针对航空拖曳式探测线圈阵列系统的非线性动力学与姿态稳定控制问题，提出了一套高保真动力学建模与“稳态设计-动力学”综合分析方法。该方法首先采用集中质量法离散缆绳系统，结合六自由度刚体理论描述探测线圈，构建了完整的刚柔耦合动力学模型；进一步基于静力学平衡理论设计了系统的稳态飞行构型，经实地飞行试验验证后，结合位移法与逐级分析思路反算出各缆绳原长，从而解决了复杂模型设计与仿真初始条件难以精确给定的问题。通过对三种典型强扰动工况进行仿真，结果表明：速度增量不变的前提下采用加速度峰值更低、作用时间更分散的加速策略能更有效地抑制系统姿态扰动与张力冲击；后置气动薄膜可增强系统动态机动稳定性，但受薄膜自重与环境气流扰动耦合影响，面临静态偏移与结构载荷增大的制约；系统的横向扰动剧烈程度主要由正侧风分量主导；转弯等复杂机动中塔式结构几何构型赋予系统自稳性，但高速机动仍会显著增加横向外摆幅度与结构载荷。
To address the challenges of nonlinear dynamics and attitude stability control in airborne towed detection coil array systems, this paper proposes a high-fidelity dynamic modeling and "steady-state design-dynamics" integrated analysis method. The method first employs the lumped mass method to discretize the cable system and combines six-degree-of-freedom (6-DOF) rigid body theory to model the detection coils, constructing a complete rigid-flexible coupled dynamic model. Furthermore, a steady-state flight configuration is designed based on static equilibrium theory. After validation through field flight tests, the unstretched lengths of all cables are back-calculated using the displacement method and a progressive analysis approach, thereby precisely resolving the difficulties in system design and determining simulation initial conditions for the complex model. Simulations under three typical severe disturbance conditions indicate that: under constant velocity increment, a gentler acceleration strategy with a lower peak and more dispersed duration more effectively suppresses attitude disturbances and tension impacts; a rear aerodynamic membrane enhances dynamic maneuvering stability, but subject to the coupling effects of membrane self-weight and environmental airflow disturbances, it faces constraints regarding static attitude offset and increased structural loads; the severity of lateral disturbances is primarily dominated by the perpendicular crosswind component; and in complex maneuvers such as turning, the geometric configuration of the tower structure endows the system with self-stability, although high-speed maneuvers still significantly increase lateral swing amplitude and structural loads.
[1]Xin W ,Guoqiang X ,Yiming H .The Progress of the Helicopter-Borne Transient Electromagnetic Method and Technology in China[J].IEEE Access,2020,832757-32766.
[2]嵇艳鞠,林君,关珊珊,等.直升机航空TEM中心回线线圈姿态校正的理论研究[J].地球物理学报,2010,53(01):171-176.
[3]马东立, 刘亚峰, 林鹏. 航空拖曳诱饵系统的动态特性研究[J]. 航空学报, 2014, 35(1): 161-170.
[4]Ma D, Wang S, Yang M, et al. Dynamic simulation of aerial towed decoy system based on tension recurrence algorithm[J]. Chinese Journal of Aeronautics, 2016, 29(6): 1484-1495.
[5]杜一江. 航空拖曳诱饵系统机动过程缆绳张力仿真[J]. 航空学报, 2021, 42(9): 293-302.
[6]王飞, 丁伟, 邓德衡, 等. 水下多缆多体拖曳系统运动建模与模拟计算[J]. 上海交通大学学报, 2020, 54(5): 441-450.
[7]DOROUDGAR S. Static and dynamic modeling and simulation of the umbilical cable in a tethered un-manned aerial system[D]. Burnaby: Simon Fraser Un-iversity, 2016.
[8]侯森浩, 唐晓强, 孙海宁, 等. 面向航天器分离的高速索力传递特性[J]. 清华大学学报(自然科学版), 2021, 61(3): 177-182.
[9]ZHAO T, SCHNEIDER-JUNG F, LINN J, et al. Simulation and parameterization of nonlinear elastic behavior of cables[J]. Multibody System Dynamics, 2024, 63: 537-556.
[10]Wu J, Yang X, Xu S, et al. Numerical investigation on underwater towed system dynamics using a novel hydrodynamic model[J]. Ocean engineering, 2022, 247: 110632.
[11]QUISENBERRY J E, ARENA A S. Dynamic simulation of low altitude aerial tow systems[C]// AIAA Atmospheric Flight Mechanics Conference and Exhibit. Providence, Rhode Island: AIAA, 2004.
[12]阎永举, 李道春, 向锦武, 等. 基于Kane方程的拖曳式诱饵释放过程动态特性分析[J]. 航空学报, 2014, 35(7): 1912-1921.
[13]WILLIAMS P, TRIVAILO P. Dynamics of circularly towed aerial cable systems, part I: optimal configurations and their stability [J]. Journal of Guidance, Control, and Dynamics, 2007, 30(3): 753-765.
[14]WILLIAMS P. Optimization of circularly towed cable system in crosswind[J]. Journal of Guidance, Control, and Dynamics, 2010, 33(4): 1251-1263.
[15]WILLIAMS P, TRIVAILO P. Cable-supported sliding payload deployment from a circling fixed-wing aircraft[J]. Journal of Aircraft, 2006, 43(5): 1567-1570.
[16]SUN L, HEDENGREN J D, BEARD R W. Optimal trajectory generation using model predictive control for aerially towed cable systems [J]. Journal of Guidance, Control, and Dynamics, 2014, 37(2): 525-539.
[17]FERRIN J, NICHOLS J, MCLAIN T. Design and control of a maneuverable towed aerial vehicle[C]// AIAA Guidance, Navigation, and Control Conference. Min-neapolis, Minnesota: AIAA, 2012.
[18]苏子康, 李春涛, 俞悦, 等. 绳系拖曳飞行器高抗扰轨迹跟踪控制[J]. 北京航空航天大学学报, 2021, 47(11): 2234-2248.
[19]Ma T, Wei Z, Wang X, et al. Simulation of the reel-in operation of towed target system with constant-length method[C]//AIAA Scitech 2019 Forum. 2019: 0437.
[20]Ma T, Wei Z, Chen H, et al. Simulation of the dynamic retrieval process of a towed target system under towing airplane’s wake and atmospheric turbulence[J]. Proceed-ings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2020, 234(9): 1518-1530.
[21]苏子康, 陈海通, 李春涛, 等. 非匹配包线下无人机空基回收拖曳系统协调运动规划[J]. 航空学报, 2023, 44(10): 327377.
[22]Chen X, Hong B, Lin Z, et al. Lumped mass model for flexible cable: A review[C]//Journal of Physics: Con-ference Series. IOP Publishing, 2021, 1995(1): 012029.
[23]Khan A, Wang X, Li Z, et al. Analytical and Numerical Study of Underwater Tether Cable Dynamics for Seabed Walking Robots Using Quasi-Static Approximation[J]. Journal of Marine Science and Engineering, 2023, 11(8): 1539.
[24]Hall M. Generalized quasi-static mooring system modeling with analytic jacobians[J]. Energies, 2024, 17(13): 3155.
[25]Li W, Chen S, Huang H. System reduction-based approximate reanalysis method for statically indeter-minate structures with high-rank modification[C]//Struc-tures. Elsevier, 2023, 55: 1423-1436.
CJA