基于动态逆的空空导弹奇异摄动中制导律

结合奇异摄动和动态逆方法,以飞行时间和末端能量的线性组合为性能指标,推导了一种近最优中制导律.导弹状态方程根据状态变量时间常数写成三时间尺度系统.降阶系统包括纵程、横程和比能动力学方程.用最优控制理论求解出降阶系统最优解,即原系统的外解.动态逆应用于边界层修正,得到一个闭环控制器,其性能可根据爬升、高空等高飞行和下滑阶段或其他情况的不同要求进行调整.仿真结果表明:该制导律满足了对弹道平滑度、飞行时间和末端能量的要求.中段末端航向误差小,为中、末制导的平稳交接班提供了保障.

Singular perturbation midcourse guidance law based on dynamic inversion for air-to-air missile

A near optimal midcourse guidance law incorporating a linear combination of flight time and terminal specific energy as the performance index was derived using singular perturbation theory and dynamic inversion. Missile state functions were put into three time-scale system according to the time constants of state variables. The reduced-order model consists of down range, cross range and specific energy dynamic. Optimal solution of reduce-order system, so called outer solution of original system, was obtained using optimal control theory. Dynamic inversion was applied to boundary layer correction for a close-loop controller. The performance of the controller could be regulated in accordance with different requirement of rise, cruise and descent stage or other instance. Simulation result shows that this guidance law satisfies requirements on trajectory smoothness, flight time and terminal specific energy. At the end of midcourse stage, missile heading error was small enough to ensure smooth transition from midcourse guidance stage to terminal guidance stage.