Quadrature-control of hemispherical resonator gyros under force-rebalance mode

The concepts of general-control and quadrature-control for hemispherical resonator gyros (HRG) under the force-rebalance mode were introduced, and then the azimuth of radial vibration antinode on the hemispherical resonator's verge was deduced. After that, the state equation about vibration displacement and velocity was established on the basis of the dynamics equations of the resonator with the density distributed nonuniformity in the circular direction. Later on, the analytic solutions of the vibration displacement and the velocity were achieved by solving this state equation. Finally the ratio expressions of main excitation and rebalance excitation were derived under both of the two working modes, thus the input angular rate of HRG was obtained. It was proved that by comparing and calculating the angular rate outputs under these two modes, the errors caused by machining defects were greatly inhibited under the quadrature control mode. The range of fourth harmonic error about density's nonuniformity was given to ensure the accuracy of HRG under these two modes.