基于三点法拦截几何的导弹滑模制导律设计

Design of Sliding Mode Control Guidance Law of Missile Based on Three-point Intercept Geometry

针对传统的三点法制导律在六自由度弹道仿真时的应用限制,设计了一种基于三点法弹目拦截几何的滑模制导律。在地面坐标系下利用方向余弦阵,推导出了三维空间中三点法制导律的弹目拦截几何;将目标机动视为模型扰动量,建立了三点法拦截几何的状态空间方程;基于滑模控制理论,通过选取合适的滑模面并通过极点配置确定其参数,设计了一种滑模制导律;依据Lyapunov稳定性理论,对所设计的制导律进行了稳定性证明并进行了数值仿真。仿真结果表明,在导弹整个飞行过程中,坐标原点、导弹和目标始终都在一条直线上,严格符合三点法弹目拦截几何,并且制导指令相对平滑,符合实际需求。

Aiming at the limit of three-point guidance applied in 6-DOF trajectory simulation,a sliding mode control(SMC) guidance law was proposed based on three-point intercept geometry. By using direction cosine matrix(DCM),the three dimensional intercept geometry of missile-target was modelled in the ground coordinate frame. Taking target maneuver as the model disturbance,the state-space model of three-point intercept geometry was given. An appropriate sliding surface was chosen,and its parameters were determined by pole configuration method,and the guidance law was derived based on SMC theory. Based on Lyapunov stability theory,the stability of the proposed guidance law was proved. The numerical simulation results show that,the origin point together with the position of missile and target are always on the same line in the ground coordinate frame,which satisfies the three-point intercept geometry. The guidance command is relatively smooth during the whole flying process,and it meets the actual requirements.