基于最优误差动力学的变速导弹飞行路程控制制导律  

Flying range control guidance for varying⁃speed missiles based on optimal error dynamics

作　　者：刘远贺 黎克波[1,2] 何绍溟 梁彦刚 LIU Yuanhe;LI Kebo;HE Shaoming;LIANG Yangang(College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410072,China;Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions,Changsha 410072,China;School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]国防科技大学空天科学学院,长沙410072 [2]空天任务智能规划与仿真湖南省重点实验室,长沙410072 [3]北京理工大学宇航学院,北京100081

出　　处：《航空学报》2023年第7期163-176,共14页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(12002370)。

摘　　要：针对基于常速假设的飞行时间控制制导律在实际应用中存在性能下降的问题,将飞行时间控制问题转化为飞行路程控制问题,提出一种适用于变速导弹的飞行路程控制制导方案。首先,基于古典微分几何曲线原理构建弧长域内导弹打击固定目标的相对运动方程,消除了导弹速度大小变化的影响。其次,基于高斯超几何函数,推导了纯比例导引律制导下变速导弹对固定目标的剩余飞行路程精确解。然后,进一步基于最优误差动力学方法,在不考虑小角假设和其他近似假设的前提下,设计了变速导弹全局非线性飞行路程控制制导律。最后,通过数值仿真验证了所提方法的有效性。To solve the problem of performance degradation of current impact time control guidance based on con⁃stant speed assumption in practical application,a feasible flying range control guidance scheme with time-varying speed is proposed in this paper.The relative motion equation of the missile against the stationary target in the arclength domain is derived based on the classical differential geometric curve principle,which reduces the influence of time-varying speed on the relative motion of missile and target.Furthermore,the exact solution for the range-to-go guided by pure proportional navigation is derived using the Gaussian hypergeometric function.On this basis,a flying range control guidance law is designed with the optimal error dynamics method,and the effectiveness of the proposed guidance is verified by simulation.

关 键 词：古典微分几何曲线原理 变速导弹 高斯超几何函数 最优误差动力学 飞行路程控制 

分 类 号：V448.2[航空宇航科学与技术—飞行器设计]