两轴快速反射镜视轴指向与速率补偿分析

为精确控制两轴快速反射镜的视轴指向，根据矢量形式斯涅尔定律建立了反射镜转角与视轴指向角间的运动学耦合方程。通过非线性校正实现视轴指向方程解耦，对于行程为20 mrad的两轴快速反射镜在入射角为45时视轴指向误差小于8rad，相比线性近似，视轴指向精度提高75倍。为保证视轴稳定，根据矢量速率方程推导出补偿基座扰动角速率的反射镜转动角速率方程，通过对三角函数进行泰勒展开，舍去高阶项，得到快反镜转动角速率近似计算公式，分析了不同入射角下的残余视轴转动角速率，得出视轴转动角速率Ly残差远大于Lz，且入射角i为45时残差最小，此时残余视轴转动角速率与基座扰动角速率之比小于0.164%，可满足计算精度要求。为快速反射镜伺服控制系统位置、速度指令生成提供理论依据。

Analysis of LOS pointing and rate compensation for two-axis FSM

In order to control line-of-sight(LOS) pointing with two-axis fast-steering mirror(FSM) accurately, kinematic equations was set to describe the relationship between LOS pointing and angular displacement of FSM deriving from Snell's law of reflection. LOS pointing equations were decoupled with non-linear correction. LOS pointing error was less than 8rad for two-axis FSM whose tilt angles were both 20 mrad with beam incidence angle equaling to 45. LOS pointing accuracy rose 75 times compared with linear approximation. To hold the LOS stationary, rate equations were established in terms of vector rate synthesis to compensate the angular rate of the mounted vehicle in inertial space. Angular rate equations for FSM were simplified via Taylor expansion and high order truncation. The residual angular rate of LOS with different beam incidence angles was calculated, which indicated that the residual error ofLy was far greater thanLz. The ratio between residual LOS angular rate and angular rate of mounted vehicle was minimal and less than 0.164% when beam incidence angle was 45, which satisfied the accuracy requirements. The equations deduced suppliy theoretic reference of position and velocity command generation for FSM control system.