纯比例导引律解析解与三维碰撞角约束制导

为提高空地导弹碰撞角约束制导的精度和鲁棒性,增强其对防空系统的突防能力和对目标的打击效果,基于纯比例导引律（pure proportional navigation,PPN）拦截固定目标的解析解,提出了一种新的三维碰撞角约束制导律（three-dimensional PPN-based impact-angle-control guidance law,3D-PPNIACG）。首先,基于PPN拦截固定目标解析解,分析了基于PPN的二维碰撞角约束制导律（two-dimensional PPN-based impact angle constraint guidance law,2D-PPNIACG）的拦截制导性能,包括最大过载、能量消耗与捕获区域。其次,基于2D-PPNIACG和三维拦截制导的垂直分解方法,结合对空间几何关系的深入分析,提出了控制铅垂面内落角和水平面内碰撞角的三维碰撞角约束制导律（3D-PPNIACG）,并对该制导律的实用性和鲁棒性进行了充分讨论。最后通过数值仿真,验证了3D-PPNIACG在碰撞角约束制导中的有效性和鲁棒性。研究和仿真结果表明,所提出的3D-PPNIACG结构简单、易于实现、鲁棒性好,在考虑测量误差、动力学响应延迟等现实因素的情况下,可有效实现水平面内的碰撞角约束制导和铅垂面内的落角约束制导,具有良好的应用前景。

Analytical solution of pure proportional navigation guidance law and three-dimensional guidance with impact angle constraint

For improving the accuracy and robustness of the impact-angle-control guidance of air-to-surface missiles to enlarge the penetration ability against the air-defense system and the impact effect, based on the analytical solution of pure proportional navigation (PPN) guidance law against stationary targets, a three-dimensional PPN-based impact-angle-control guidance law (3D-PPNIACG) was proposed. First, based on the analytical solution of PPN against stationary targets, the guidance performance of two-dimensional PPN-based impact angle constraint guidance law (2D-PPNIACG) was analyzed, including maximum commanded acceleration, velocity increment, and capture region. Then, based on the 2D-PPNIACG and the orthogonal decomposition method of three-dimensional guidance, and with the help of the spatial geometric relationship between missile and target, 3D-PPNIACG was put forward, which can guarantee the impact-angle-control in vertical plane as well as horizontal plane. Finally, the guidance performance of 3D-PPNIACG was analyzed through numerical simulation cases, and the effectiveness and robustness of this guidance law were verified. The study and simulation results show that the proposed 3D-PPNIACG has the advantages of simple structure, ease of implementation, and good robustness, which can realize the impact-angle-control in both vertical and horizontal planes and hence has good application prospect.