单通道控制的旋转弹锥形运动稳定性研究

摘要

The coning motion is a basic angular behavior of spinning missiles,and the research on the stability of coning motion has been the heated topic in the field of spinning missle. The linearized 6-DOF equations of angular motion for a spinning missile with one pair of canards were established in the rolling body frame. The influence of aerodynamic asymmetry due to the canards on the angular motion was revealed via numerical simulations.The analytical stability condition of coning motion was given by Routh cri-terion, which can be transformed to be an equivalent of rotation rate with stable coning motion. Simulations under different spinning rate demonstrate that the stability condition was reliable.In the case of a given spinning rate,the sinusoidal canard with activating frequency in the neighborhood of the slow mode can induce strong resonance instability.The research results can provide references to the system design, guidance and control design of spinning missiles with one single pair of canards.%锥形运动是旋转弹角运动的基本形式，其稳定性问题一直是旋转弹领域的研究热点。以一对鸭舵作用下的单通道控制旋转弹为研究对象，给出了弹体坐标系下的线性化角运动模型，通过数值仿真，揭示了一对鸭舵带来的气动不对称对其角运动特性的影响规律。利用劳斯判据，给出了解析形式的锥形运动稳定条件，该条件可等效为锥形运动稳定条件下的转速范围，不同转速下的仿真结果证明了该稳定条件的正确性。在相同的转速条件下，正弦式鸭舵的控制频率在慢模态衰减频率附近时，可诱发强烈的共振不稳定。研究结果可为一对鸭舵作用下的旋转弹总体设计及制导控制系统设计提供参考。