focuses on a system basedon a vibratory microgyroscope which operates in the low-pass mode with a moderateresonance gain and with an open-loop configuration of the secondary (sense) resonator.Both the primary (drive) and the secondary resonators are assumed to have a high qualityfactor. Furthermore, the gyroscope employs electrostatic excitation and capacitivedetection. The thesis is divided into three parts. The first part provides the background informationnecessary for the other two parts. The basic properties of a vibratory microgyroscope,together with the most fundamental non-idealities, are described, a shortintroduction to various manufacturing technologies is given, and a brief review of publishedmicrogyroscopes and of commercial microgyroscopes is provided. The second part concentrates on selected aspects of the system-level design of amicro-electro-mechanical angular velocity sensor. In this part, a detailed analysis isprovided of issues related to different non-idealities in the synchronous demodulation,the dynamics of the primary resonator excitation, the compensation of the mechanicalquadrature signal, and the zero-rate output. The use of ΣΔ modulation to improveaccuracy in both primary resonator excitation and the compensation of the mechanicalquadrature signal is studied. The third part concentrates on the design and implementation of the integratedelectronics required by the angular velocity sensor. The focus is primarily on the designof the sensor readout circuitry, comprising: a continuous-time front-end performingthe capacitance-to-voltage (C/V) conversion, filtering, and signal level normalization;a bandpass ΣΔ analog-to-digital converter, and the required digital signal processing(DSP). The other fundamental circuit blocks, which are a phase-locked loop requiredfor clock generation, a high-voltage digital-to-analog converter for the compensationof the mechanical quadrature signal, the necessary charge pumps for the generationof high voltages, an analog phase shifter, and the digital-to-analog converter used togenerate the primary resonator excitation signals, together with other DSP blocks, areintroduced on a more general level. Additionally, alternative ways to perform the C/Vconversion, such as continuous-time front ends either with or without the upconversionof the capacitive signal, various switched-capacitor front ends, and electromechanicalΣΔ modulation, are studied. In the experimental work done for the thesis, a prototype of a micro-electro-mechanicalangular velocity sensor is implemented and characterized. The analog partsof the system are implemented with a 0.7-µm high-voltage CMOS (ComplimentaryMetal-Oxide-Semiconductor) technology. The DSP part is realized with a field-programmablegate array (FPGA) chip. The ±100°/s gyroscope achieves 0.042°/s/√H̅z̅spot noise and a signal-to-noise ratio of 51.6 dB over the 40 Hz bandwidth, with a100°/s input signal. The implemented system demonstrates the use of ΣΔ modulation in both the primaryresonator excitation and the quadrature compensation. Additionally, it demonstratesphase error compensation performed using DSP. With phase error compensation,the effect of several phase delays in the analog circuitry can be eliminated, andthe additional noise caused by clock jitter can be considerably reduced

Design, Modeling, and Nonlinear Dynamics of a Cantilever Beam-Rigid Body Microgyroscope

A new type of cantilever beam gyroscope is introduced, modeled, and analyzed. The main structure includes a cantilever beam and a rigid body attached to the free end of the beam. The model accounts for the eccentricity, that is the offset of the center of mass of the rigid body relative to the beam's free end. The first and second moments of mass and the rotary inertia appear in the equations of motion and boundary conditions. The common mechanism of electrostatic actuation of microgyroscopes is used with the difference of computing the force at the center of mass resulting in the electrostatic force and moment in the boundary conditions. By using the extended Hamilton's principle, the method of assumed modes, and Lagrange's differential equations, the equations of motion, boundary conditions, and the discretized model are developed. The generalized model simplifies to other beam gyroscope models by setting the required parameters to zero. Considering the DC and AC components of the actuating and sensing methods, the response is resolved into the static and dynamic components. The static configuration is studied for an increasing DC voltage. For the uncoupled system of equations, the explicit equation relating the DC load and the static configuration is computed and solved for the static configuration of the beam-rigid body in each direction. Including the rotation rate, the stationary analysis is performed, the stationary pull-in voltage is identified, and it is shown that the angular rotation rate does not affect the static configuration. The modal frequencies of the beam-rigid body gyroscope are studied and the instability region due to the rotation rate is computed. It is shown that the gyroscope can operate in the frequency modulation mode and the amplitude modulation mode. To operate the beam-rigid body gyroscope in the frequency modulation mode, the closed-form relation of the observed modal frequency split and the input rotation rate is computed. The calibration curves are generated for a variety of DC loads. It is shown that the scale factor improves by matching the zero rotation rate natural frequencies. The method of multiple scales is used to study the reduced-order nonlinear dynamics of the oscillations around the static equilibrium. The modulation equations, the ``slow'' system, are derived and solved for the steady-state solutions. The computational shooting method is employed to evaluate the results of the perturbation method. The frequency response and force response plots are generated. For combinations of parameters resulting in a single-valued response, the two methods are in excellent agreement. The synchronization of the response occurs in the sense direction for initially mismatched natural frequencies. The global stability of the system is studied by drawing phase-plane diagrams and long-time integration of response trajectories. The separatrices are computed, the jump phenomena is numerically shown, and the dynamic pull-in of the response is demonstrated. The fold bifurcation points are identified and it is shown that the response jumps to the higher/lower branch beyond the bifurcation points in forward/backward sweep of the amplitude and the excitation frequency of AC voltage. The mechanical-thermal (thermomechanical) noise effect on the sense response is characterized by using a linear approximation of the system and the nonlinear "slow" system obtained by using the method of multiple scales. To perform linear analysis, the negligible effect of Coriolis force on the drive amplitude is discarded. The second-order drive resonator is solved for the drive amplitude and phase. Finding the sense response due to the thermal noise force and the Coriolis force and equating them computes the mechanical-thermal noise equivalent rotation rate in terms of system parameters and mode shapes. The noise force is included in the third-order equation of the perturbation and equation to account for that in the reduced-order nonlinear response. The numerical results of linear and reduced-order nonlinear thermal noise analyses agree. It is shown that higher quality factor, higher AC voltage, and operating at lower DC points result in better resolution of the microsensor

A dual-mass resonant mems gyroscope design with electrostatic tuning for frequency mismatch compensation

The micro-electro-mechanical systems (MEMS)-based sensor technologies are considered to be the enabling factor for the future development of smart sensing applications, mainly due to their small size, low power consumption and relatively low cost. This paper presents a new structurally and thermally stable design of a resonant mode-matched electrostatic z-axis MEMS gyroscope considering the foundry constraints of relatively low cost and commercially available silicon-on-insulator multi-user MEMS processes (SOIMUMPs) microfabrication process. The novelty of the proposed MEMS gyroscope design lies in the implementation of two separate masses for the drive and sense axis using a unique mechanical spring configuration that allows minimizing the cross-axis coupling between the drive and sense modes. For frequency mismatch compensation between the drive and sense modes due to foundry process uncertainties and gyroscope operating temperature variations, a comb-drive-based electrostatic tuning is implemented in the proposed design. The performance of the MEMS gyroscope design is verified through a detailed coupled-field electric-structural-thermal finite element method (FEM)-based analysis

Design and Analysis of Nano Vibratory Beam Gyroscope

Gyroscope is an angular rate measurement sensor having broad application in the field of automotive, military services, aerospace and consumer electronics industries. Silicon micro machined MEMS vibratory gyroscopes have better advantages compared to conventional gyroscope. Nano beam vibratory gyroscope is one of the simple gyroscope. It has relatively small size, light weight, low power consumption, low cost and simple structure. When a gyroscope is made to rotate at its base along with some excitation in one of the bending direction, due to Coriolis effect, there will be significant displacement in other bending direction. Dynamic modeling of beam gyroscope is very interesting area. In the micro/nano level actuation and sensing are with electrostatics principles. This report presents the modeling and analytical simulation task of a nano cantilever beam gyroscope. Static and dynamic analysis of a nano/micro cantilever gyroscope with a tip mass is studied. Pull-in instability corresponding voltage is estimated from static and frequency response. Pull-in stability regions are identified as a function of beam length, tip mass value, elastic modulus of the beam. Nonlinearities due to geometry and the external forces including electrostatic and van der Waals forces are considered during modelling. Squeeze film and slide film damping are considered to account the damping force between the tip mass and sense and drive direction. The dynamic solution is obtained by using Galerkin’s reduction scheme. The time response and the frequency domain graphs are arrived for different parameters on both sense and drive directions. The interactive program developed in the work are helpful to account any experiments for additional force at nano leve

Coherent oscillations of a levitated birefringent microsphere in vacuum driven by nonconservative rotation-translation coupling

Funding: UK Engineering and Physical Sciences Research Council (EP/P030017/1) and Czech Science Agency (GA19-17765S).We demonstrate an effect whereby stochastic, thermal fluctuations combine with nonconservative optical forces to break detailed balance and produce increasingly coherent, apparently deterministic motion for a vacuum-trapped particle. The particle is birefringent and held in a linearly polarized Gaussian optical trap. It undergoes oscillations that grow rapidly in amplitude as the air pressure is reduced, seemingly in contradiction to the equipartition of energy. This behavior is reproduced in direct simulations and captured in a simplified analytical model, showing that the underlying mechanism involves nonsymmetric coupling between rotational and translational degrees of freedom. When parametrically driven, these self-sustained oscillators exhibit an ultranarrow linewidth of 2.2 μHz and an ultrahigh mechanical quality factor in excess of 2 × 108 at room temperature. Last, nonequilibrium motion is seen to be a generic feature of optical vacuum traps, arising for any system with symmetry lower than that of a perfect isotropic microsphere in a Gaussian trap.Publisher PDFPeer reviewe