Sensing System and Methods for Measuring Oscillations in the Resonator of a Hemispherical Resonator Gyroscope

The paper considers a hemispherical resonator gyroscope and methods for combining eight capacitive displacement sensors into a measuring instrument. We propose a circuit diagram for a measuring instrument based on operational amplifiers. The diagram makes it possible to implement oscillation measurement for direct and alternating resonator voltages as well as a combined scenario. We derived a mathematical model simulating the output signal of the measuring instrument. We analysed the sensitivity of our system for different implementations of the measuring instrument. For the case when the modulating signal frequency and resonator oscillation frequency are multiples of each other, we derived expressions to find the angular wave position and offset signals for the control system. We used the linear term of the signal model to derive these equations, provided estimations of the errors occurring and guidelines on reducing them. We also investigated the case when the frequencies of the modulating and modulated signals are not multiples. We consider a general approach to evaluating wave pattern parameters, taking the emerging errors into account

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