旋转弹体直气复合控制交叉耦合效应引起的动态稳定性问题研究

The direct force/aerodynamic compound control can speed up the response speed of the missile under low dynamic pressure conditions and improve maneuverability. However, when the missile body rotates, the control coupling caused by the compound control will interact with the gyro effect and the Magnus effect, causing severe cross-coupling, resulting in the dynamic instability of the projectile in the form of non-convergence cone motion..Therefore, in this project, the method of using the complex coefficient system theory to study the dynamic stability problem of the direct force/aerodynamic of spinning missile under the control and guidance loop is proposed. The strong cross-coupling nonlinear dynamic model of the spinning missile is transformed into a complex coefficient system description, and the typical topology control system and the guidance system model with parasitic feedback loop are constructed respectively to obtain the complex coefficient differential equations of the control system and the guidance system. The dynamic stability conditions of the corresponding system are solved using the complex coefficient stability theorem, and the derived stability conditions are verified by numerical simulation. On this basis, the stability region of a spinning missile with the direct force/aerodynamic compound control is obtained, the instability mechanism is explored, and the influence of system parameters and isolation on dynamic stability is analyzed..This project is expected to explore a set of versatile research methods for the dynamic stability of a spinning missile with the direct force/aerodynamic compound control, which provides a theoretical basis for the research and application of a spinning missile with the direct force/aerodynamic compound control. It also provides a reference for the stability study of strongly coupled nonlinear systems.

直气复合控制能加快导弹低动压条件下的响应速度，提高机动性。然而当弹体旋转时，直接力/气动力引起的控制耦合，将与陀螺效应、马格努斯效应相互作用，引起严重的交叉耦合，导致弹体可能出现不收敛锥形运动形式的动不稳定。.对此，本项目提出分别在控制、制导回路下，利用复系数系统理论方法研究直气复合控制旋转弹的动态稳定问题。将旋转弹体的强交叉耦合非线性动力学模型转化为复系数系统描述，分别构建典型拓扑结构控制系统、含有隔离度寄生回路的制导系统模型，求得控制系统、制导系统的复系数微分方程描述，应用复系数稳定定理求解对应系统的动态稳定性条件，并进行仿真验证。在此基础上，求解直气复合控制旋转弹的稳定域，探究失稳机理，分析系统参数、隔离度对动态稳定性的影响。.本项目期望探索一套具有通用性的直气复合控制旋转弹动态稳定性研究方法，为直气复合控制旋转弹的研究及应用提供理论基础，亦为强耦合非线性系统的稳定性研究提供借鉴。

面向低动压条件下提升弹体响应速度和机动能力的需求，针对直接力/气动力复合控制旋转弹体交叉耦合效应引起的动态稳定性问题，本文面向采用姿控发动机的旋转导弹进行制导控制系统设计和关键参数选取，并推导其动态稳定性判定条件。首先，针对直接力/气动力复合作用需求，考虑实现姿态控制功能的连续直接力，建立旋转弹体的动力学方程并通过小扰动假设对其进行简化。其次，针对旋转弹体的控制系统，选用含有姿态控制回路的三回路自动驾驶仪，将气动力执行机构和直接力执行机构分别简化为二阶系统和一阶惯性系统，建立数学模型。接下来，采用复系数系统理论，选择气动舵偏转角和直接力作为复变量，基于所设计的控制系统结构，用复系数微分方程代替传统的动力学方程描述，求解典型拓扑驾驶仪结构下直接力/气动力复合控制旋转弹体的动态稳定性判定条件，并研究直接力/气动力分配占比和控制系统设计参数对其稳定域的影响，通过数值仿真验证判定条件是否正确。最后，根据以上研究内容，选用比例导引制导方法，加入隔离度寄生回路，推导含有隔离度寄生回路下直接力/气动力复合控制旋转导弹的动态稳定性条件，并研究其失稳机理和稳定边界问题。本项目的研究成果能够为后续的直接力/气动力复合控制旋转弹体飞行器的总体设计提供理论依据，亦可为强交叉耦合非线性系统的稳定性问题的研究提供参考思路。

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