电动力绳系离轨系统是一种典型的空间碎片主动消除技术，本文针对电动力绳离轨系统在初始阶段展开的控制问题，仅通过调节有限的系绳张力与电流，不依赖其他推进器，将导电系绳释放至期望长度并抑制系绳的摆动。首先，采用倾斜偶极子地磁场模型，建立考虑系绳质量的近地轨道二体电动力绳系卫星系统动力学模型；其次，在系绳张力与电流存在约束的条件下，采用反步法结合抗饱和辅助函数解决控制输入受限问题，并引入动态尺度广义逆实现了欠驱动电动力绳系统展开稳定控制问题；然后，应用Lyapunov稳定性定理证明了其闭环系统的稳定性；最后，在MATLAB/SIMULINK平台上进行了仿真验证。结果表明：通过调节系绳张力与电流，可以将系绳释放到指定位置，同时控制输入满足约束条件。
The deorbiting electrodynamic tether system is a typical active space debris removal technology. In this paper, the feedback control of the tension and current is investigated for the deployment of an electro-dynamic tether system without the consumption of chemical propellants. First, considering the effect of the tether mass, a dynamic model for the two-body electro-dynamic tether system in low earth orbit is developed based on the geomagnetic field modeled using a tilted dipole approximation. Then, a control scheme forthe physical bounds of the tether tension and electric current is proposed by using the anti-windup compensator and the backstepping method. Furthermore, with the introduction of dynamically scaled generalized inversion, the control law is improved to achieve deployment stabilization of the underactuated electro-dynamic tether system. Within the Lyapunov framework, the stablilization of the system state is analyzed. Finally, simulation study is carried out on the platform of MATLAB/SIMULINK to evaluate the performance of the control strategy. The results indicate that the length of the tether converges to the desired value by controlling the tension and current while the feedback control inputs remain within the prescribed bounds all the time.
[1] SHIAH A, HWANG K S, WU S T, et al. Three-dimensional simulation of current collection in space[J]. Planetary and Space Science, 1997, 45(4):475-482.[2] PARDINI C, HANADA T, KRISKO P H. Benefits and risks of using electrodynamic tethers to de-orbit spacecraft[J]. Acta Astronautica, 2009, 64(5):571-588.[3] HOYT R P. Stabilization of electrodynamic tethers[C]//Proceedings of 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. Reston, VA:AIAA, 2002:1-8.[4] 蔡洪, 杨育伟, 郭才发. 电动力绳系研究进展[J]. 宇航学报, 2014, 35(11):1223-1232. CAI H, YANG Y W, GUO C F. Review of electrodynamic tether system[J]. Journal of Astronautics, 2014, 35(11):1223-1232(in Chinese).[5] SOMENZI L, IESS L, PELAEZ J. Linear stability analysis of electrodynamic tethers[J]. Journal of Guidance, Control, & Dynamics, 2012, 28(5):843-849.[6] ZHONG R, ZHU Z H. Dynamics of nanosatellite deorbit by bare electrodynamic tether in low earth orbit[J]. Journal of Spacecraft & Rockets, 2015, 50(3):691-700.[7] LI G Q, ZHU Z H, Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration[J]. Celestial Mechanics & Dynamical Astronomy, 2015, 123(4):363-386.[8] 潘伟, 路长厚, 李吉栋, 等. 基于傅里叶展开的电动力绳系卫星最优控制[J]. 航空学报, 2011, 32(9):1714-1721. PAN W, LU C H, LI J D, et al. Optimal control of electrodynamic tethered satellites based on Fourier series expansion[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(9):1714-1721(in Chinese).[9] RUPP C C. A tether tension control law for tethered subsatellites deployed along local vertical:NASA-TM-X-64963[R]. Wahsington, D.C.:NASA, 1975, 1-28.[10] SUN G H, ZHU Z H. Fractional-order tension control law for deployment of space tether system[J]. Journal of Guidance, Control, & Dynamics, 2014, 37(6):2062-2066.[11] STEINDL A, TROGER H. Optimal control of deployment of a tethered subsatellite[J]. Nonlinear Dynamics, 2003, 31(3):257-274.[12] WILLIAMS P. Optimal deployment/retrieval of tethered satellites[J]. Journal of Spacecraft & Rockets, 2008, 45(2):324-343.[13] WEN H, ZHU Z H, JIN D P, et al. Space tether deployment control with explicit tension constraint and saturation function[J]. Journal of Guidance, Control, & Dynamics, 2016, 39(4):915-920.[14] STEINDL A, Optimal control of the deployment (and retrieval) of a tethered satellite under small initial disturbances[J]. Meccanica, 2014, 49(8):1879-1885.[15] KUMAR K, PRADEEP S. Strategies for three dimensional deployment of tethered satellites[J]. Mechanics Research Communications, 1998, 25(5):543-550.[16] WEN H, JIN D, HU H. Three-dimensional deployment of electro-dynamic tether via tension and current control with constraints[J]. Acta Astronautica, 2016, 129:253-259.[17] VALLADO D A. Fundamental of astrodynamics and applications[M].New York:Microcosm Press, 2007:103-117.[18] WILLIAMS P. Libration control of electrodynamic tethers using predictive control with time-delayed feedback[J]. Journal of Guidance, Control, & Dynamics, 2015, 32(4):1254-1268.[19] POLYCARPOU M M, IOANNOU P A. A robust adaptive nonlinear control design[J], Automatica, 1996, 32(3):423-427.[20] SLOTINE J J E, LI W. Applied nonlinear control[M]. Beijing:China Machine Press, 2004:121-155.[21] 黄静, 李传江, 马广富, 等. 基于广义逆的欠驱动航天器姿态机动控制[J]. 自动化学报, 2013, 39(3):285-292. HUANG J, LI C J, MA G F, et al. Generalised inversion based maneuver attitude control for underactuated spacecraft[J]. Acta Automatica Sinica, 2013, 39(3):285-292(in Chinese).
CJA