摘要
基于剩余飞行时间的指数函数构建了扩展的权函数和目标函数,引入常值机动目标,利用最优控制理论,扩展得到最优弹道成型制导律簇。针对无制导动力学滞后的制导系统,利用施瓦茨不等式,求解得到了在初始位置误差、方向误差、目标常值机动及终端落角约束作用下的制导律加速度指令解析解。分析指出,当罚函数中剩余飞行时间的指数大于0时,加速度指令在弹道末端趋近于0.利用无量纲化方法和伴随法,研究了含有一阶动力学滞后的制导系统在初始方向误差和终端落角约束作用下的无量纲位置和角度脱靶量特性。结果表明:当末导时间为制导系统动力学滞后时间常数的15倍左右时,落角约束、初始方向误差引起的位置和角度脱靶量均趋近于0;且初始方向误差角和终端落角方向相反时的位置和角度脱靶量要小于二者同号时的情况。
The extended weighted and object functions are proposed based on the time-to-go exponential function. The optimal control theory is used to deduce a family of extended optimal trajectory shaping guidance laws for the constant maneuvering target. According to Schwartz inequality, the analytical solu- tion of the guidance law acceleration command is derived by introducing the initial displacement, initial heading error, target maneuver and final impact angle into the lag-free guidance system. The analysis shows that the final acceleration command approaches to zero when the exponent of the time-to-go expo- nential function is greater than zero. The non-dimensional position and angle miss distance of guidance system with first order lag are studied using the non-dimensional method and the adjoint method. The re- suits show that the position and angle miss distance induced by the heading error and final impact angle approach to zero when the missile terminal guidance time is about 15 times of the system lag time con- stant. And also, the position and angle miss-distance are smaller when the signs of initial heading error angle and final impact angle are opposite.
出处
《兵工学报》
EI
CAS
CSCD
北大核心
2013年第7期801-809,共9页
Acta Armamentarii
基金
国家自然科学基金项目(61172182)
关键词
飞行器控制、导航技术
扩展弹道成型
剩余飞行时间
最优控制
施瓦茨不等式
脱靶量
control and navigation technology of aerocrafl
extended trajectory shaping
time-to-go
op-timal control
Schwartz inequality
miss distance