基于Gauss伪谱法的制导炸弹攻击区的计算方法

Attack Area Calculation of Guided Bombs Based on Gauss Pseudo-Spectral Method

针对新型制导炸弹攻击区的求解问题,建立了受约束条件下的制导炸弹动力学模型;通过引入加权侧向射程和纵向射程的组合性能函数,将攻击区的求解问题转化为最优控制问题;采用Gauss伪谱法进行求解,并分析了制导炸弹导引头启控点处的速度、弹道倾角对攻击区的影响。仿真结果表明:Gauss伪谱法可有效地解决制导炸弹攻击区的求解问题,且炸弹攻击区随着速度、弹道倾角的增大而增大,但当弹道倾角大于零时,增加弹道倾角对攻击区的影响相对较小。

To solve the problem of the attack area of the new type guided bomb, the dynamic model of guided bombs is built under the constraint conditions. The performance function with a weighted combination of the lateral and longitudinal ranges of the guided bomb is introduced, and the attack area problem is turned into the optimal control problem. Then, Gauss Pseudo-spectral Method is used to solve it. The impact of the speed and Flight Path Angle （FPA） at the starting control point of the guided bomb on the attack area is analyzed. The simulation results show that： 1 ）Gauss Pseudo-spectral Method can effectively solve the problem of the attack area of the guided bomb, and the attack area of bombs is increased with the speed and FPA ; and 2） When the trajectory angle is larger than zero, the increasing of FPA has a relatively small impact on the attack area.