基于角度关系的几何制导律研究

Research on geometric guidance law based on angle relation

基于受保护飞行器、防御弹和攻击弹在空间形成的角度关系设计了一种几何制导律。首先,通过分析三者在空间形成的三角形几何关系,将受保护飞行器和防御弹作为一个协同体,以防御弹位于攻击弹和受保护飞行器的连线上为基本准则,给出二维几何制导律的表达式,并对所设计制导律的稳定性进行证明推导。其次,利用矢量运算将设计的二维制导律在三维空间进行了扩展,给出了三维空间中几何制导律的表达式。最后,仿真表明,设计的几何制导律能够有效保护飞行器安全,相对于比例导引,拦截时间短,制导精度髙,过载变化较为平稳,克服了比例导引末端过载发散的情况,降低了对执行机构的要求。

Based on the angle relation among the protected aircraft, offensive missile and defensive missile, a new geometric law is derived. Firstly, the geometric relation among the three players is analyzed, the protected aircraft and the defensive missile are regard as a cooperative player, the geometric guidance law in two-dimensional space is developed based on the idea of controlling the defensive missile in the line between the offensive missile and the protected aircraft, also the stability of the geometric law is proved. Secondly, the designed guidance law is extended to the three-dimensional space by vector operations, so the three-dimensional guidance law is given. Simulation results show that the safetyness of the protected aircraft can be guaranteed using the derived gudiance law. Compared with the proportional guidance law, the geometric guidance law shortens the intercept time and improves the guidance precision greatly, and it overcomes the load divergence when using the PN guidance and reduces the requirement of the actuator.