High-Performance Micromachined Vibratory Rate- and Rate-Integrating Gyroscopes.

We aim to reduce vibration sensitivity by developing gyros that operate in the balanced mode. The balanced mode creates zero net momentum and reduces energy loss through an anchor. The gyro can differentially cancel measurement errors from external vibration along both sensor axes. The vibration sensitivity of the balanced-mode gyroscope including structural imbalance from microfabrication reduces as the absolute difference between in-phase parasitic mode and operating mode frequencies increases. The parasitic sensing mode frequency is designed larger than the operating mode frequency to achieve both improved vibration insensitivity and shock resistivity. A single anchor is used to minimize thermoresidual stress change. We developed two gyroscope based on these design principles. The Balanced Oscillating Gyro (BOG) is a quad-mass tuning-fork rate gyroscope. The relationship between gyro design and modal characteristics is studied extensively using finite element method (FEM). The gyro is fabricated using the planar Si-on-glass (SOG) process with a device thickness of 100 micrometers. The BOG is evaluated using the first-generation analog interface circuitry. Under a frequency mismatch of 5Hz between driving and sense modes, the angle random walk (ARW) is measured to be 0.44deg/sec/sqrt(Hz). The Cylindrical Rate-Integrating Gyroscope (CING) operates in whole-angle mode. The gyro is completely axisymmetric and self-aligned to maximize mechanical isotropy. The gyro offers a large frequency ratio of ~1.7 between parasitic and the wineglass modes. The CING is fabricated using the 3D Si-on-glass (SOG) process with a device thickness of 300 micrometers. The 1st and 2nd generation CINGs operate at 18kHz and 3kHz, respectively and demonstrate a frequency mismatch of <1% and a large Q (~20,000 at 18kHz and ~100,000 at 3kHz under exact mode matching). In the rate-sensing mode, the first-generation CING (18kHz) demonstrates an Ag of 0.05, an angle random walk (ARW) of 7deg/sqrt(hr), and a bias stability of 72deg/hr without temperature compensation. In the rate-sensing mode, the second-generation CING measures an Ag of 0.0065, an ARW of 0.09deg/sqrt(hr), and a bias stability of 129deg/hr without temperature compensation. In the rate-integration mode, the second-generation CING demonstrates precession with an Ag of 0.011±0.001 under a frequency mismatch of 20~80mHz during several hours of operation.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91440/1/jycho_1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/91440/2/jycho_2.pd

Fixed-wing MAV attitude stability in atmospheric turbulence, part 1: Suitability of conventional sensors

Fixed-wing Micro-Aerial Vehicles (MAVs) need effective sensors that can rapidly detect turbulence induced motion perturbations. Current MAV attitude control systems rely on inertial sensors. These systems can be described as reactive; detecting the disturbance only after the aircraft has responded to the disturbing phenomena. In this part of the paper, the current state of the art in reactive attitude sensing for fixed-wing MAVs are reviewed. A scheme for classifying the range of existing and emerging sensing techniques is presented. The features and performance of the sensing approaches are discussed in the context of their application to MAV attitude control systems in turbulent environments. It is found that the use of single sensors is insufficient for MAV control in the presence of turbulence and that potential gains can be realised from multi-sensor systems. A successive paper to be published in this journal will investigate novel attitude sensors which have the potential to improve attitude control of MAVs in Turbulenc

Design and Analysis of Extremely Low-Noise MEMS Gyroscopes for Navigation

Inertial measurement sensors that include three gyroscopes and three accelerometers are key elements of inertial navigation systems. Miniaturization of these sensors is desirable to achieve low manufacturing cost, high durability, low weight, small size, and low energy consumption. However, there is a tradeoff between miniaturization of inertial sensors and their performance. Developing all the necessary components for navigation using inertial sensors in a small volume requires major redesign and innovation in these sensors. The main goal of this research is to identify, analyze and optimize parameters that limit the performance of miniaturized inertial gyroscopes and provide comprehensive design guidelines for achieving multi-axis navigation-grade MEMS gyroscopes. It is shown that the fundamental performance limit of inertial gyroscopes is angle random walk (ARW) due to thermo-mechanical and electronic noises. Theoretical models show that resonant frequency, frequency mismatch between sensing and driving modes, effective mass, quality factor (Q), driving amplitude, sensing gap, sensing area and angular gain are the most important parameters that need to be optimized for best noise and most practical device design. In this research, two different structures are considered for low-noise MEMS gyroscopes: 1) shell gyroscopes in yaw direction, and 2) a novel super sensitive stacked (S3) gyroscope for pitch/roll directions. Extensive analytical and FEM numerical modeling was conducted throughout this research to investigate the mechanisms that affect Q and noise in shell resonators used in yaw-rate gyroscopes. These models provided insight into ways to significantly improve resonator design, structure, fabrication, and assembly and helped fabricate fused silica shells with Qs as high as 10 million (at least an order of magnitude larger than other similar shells). Noise performance of these fused silica shell gyroscopes with 5 mm dimeter improved by about two orders of magnitude (< 5×10-3 °/√hr), representing one of the best noise performances reported for a MEMS gyroscope. To build a high-performance MEMS-based planar vibratory pitch/roll gyroscope, it is critical to have a resonator with high Q in the out-of-plane resonant mode. Existing out-of-plane resonators suffer from low Q due to anchor loss or/and thermoelastic dissipation (TED). Increasing the thickness of the out-of-plane resonator reduces TED, but this increases the anchor loss. To reduce anchor loss significantly, a novel structure called S3 is designed. In this structure, two similar resonators are stacked on top of each other and move in opposite directions, thus providing a balanced stacked resonator with reduced anchor loss. The reduction of anchor loss allows larger thickness of silicon S3 gyroscopes, leading to a very low TED. A large-scale model of a stacked balanced resonator is fabricated and tested. The initial results show more than 50 times improvement in Q (measured in air) when resonators are stacked. It is expected that by testing this device in vacuum, Q would improve by more than three orders of magnitude. The S3 design also has an extremely large effective mass, a very large angular gain, a large driving amplitude, a very small sensing gap, and a large sensing area. It is estimated that a 500 µm thick silicon S3 gyroscope provides ARW of about 1.5×10-5 °/√hr (more than two orders of magnitude better performance than a navigation-grade gyroscope). This extraordinary small value can be improved for 1mm thick fused silica to 7.6×10-7 °/√hr if the technology for etching fused silica could be developed in the future.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147701/1/darvishi_1.pd

High-Q Fused Silica Micro-Shell Resonators for Navigation-Grade MEMS Gyroscopes

This research aims to develop the resonator for a navigation-grade microelectromechanical system (MEMS) Coriolis vibratory gyroscope (CVG) that will bring inertial navigation capabilities to a wider range of applications by reducing gyroscope size and cost. To achieve the desired gyroscope performance, the gyroscope resonator must have low energy dissipation and a highly symmetric structure. Several challenges arise at the micro-scale due to the increased sensitivity to imperfections and increased susceptibility to energy loss mechanisms. This work investigates the lower limit on energy dissipation in a micro-shell resonator known as the birdbath (BB) resonator. The BB resonator is designed to mitigate the energy loss mechanisms that commonly limit MEMS resonators, including anchor loss and thermoelastic dissipation, through a unique shape and fabrication process and through the use of fused silica as the structural material. A blowtorch molding process is used to form high aspect ratio fused silica shells with a range of wall profiles, providing a high level of control in three dimensions that is not possible with conventional micromachining techniques. Prototype BB resonators were developed prior to this dissertation work but they achieved low quality factors (Q) and low ring-down time constants (T) on the order of 100 thousand and 1 s, respectively. The goal of this work is to drastically increase performance above these initial results. Each relevant energy loss mechanism is considered in order to identify the dominant loss mechanism for a given device. Process improvements are implemented to mitigate each loss mechanism, including improved thermal management during blowtorch molding, cleaner lapping and polishing, reduced upfront surface contamination, and methods to remove contaminants after fabrication. Following optimization, Qs up to 10 million and Ts up to 500 s are measured, representing a marked improvement over the prototype resonators. It is found that BB resonators are now limited by surface loss, as indicated by the observed inverse relationship between Q and surface-to-volume ratio. The surface-loss-limited regime results in a high sensitivity to added surface layers. The addition of a conductive layer to enable electrostatic transduction is found to have a large impact, decreasing Q by 50% with the addition of only 30 angstroms of metal. It is suggested that the origin of this loss may be interfacial slippage due to a large increase in stress that occurs at the interface during oscillation. Experimental investigation into the dependence of Q on conductive layer composition, thickness, deposition conditions, and post-deposition treatments is carried out. Following treatments to removed adsorbed contaminants from the surface, resonators with a 15/50 angstrom Ti/Pt layer are found to maintain 60% of their initial Qs. Indium tin oxide (ITO) is identified as a promising conductive layer candidate, with initial experiments producing shells that maintain 70% of their initial Q. The values of Q and T produced in this work are unprecedented for MEMS resonators. Even accounting for the losses that accompany conductive layer deposition, birdbath resonator gyroscopes are expected to achieve navigation-grade performance.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146096/1/taln_1.pd

Phase-advanced attitude sensing and control for fixed-wing micro aerial vehicles in turbulence

The scale of fixed-wing Micro Aerial Vehicles (MAVs) lend them to many unique applications. These applications often require low speed flights close to the ground, in the vicinity of large obstacles and in the wake of buildings. A particular challenge for MAVs is attitude control in the presence of high turbulence. Such flights pose a challenging operational environment for MAVs, and in particular, ensuring sufficient attitude control in the presence of significant turbulence. Low-level flight in the atmospheric boundary layer without sufficient attitude control is hazardous, mainly due to the high levels of turbulence intensity close to the ground. MAV accidents have occurred due to the lack of a reliable attitude control system in turbulent conditions as reported in the literature. Challenges associated with flight control of fixed-wing MAVs operating in complex environments are significantly different to any larger scale vehicle. The scale of MAVs makes them particularly sensitive to atmospheric disturbances thus limiting their operation. A review of the literature revealed that rolling inputs from turbulence were the most challenging whereby conventional inertial-based attitude control systems lack the responsiveness for roll control in high turbulence environments. The solution might lie with flying animals, which have adapted to flight within turbulence. The literature survey identified bio-inspired phase-advanced sensors as a promising sensory solution for complementing current reactive attitude sensors. The development of a novel bio-inspired phase-advanced sensor and associated control system, which can sense the flow disturbances before an attitude perturbation, is the focus of this research. The development of such a system required an in-depth understanding of the features of the disturbing phenomena; turbulence. Correlation studies were conducted between the oncoming turbulence and wing-surface pressure variations. It was found that the highest correlation exists between upstream flow pitch angle variation and the wing-surface pressure fluctuations. However, due to the insufficient time-forward advantage, surface pressure sensing was not used for attitude control. A second sensing approach was explored to cater for the control system&amp;rsquo;s time-lags. Multi-hole pressure probes were embedded in the wings of the MAV to sense flow pitch angle and magnitude variation upstream of the wing. The sensors provide an estimate of the disturbing turbulence. This approach caters for the time-lags of the system providing sufficient time to counteract the gust before it results in an inertial response. Statistical analysis was used to assess the disturbance rejection performance of the phase-advanced sensory system, which was benchmarked against a conventional inertial-based sensory system in a range of turbulence conditions. Unconstrained but controlled test flights were conducted inside the turbulence environment of two wind-tunnels, in addition to outdoor flight testing in the atmosphere. These three different turbulence conditions enabled testing of a wide range of turbulence spectra believed to be most detrimental to the MAV. A significant improvement in disturbance rejection performance was observed in relation to conventional inertial-based sensory systems. It can be concluded that sensory systems providing time-forward estimates of turbulence can complement conventional inertial-based sensors to improve the attitude stability performance

Technologies for single chip integrated optical gyroscopes

Optical gyroscopes are being employed for navigational purposes for decades now and have achieved comparable or better reliability and performance than rotor-based gyroscopes. Mechanical gyros are however generally bulky, heavy and consume more power which make them unsuitable for miniaturized applications such as cube satellites and drones etc. Therefore, much effort is being expended worldwide to fabricate optical gyros having tactical grade robustness and reliability, small size, weight, cost and power consumption with minimal sacrifice of sensitivity. Integrated optics is an obvious approach to achieving this. This work comprises detailed comparative analysis of different types and structures of integrated optical gyroscopes to find out the suitable option for applications which require a resolution of <10 o/h. Based on the numerical analysis, Add-drop ring resonator-based gyro is found to be a suitable structure for integration which has a predicted shot noise limited resolution of 27 o/h and 2.71 o/h for propagation losses of 0.1 dB/cm and 0.01 dB/cm respectively. An integrated gyro is composed of several optical components which include a laser, 3dB couplers, phase/frequency modulators, sensing cavity and photodetectors. This requires hybrid integration of multiple materials technologies and so choices about which component should be implemented in which technology. This project also undertakes theoretical optimization of few of the above-mentioned optical components in materials systems that might offer the most convenient/tolerant option, this including 3dB coupler, thermo-optic phase modulator and sensing cavity (resonator and waveguide loop). In particular, the sensing element requires very low propagation loss waveguides which can best be realised from Si3N4 or Ta2O5. The optimised Si3N4 or Ta2O5 waveguides however are not optimal for other functions and this is shown and alternatives explored where the Si3N4 or Ta2O5 can easily be co-integrated. The fabrication process of low loss Si3N4 and Ta2O5 waveguides are also reported in this thesis. Si3N4 films were grown by using low pressure chemical vapor deposition (LPCVD) technique. Dry etching of Si3N4 films have been optimized to produce smooth and vertical sidewalls. Experimental results predicted that the propagation loss of 0.009 dB/cm is achievable by using optimum waveguide dimensions and silica cladding with the relatively standard processes available within the Laser Physics Centre at the Australian National University. A CMOS back end of line compatible method was developed to deposit good quality Ta2O5 films and silica claddings through ion beam sputtering (IBS) method. Plasma etching of Ta2O5 waveguides has been demonstrated by using a gas combination of CHF3/SF6/Ar/O2. Oxygen was introduced into the chamber to produce non-vertical sidewalls, so the waveguides could be cladded without voids with IBS silica. Average propagation losses of 0.17 dB/cm were achieved from Ta2O5 waveguides which appeared after extensive investigation to be limited by the spatial inhomogeneity of the processing. Lastly, a detailed theoretical and experimental analysis was performed to find out the possible causes of the higher average propagation loss in Ta2O5 waveguides, some sections being observed with 0.02 dB/cm or lower losses

Adaptively controlled MEMS triaxial angular rate sensor

Prohibitive cost and large size of conventional angular rate sensors have limited their use to large scale aeronautical applications. However, the emergence of MEMS technology in the last two decades has enabled angular rate sensors to be fabricated that are orders of magnitude smaller in size and in cost. The reduction in size and cost has subsequently encouraged new applications to emerge, but the accuracy and resolution of MEMS angular rate sensors will have to be greatly improved before they can be successfully utilised for such high end applications as inertial navigation. MEMS angular rate sensors consist of a vibratory structure with two main resonant modes and high Q factors. By means of an external excitation, the device is driven into a constant amplitude sinusoidal vibration in the first mode, normally at resonance. When the device is subject to an angular rate input, Coriolis acceleration causes a transfer of energy between the two modes and results in a sinusoidal motion in the second mode, whose amplitude is a measure of the input angular rate. Ideally the only coupling between the two modes is the Coriolis acceleration, however fabrication imperfections always result in some cross stiffness and cross damping effects between the two modes. Much of the previous research work has focussed on improving the physical structure through advanced fabrication techniques and structural design; however attention has been directed in recent years to the use of control strategies to compensate for these structural imperfections. The performance of the MEMS angular rate sensors is also hindered by the effects of time varying parameter values as well as noise sources such as thermal-mechanical noise and sensing circuitry noise. In this thesis, MEMS angular rate sensing literature is first reviewed to show the evolu- tion of MEMS angular rate sensing from the basic principles of open-loop operation to the use of complex control strategies designed to compensate for any fabrication imperfections and time-varying effects. Building on existing knowledge, a novel adaptively controlled MEMS triaxial angular rate sensor that uses a single vibrating mass is then presented. Ability to sense all three components of the angular rate vector with a single vibrating mass has advantages such as less energy usage, smaller wafer footprint, avoidance of any mechanical interference between multiple resonating masses and removal of the need for precise alignment of three separate devices. The adaptive controller makes real-time estimates of the triaxial angular rates as well as the device cross stiffness and cross damping terms. These estimates are then used to com- pensate for their effects on the vibrating mass, resulting in the mass being controlled to follow a predefined reference model trajectory. The estimates are updated using the error between the reference model trajectory and the mass&#039;s real trajectory. The reference model trajectory is designed to provide excitation to the system that is sufficiently rich to enable all parameter estimates to converge to their true values. Avenues for controller simplification and optimisation are investigated through system simulations. The triaxial controller is analysed for stability, averaged convergence rate and resolution. The convergence rate analysis is further utilised to determine the ideal adaptation gains for the system that minimises the unwanted oscillatory behaviour of the parameter estimates. A physical structure for the triaxial device along with the sensing and actuation means is synthesised. The device is realisable using MEMS fabrication techniques due to its planar nature and the use of conventional MEMS sensing and actuation elements. Independent actuation and sensing is achieved using a novel checkerboard electrode arrangement. The physical structure is refined using a design automation process which utilises finite element analysis (FEA) and design optimisation tools that adjust the design variables until suitable design requirements are met. Finally, processing steps are outlined for the fabrication of the device using a modified, commercially available polysilicon MEMS process

Using electrostatic nonlinearities to enhance the performance of ring-based Coriolis vibratory gyroscopes

This research investigates electrostatic nonlinearities in capacitively operated ring-based Coriolis vibrating gyroscopes (CVG’s). Large amplitude vibrations of the ring amplify the Coriolis force and are beneficial to achieving high-precision rate sensing. However, due to the miniature sizes of these devices and the narrow capacitive gaps, electrostatic nonlinearities manifest at relatively small ring displacements, thus resulting in the sensor output differing from what is expected of a standard linear device. As such, the current theory of operation commonly perceives electrostatic nonlinearities as an obstacle towards the development of high performance sensors. Electrostatic nonlinearities is the dominant source of nonlinearity in ring-based CVG’s. This work develops a mathematical model to analyse the influence of electrostatic nonlinearities on device performance. When the device operates using a basic electrostatic configuration incorporating only bias and drive voltages, it is found that the bias voltage induces single and mode-coupled cubic restoring forces, which are the main mechanisms through which electrostatic nonlinearities affect the ring dynamics and sensor output. These nonlinear restoring forces result in the amplitude-dependency of the drive and sense mode frequencies, and the presence of self-induced parametric excitation. These effects, in conjunction with the structural imperfections of the ring, degrade rate sensing performance by reducing the rate sensitivity and introducing bias rates and quadrature errors at larger drive amplitudes. A detailed theoretical analysis of the sense dynamics concludes that, depending on the interaction between the imperfections and the electrostatic nonlinearities, there are specific cases where the self-induced parametric excitation can enhance the rate sensitivity of the device. However, this enhancement cannot be achieved while retaining a trimmed sense response to keep the bias rate and quadrature error nullified. An analysis of the sense response and the modal forces shows that the imperfection-induced linear elastic coupling force and the nonlinear frequency imbalance are specifically responsible for the sensor output degradation. These nonlinear behaviours have also been validated against finite element results. The research also investigates the strategic use of electrostatic forces to counteract the effects of nonlinearity and enhance device performance. It is shown that through careful selection of the voltages applied to the electrodes, the form of the resulting electrostatic forces can be tailored to manipulate the sense mode dynamics for device performance enhancement. The presented work develops a general framework to achieve this direct electrostatic force manipulation by considering the variations of the capacitance, voltage and electrostatic potential energy from electrode to electrode, which then enables direct control of the form of the total electrostatic potential energy. Through the use of the framework, this research shows that the electrostatic nonlinearities can be manipulated to replicate the sensor outputs of a linear, trimmed device at larger drive amplitudes, or achieving parametric amplification of the sense response to enhance rate sensitivity without inducing bias rates and quadrature errors. The proposed general framework is used to determine the electrostatic configurations capable of negating self-induced parametric excitation by generating a separate parametric excitation in antiphase with the self-induced parametric excitation. The proposed implementation has potential to reduce sensor output nonlinearity and is most effective in devices where the drive amplitude dependencies of the drive and sense modes are equal, thus resulting in amplitude-insensitive frequency detuning in a manner similar to linear devices. This implementation can also be used in conjunction with a balancing voltage component to eliminate quadrature errors present in the sensor output caused by linear elastic coupling and nonlinear frequency imbalance. The combination of using parametric pumping and balancing voltage components trims the sensor output and have potential to suppress the sensor output nonlinearity further. The effectiveness of the chosen electrostatic configuration is validated against results from transient finite element studies. Rate measuring performance is enhanced further by parametrically exciting the sensor output to increase the quality factor of the device. To achieve enhanced performance the parametric excitation must be phase-tuneable and the proposed general framework is used to select electrostatic configurations capable of providing the required parametric excitation. Two approaches to develop the required parametric excitation are investigated. The first approach exploits linear electrostatic forces whilst the second approach uses quadratic electrostatic forces. Both approaches are shown to have potential to improve rate sensitivity through Q factor enhancing effects. However, the parametric excitation from the quadratic electrostatic forces is generally weaker unless compensated using larger parametric pumping voltages. On the other hand, it is found that the quadratic electrostatic forces promote nonlinear frequency balancing and so this approach is considered advantageous for achieving trimmed sensor output

Using electrostatic nonlinearities to enhance the performance of ring-based Coriolis vibratory gyroscopes

This research investigates electrostatic nonlinearities in capacitively operated ring-based Coriolis vibrating gyroscopes (CVG’s). Large amplitude vibrations of the ring amplify the Coriolis force and are beneficial to achieving high-precision rate sensing. However, due to the miniature sizes of these devices and the narrow capacitive gaps, electrostatic nonlinearities manifest at relatively small ring displacements, thus resulting in the sensor output differing from what is expected of a standard linear device. As such, the current theory of operation commonly perceives electrostatic nonlinearities as an obstacle towards the development of high performance sensors. Electrostatic nonlinearities is the dominant source of nonlinearity in ring-based CVG’s. This work develops a mathematical model to analyse the influence of electrostatic nonlinearities on device performance. When the device operates using a basic electrostatic configuration incorporating only bias and drive voltages, it is found that the bias voltage induces single and mode-coupled cubic restoring forces, which are the main mechanisms through which electrostatic nonlinearities affect the ring dynamics and sensor output. These nonlinear restoring forces result in the amplitude-dependency of the drive and sense mode frequencies, and the presence of self-induced parametric excitation. These effects, in conjunction with the structural imperfections of the ring, degrade rate sensing performance by reducing the rate sensitivity and introducing bias rates and quadrature errors at larger drive amplitudes. A detailed theoretical analysis of the sense dynamics concludes that, depending on the interaction between the imperfections and the electrostatic nonlinearities, there are specific cases where the self-induced parametric excitation can enhance the rate sensitivity of the device. However, this enhancement cannot be achieved while retaining a trimmed sense response to keep the bias rate and quadrature error nullified. An analysis of the sense response and the modal forces shows that the imperfection-induced linear elastic coupling force and the nonlinear frequency imbalance are specifically responsible for the sensor output degradation. These nonlinear behaviours have also been validated against finite element results. The research also investigates the strategic use of electrostatic forces to counteract the effects of nonlinearity and enhance device performance. It is shown that through careful selection of the voltages applied to the electrodes, the form of the resulting electrostatic forces can be tailored to manipulate the sense mode dynamics for device performance enhancement. The presented work develops a general framework to achieve this direct electrostatic force manipulation by considering the variations of the capacitance, voltage and electrostatic potential energy from electrode to electrode, which then enables direct control of the form of the total electrostatic potential energy. Through the use of the framework, this research shows that the electrostatic nonlinearities can be manipulated to replicate the sensor outputs of a linear, trimmed device at larger drive amplitudes, or achieving parametric amplification of the sense response to enhance rate sensitivity without inducing bias rates and quadrature errors. The proposed general framework is used to determine the electrostatic configurations capable of negating self-induced parametric excitation by generating a separate parametric excitation in antiphase with the self-induced parametric excitation. The proposed implementation has potential to reduce sensor output nonlinearity and is most effective in devices where the drive amplitude dependencies of the drive and sense modes are equal, thus resulting in amplitude-insensitive frequency detuning in a manner similar to linear devices. This implementation can also be used in conjunction with a balancing voltage component to eliminate quadrature errors present in the sensor output caused by linear elastic coupling and nonlinear frequency imbalance. The combination of using parametric pumping and balancing voltage components trims the sensor output and have potential to suppress the sensor output nonlinearity further. The effectiveness of the chosen electrostatic configuration is validated against results from transient finite element studies. Rate measuring performance is enhanced further by parametrically exciting the sensor output to increase the quality factor of the device. To achieve enhanced performance the parametric excitation must be phase-tuneable and the proposed general framework is used to select electrostatic configurations capable of providing the required parametric excitation. Two approaches to develop the required parametric excitation are investigated. The first approach exploits linear electrostatic forces whilst the second approach uses quadratic electrostatic forces. Both approaches are shown to have potential to improve rate sensitivity through Q factor enhancing effects. However, the parametric excitation from the quadratic electrostatic forces is generally weaker unless compensated using larger parametric pumping voltages. On the other hand, it is found that the quadratic electrostatic forces promote nonlinear frequency balancing and so this approach is considered advantageous for achieving trimmed sensor output

Rotorcraft Blade Angle Calibration Methods

The most vital system of a rotorcraft is the rotor system due to its effects on the overall flight quality of the vehicle. Therefore, it is of importance to be able to accurately determine blade position during flight so that fine adjustments can be made to ensure a safe and efficient flight. In this study, a current calibration method focusing on the pitch, flap, and lead-lag blade angles is analyzed and found to have larger than acceptable error associated with the sensor calibrations. A literature review is conducted which reveals four novel methods that can potentially increase the accuracy of the sensor calibrations. An uncertainty analysis is conducted aiding in the decision of which of the four methods would best improve the calibration accuracy. The results conclude that a simpler method can be applied and calibration times can greatly be reduced while increasing the accuracy of the calibration. Finally, a new calibration method is proposed utilizing the newly chosen sensor that can be later implemented into the system