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Dynamic stability of rolling missiles employing a two-loop autopilot with consideration for the radome aberration parasitic feedback loop

机译：考虑天线罩像差寄生反馈回路的采用两回路自动驾驶仪的滚动导弹的动态稳定性

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The dynamic stability of a radar homing rolling missile is extremely complex due to the interaction of the parasitic radome aberration feedback loop and the cross-coupling between the pitch and yaw, which are problems that have not been presented in previous studies. This paper presents mathematical models representative of the parasitic radome aberration feedback loop and proportional navigation guidance (PNG) system with a two-loop autopilot for rolling missile guidance based on reasonable assumptions. A PNG system equation is further proposed in the form of a complex summation. Based on the proposed mathematical models, the sufficient and necessary condition for the dynamic stability of the rolling missile is analytically derived according to the stability criterion of a system with complex coefficients. The proposed dynamic stability condition is verified by numerical simulation. Moreover, the stable region is obtained by solving the dynamic stability condition under different cases. An analysis of the effects of system parameters indicates that the stable region of a rolling missile is smaller than that of a non rolling missile. Furthermore, it is shown that the stable region is affected by a number of factors, such as the rolling rate and the total delay angle. The dynamic stability condition derived in this paper is useful for evaluating the stability of a rolling missile with consideration for the parasitic radome aberration feedback loop, and the conclusions obtained can provide guidance for the design of PNG systems for rolling missiles. (C) 2016 Elsevier Masson SAS. All rights reserved.
机译：由于寄生天线罩像差反馈回路与俯仰和偏航之间的交叉耦合的相互作用，雷达制导的滚动导弹的动态稳定性极为复杂，这是先前研究中未曾提出的问题。本文基于合理的假设，提出了代表具有两回路自动驾驶仪的寄生天线罩像差反馈回路和比例导航制导（PNG）系统的数学模型，该系统具有两回路自动驾驶仪。进一步以复和的形式提出了PNG系统方程。根据所提出的数学模型，根据复杂系数系统的稳定性判据，解析得出了滚动导弹动力稳定性的充要条件。通过数值模拟验证了所提出的动态稳定性条件。此外，通过求解不同情况下的动态稳定条件来获得稳定区域。对系统参数影响的分析表明，滚动导弹的稳定区域小于非滚动导弹的稳定区域。此外，示出了稳定区域受许多因素影响，例如轧制速度和总延迟角。本文推导的动态稳定性条件对于考虑寄生天线罩像差反馈回路的滚动导弹的稳定性评估是有用的，所获得的结论可为滚动导弹PNG系统的设计提供指导。 （C）2016 Elsevier Masson SAS。版权所有。

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