Arifin, Davin
(2023)
Using electrostatic nonlinearities to enhance the performance of ring-based Coriolis vibratory gyroscopes.
PhD thesis, University of Nottingham.
Abstract
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.
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