为了获得Risley棱镜系统光束指向控制精度指标设计及性能提升的依据，对系统光束指向控制精度随轴系角度测量精度的非线性变化规律进行了研究。首先，以一级近轴近似矢量合成模型为基础，采用正解方法根据双棱镜方位推导了出射光束指向的解析表达式; 然后，结合单自由度轴系伺服控制经验，通过泰勒级数展开的方式推导出了光束指向控制精度与轴系角度测量精度之间的非线性解析表达式，并由此获得了界定限判据; 最后，分别对小偏向角系统和大偏向角系统进行了仿真分析，获得了光束指向控制精度在全视场区域内的变化情况。结果表明，本文研究所得的非线性解析式描述了影响系统光束指向控制精度诸多因素之间的相互关系,能够为Risley棱镜光束指向系统的设计及整体性能的优化提供依据。

In order to obtain the basis for index design of beam steering control precision and performance improvement for Risley prism system, the nonlinear relationship between Risley prism beam steering control precision and shaft angle measurement precision is investigated. First, based on the first-order paraxial approximation vector synthesis model, the analytical expression of the direction of the outgoing beam is derived from the double prisms position by the forward solution method. And then, based on the servocontrol experience of single degree of freedom shaft, the nonlinear analytical expression between the beam steering control precision and the shaft angle measurement precision is deduced by the Taylor series expansion method, and thus the dividing line criterion is obtained. Finally, the small deflection angle system and the large deflection angle system are simulated and analyzed respectively, and the change of the beam steering control precision over the whole field of view is obtained. Results show that the nonlinear analytical expression derived in this paper represents the relationship among the factors that affect the control precision of the system, which provides the basis for the design and optimization of the Risley prism beam steering system.