基于匹配渐进展开的跳跃式再入解析预测-校正制导律设计

为了适应低升阻比飞行器再入返回的大航程要求,针对大气跳跃再入飞行环境复杂并难以直接获得解析解的特点,基于匹配渐进展开法设计了一种跳跃式再入解析预测-校正制导方法。首先分析了低升阻比飞行器大气跳跃再入轨迹的飞行剖面和制导分段方法;然后分别推导了其运动方程以重力作用为主导的外解和以气动力作用为主导的内解的渐进展开形式,并通过匹配获得了统一的封闭解析表达式;接着基于此解析解实时预测飞行器的剩余航程,并通过不断迭代升阻比垂向分量以满足最后的落点精度;最后针对跳跃再入飞行的不同阶段设计了不同的制导策略以获得最终的倾侧角指令。仿真结果表明采用跳跃式再入返回技术,阿波罗指令舱的航程能够达到8 348 km,而解析预测-校正制导律的落点精度为0.338 km,证明了此方法的有效性。

Design of analytical prediction-correction skip entry guidance law based on matched asymptotic expansions

In order to adapt to the demand of the long range for the entry return of low lift-drag ratio aircraft, and considering the difficulty of obtaining the analytical solution directly due to the complex flying environment of the atmospheric skip entry, an analytical prediction-correction skip entry guidance law based on the matched asymptotic expansion method is designed. The flight profile and guidance section method of low lift-drag ratio aircraft atmospheric skip entry flight are given at first. Then the outer expansions for the gravitational-dominated region and the inner expansions for the aerodynamic-dominated region are derivated respectively, and the closed-form analytical composite expansions of the governing equations are obtained by matching the asymptotic expansions. Based on the analytical expansions, the range-to-go to the target is computed in real time, and the vertical-lift-drag ratio component is adjusted using a secant iteration method until the predicted downrange error is satisfied. Finally, different guidance strategies are designed for different stages of skip entry flight to obtain the terminal command of bank angle. The simulation results show that the range of Apollo command module can be 8 348 km with technology of skip entry return, while the landing error of the analytical prediction-correction guidance law is 0.338 km, which prove the effectiveness of the method.