考虑一阶驾驶仪动力学的角度控制最优制导律

Optimal Impact-Angle-Control Guidance Law Considering a First-Order Autopilot Dynamics

为研究考虑驾驶仪动力学的最优制导律,构造了引入一阶驾驶仪动力学的导弹运动方程.基于带终端状态约束的最优控制问题,将传统的目标权函数扩展为导弹剩余飞行时间负n次幂的形式,推导得到考虑一阶驾驶仪动力学的最优制导律通用表达式.通过将目标函数的终端状态权系数选为无穷大,化简得到考虑一阶驾驶仪动力学的角度控制最优制导律OIACGL-1,并讨论了OIACGL-1的两种简化形式.引入落角约束和初始方向误差,分析了OIACGL-1系统的归一化加速度特性;分析指出,OIACGL-1系统在n≥0时的终端加速度指令严格为0,对应的终端加速度响应近似为0.

In order to study the optimal guidance law with autopilot dynamics, the missile motion equations were constructed. Aiming at the optimal control problem with terminal state constraints, a generalized expression of the optimal guidance law considering a first-order autopilot dynamics was derived, extending the traditional weighting function to the-nth power form of time-to-go. By setting the object function＇s terminal-state-weighting-coefficient as infinity values, an optimal impact-angle-control guidance law considering a first-order autopilot dynamics （OIACGL-1） was proposed. Meanwhile, two simplified forms of the OIACGL-1 were discussed. For the OIACGL- 1 system with impact angle constraint and initial heading error, performance of the normalized terminal acceleration was analyzed. The analysis results show that for the OIACGL-1 system, the normalized terminal acceleration commands are always equal to exactly zero values when n= 0, while the corresponding terminal acceleration responses are approach to near zero values.