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

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.