考虑一阶驾驶仪动力学的扩展弹道成型制导系统解析研究

构造了基于time-to-go的负n次幂函数的扩展目标函数，推广得到不考虑驾驶仪动力学的扩展弹道成型制导律。将一阶驾驶仪动力学引入到扩展弹道成型制导系统中，得到三阶线性时变齐次微分方程，利用幂级数解法，求解得到闭环制导系统的位置、速度、加速度解析表达式；根据终端时刻的位置和速度解析结果，得到由一阶驾驶仪动力学引起的脱靶量和终端角度误差解析表达式。利用伴随法对解析脱靶量和终端角度误差的解析结果进行了仿真验证。仿真和解析研究结果表明，当制导时间大于驾驶仪时间常数的15倍以上时，由初始方向误差和终端落角约束引起的脱靶量、终端角度误差都基本收敛到零。

Analytic study on extended trajectory shaping guidance system with first-order autopilot dynamics

Based on the time-to-go function with -nth power, the extended objective function is presented and the extended trajectory shaping guidance law is proposed for the lag-free guidance system. A third order linear time-varying homogeneous differential equation is obtained when a first-order autopilot is introduced into the extended trajectory shaping guidance system and using the power series solution method, and the analytic solutions of position, velocity and acceleration are derived. According to the analytic results of position and velocity at final time, the analytic expressions of the miss distance and terminal impact angle error due to first-order autopilot dynamics are obtained. The analytic results of miss distance and terminal impact angle error are validated by the method of adjoint. The simulation and analytic results show that the miss distance and impact angle error induced by heading error and terminal impact angle approaches to zero when the missile guidance time is about 15 times of the autopilot lag time.