力反馈模式半球谐振陀螺仪的正交控制

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

介绍了半球谐振陀螺仪在力反馈工作模式下的普通控制与正交控制的概念,推导了半球谐振子唇沿振动和波腹方位角表达式,建立了谐振子存在密度不均匀缺陷时谐振子的动力学方程,由此得到了谐振子振动位移的状态方程,进而通过解微分方程求出了状态方程的精确解析解。然后给出了普通控制方法和正交控制方法的主激励电压与辅助激励电压比值的表达式,由此可精确估计陀螺的输入角速率。对这两种控制方法的解算角速率误差进行了比较与仿真分析,分析表明正交控制方法可有效抑制半球谐振子工艺缺陷带来的误差。最后给出了两种工作模式下为保证半球谐振陀螺角速率估计精度所要求的密度四次谐波的允差。

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.