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通过建立相对于终端弹目连线的导弹运动方程,将time-to-go的负n次幂函数引入到目标函数中,推导得到不考虑制导动力学的扩展比例导引和扩展的带落角约束的最优制导律。提出了广义最优制导律的概念,阐述了其在两种不同坐标系下的表现形式和意义。针对终端弹目连线坐标系下的广义最优制导律,利用幂级数解法对闭环弹道微分方程进行了解析求解,得到了导弹相对终端弹目连线的位置、速度和加速度指令的解析表达式,并利用仿真的方法对解析结果进行了验证。
By establishing the missile’s motion equation relative to the terminal projectile’s connection, the time-to-go negative n-power function is introduced into the objective function, and the derivative angle and extension angle are deduced without considering the guidance dynamics The Optimal Guidance Law of Constraints. In this paper, the concept of generalized optimal guidance law is proposed, and its representation and significance in two different coordinate systems are expounded. Aiming at the generalized optimal guidance law in the terminal projectile connecting line coordinate system, the closed-loop ballistic differential equation is solved by the power-series solution and the analytical expressions of the position, velocity and acceleration of the missile relative terminal projectile are obtained. The simulation results verify the analytical results.