一类扩展的弹道成型制导律

Extended Trajectory Shaping Guidance Laws

以导弹剩余飞行时间的幂函数为基础构建扩展的目标罚函数,利用Schwartz不等式,推导得到扩展的带落点和落角约束的最优制导律簇,给出了两类衍生形式的扩展弹道成型制导律簇.在终端落角约束下,针对罚函数的不同指数n、制导动力学阶数以及不同的导引头和驾驶动力学权状态,研究了第一类衍生形式弹道成型的量纲一加速度、位置、角度脱靶量特性.研究结果表明,末导时间达到制导动力学滞后时间常数的15倍左右时,量纲一位置和角度脱靶量均收敛到0附近;指数n越大,位置和角度脱靶量振荡越厉害;动力学阶数越高,位置脱靶量振荡越厉害.最后指出,提高导引头响应速度比提高驾驶仪响应速度能更有效地降低系统位置和角度脱靶量.

An extended cost function was proposed on the basis of a power function about missile remain time-to-go.According to Schwartz inequality,a family of extended optimal guidance law with both position and impact angle constraints was deduced and two kinds of extended trajectory shaping guidance laws were derived.For different missile seeker,autopilot dynamics weighted states,different system dynamics order and different exponential n of the cost function,the nondimensional acceleration,non-dimensional position and angle miss distance of the first kind trajectory shaping guidance system was studied on the restraint that final impact angle was introduced into the system.It is concluded that the position and angle miss-distance produced by the final impact angle can approach to zero when the missile terminal guidance time is about15 times as much of the system lag time.It will result in a more oscillatory position miss response when the system dynamics order increases.And when the exponential number n increases,the position and angle miss distance can be much worse.Finally,it shows that a fast response missile seeker is more effective than a fast autopilot response to reduce the system position and angle miss distance.