This paper focuses on coupling property and dynamic stability of spinning missiles equipped with a two-loop autopilot. The closed-loop characteristic equation is established in the complex form, on which we investigated the dominant factors of the cross coupling, i.e., actuator dynamics, airframe configuration and autopilot, to provide physical understandings of coupling property. By coupling analysis, it is found that coupling can be mitigated by the autopilot. However, the proposed static decoupling approach is necessary to eliminate steady coupling completely. Furthermore, by solving the forth-order characteristic equations with Cardan formula, the dynamic stability boundary is derived numerically. As actuator dynamics is extremely significant to stability, the proposed stability boundary is derived with consideration of it, and thus, it is more practical than results in previous studies. The effectiveness of decoupling method and the correctness of dynamic stability boundary is verified by mathematical simulations. Theoretical and numerical results also reveal that high actuator bandwidth and less time delay is beneficial to dynamic stability.

本文着重研究了具有两回路自动驾驶仪的旋转导弹的耦合特性和动态稳定性。建立复杂形式的闭环特性方程，在该方程上，我们研究了交叉耦合的主要因素，即执行器动力学，机身配置和自动驾驶，以提供对耦合特性的物理理解。通过耦合分析，发现自动驾驶可以减轻耦合。然而，所提出的静态去耦方法对于完全消除稳态耦合是必要的。此外，通过用Cardan公式求解四阶特征方程，可以数值导出动态稳定边界。由于执行器动力学对稳定性极为重要，因此，在考虑了它的基础上得出了建议的稳定性边界。比以前的研究结果更实用。通过数学仿真验证了解耦方法的有效性和动态稳定边界的正确性。理论和数值结果还表明，较高的执行器带宽和较小的时间延迟有利于动态稳定性。