计入大气阻力的电动力绳系系统的稳定性分析与控制
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摘要
电动力绳系系统(Electro-dynamic Tether, EDT)在航天航空中的应用十分广泛,主要可用于利用电动力绳索以高于燃料电池的效率发电,实现太空站轨道的维持；提供可以随意控制的微重力环境；对空间站的有效载荷以及日益严重的太空垃圾进行有效回收与处理；利用动量交换原理来改变空间飞行器的轨道；进行多种太空物理实验研究等。为了充分利用地磁场的作用,电动力绳系系统一般运行在近地轨道。因此这类系统在运行过程中受大气摄动影响显著。本文对计入大气阻力的电动力绳系系统的稳定性分析与控制进行了深入研究,具体工作和结论如下：
(1)给出了电动力绳系系统的轨道要素以及其工作原理,以及建立动力学模型所需要的坐标系和它们之间的转化关系。
(2)详细分析了影响大气阻力的各种因素,如大气的阻力系数,大气密度,卫星的轨道高度等。特别值得一提的是,大气密度本身又是一个非常复杂的变量,受地心纬度、轨道高度、季节变化以及昼夜变化等多种因素的影响。通过计算仿真分别得到各因素对大气阻力的影响程度。分析结果表明,影响大气阻力的因素之间是相互耦合的关系。
(3)利用拉格朗目方法分别建立了电动力绳系系统的二维和三维动力学模型,研究了两类方程的稳定性状态。广义力涉及到地球中心引力、电磁力、大气阻力。计算结果表明,大气阻力的摄动作用使原本可以维持自平衡状态的二维电动力绳系系统失去了稳定性；三维电动力绳系系统在轨道平面内外的运动相互耦合,系统在平面内受到初始扰动时,并不会引起平面外的运动,但是系统在平面外受到初始扰动时,将会引起平面内外的耦合运动；大气阻力的主要分量与系统的轨道速度反向,因此主要影响系统的平面内运动,而对平面外运动的影响并不大；随着绳索长度的增加,无论是绳索的平面内角还是平面外角的摆角幅度都有明显衰减的趋势,这是大气阻力和电磁力共同作用的结果；卫星轨道高度的增加,会使绳索的平面内角运动的发散趋势明显减小。因为随着系统轨道高度的增加,大气阻力作用减弱。
(4)对二维电动力绳系系统引入了以电流为反馈量的反馈控制方法进行控制,控制结果表明,该控制方法是有效的。
The electro-dynamic tethered (EDT) system is widely used in astronautics and aeronautics, such as, it can be mainly used to retain the orbit of space station using the electro-dynamic tether to generate power which is higher effcient than the fuel cell; provide the micro-gravity environment freely; recycle the useful loads of the space station and remove the growing space debris effectively; change the orbit of spacecraft based on the principle of momentum exchange; do experiments in the microgravity field and so on. To make full use of the role of the geomagnetic field, the EDT system generally runs in near-Earth orbit. This kind of system is perturbed by the atmosphere significantly during flying. An intensive study of the analysis and control of the electro-dynamic tethered satellite system considering the atmospheric drag is done in this thesis. The contents of research work are as follows,
(1) The orbital elements and operating principle of the EDT are introduced, and coordinate frames, which are used to establish the dynamic model, and the transformation of their relations are presented.
(2) The various influence factors of atmospheric drag, for instance, the atmospheric drag coefficient, the atmospheric density, the height of the satellite's orbit and so on, are analyzed in detail. It is particularly mentioned that the atmospheric density is a complex variable, which are influenced by the geocentric latitude, the orbit altitude, the seasonal variation and the diurnal variation and etc. The atmospheric drags under the influence of various factors are obtained by numerical simulation. The analysis results show that all influence factors of the atmospheric drag couple with each other.
(3) The two-dimension and three-dimension governing equations of the electro-dynamic tethered satellite system are derived using the Lagrangian method, and the stability states of the two equations are studied. The generalized forces include the gravity of the Earth, the electromagnetic force and the atmosphere drag. The calculation results of two-dimensional EDT system show that the self-balancing system will lose its stability because of the atmospheric drag. The analysis of three-dimensional model shows that there is a coupling between the in-plane motion and the out-of-plane motion. The system disturbed in the plane will not produce the out-of-plane motion. However, when the system is disturbed out of the plane, the in-plane motion will be caused. The atmospheric drag mainly influences on the in-plane motion, but not the out-of-plane motion of the system, because it is reverse with the orbital speed of the system. As the length of the tether increases, the swing angles of both the in-plane motion and the out-of-plane motion of the system are obviously weakened due to the disturbance both the atmospheric drag and electromagnetic force. The divergent trend of the in-plane motion of the system is substantially reduced because of the increasing of satellite orbit height because the atmospheric drag is decreased.
(4) The current feedback control method is introduced to the two-dimensional model of the EDT system. The control results show that this control method is effective.
(1)给出了电动力绳系系统的轨道要素以及其工作原理,以及建立动力学模型所需要的坐标系和它们之间的转化关系。
(2)详细分析了影响大气阻力的各种因素,如大气的阻力系数,大气密度,卫星的轨道高度等。特别值得一提的是,大气密度本身又是一个非常复杂的变量,受地心纬度、轨道高度、季节变化以及昼夜变化等多种因素的影响。通过计算仿真分别得到各因素对大气阻力的影响程度。分析结果表明,影响大气阻力的因素之间是相互耦合的关系。
(3)利用拉格朗目方法分别建立了电动力绳系系统的二维和三维动力学模型,研究了两类方程的稳定性状态。广义力涉及到地球中心引力、电磁力、大气阻力。计算结果表明,大气阻力的摄动作用使原本可以维持自平衡状态的二维电动力绳系系统失去了稳定性；三维电动力绳系系统在轨道平面内外的运动相互耦合,系统在平面内受到初始扰动时,并不会引起平面外的运动,但是系统在平面外受到初始扰动时,将会引起平面内外的耦合运动；大气阻力的主要分量与系统的轨道速度反向,因此主要影响系统的平面内运动,而对平面外运动的影响并不大；随着绳索长度的增加,无论是绳索的平面内角还是平面外角的摆角幅度都有明显衰减的趋势,这是大气阻力和电磁力共同作用的结果；卫星轨道高度的增加,会使绳索的平面内角运动的发散趋势明显减小。因为随着系统轨道高度的增加,大气阻力作用减弱。
(4)对二维电动力绳系系统引入了以电流为反馈量的反馈控制方法进行控制,控制结果表明,该控制方法是有效的。
The electro-dynamic tethered (EDT) system is widely used in astronautics and aeronautics, such as, it can be mainly used to retain the orbit of space station using the electro-dynamic tether to generate power which is higher effcient than the fuel cell; provide the micro-gravity environment freely; recycle the useful loads of the space station and remove the growing space debris effectively; change the orbit of spacecraft based on the principle of momentum exchange; do experiments in the microgravity field and so on. To make full use of the role of the geomagnetic field, the EDT system generally runs in near-Earth orbit. This kind of system is perturbed by the atmosphere significantly during flying. An intensive study of the analysis and control of the electro-dynamic tethered satellite system considering the atmospheric drag is done in this thesis. The contents of research work are as follows,
(1) The orbital elements and operating principle of the EDT are introduced, and coordinate frames, which are used to establish the dynamic model, and the transformation of their relations are presented.
(2) The various influence factors of atmospheric drag, for instance, the atmospheric drag coefficient, the atmospheric density, the height of the satellite's orbit and so on, are analyzed in detail. It is particularly mentioned that the atmospheric density is a complex variable, which are influenced by the geocentric latitude, the orbit altitude, the seasonal variation and the diurnal variation and etc. The atmospheric drags under the influence of various factors are obtained by numerical simulation. The analysis results show that all influence factors of the atmospheric drag couple with each other.
(3) The two-dimension and three-dimension governing equations of the electro-dynamic tethered satellite system are derived using the Lagrangian method, and the stability states of the two equations are studied. The generalized forces include the gravity of the Earth, the electromagnetic force and the atmosphere drag. The calculation results of two-dimensional EDT system show that the self-balancing system will lose its stability because of the atmospheric drag. The analysis of three-dimensional model shows that there is a coupling between the in-plane motion and the out-of-plane motion. The system disturbed in the plane will not produce the out-of-plane motion. However, when the system is disturbed out of the plane, the in-plane motion will be caused. The atmospheric drag mainly influences on the in-plane motion, but not the out-of-plane motion of the system, because it is reverse with the orbital speed of the system. As the length of the tether increases, the swing angles of both the in-plane motion and the out-of-plane motion of the system are obviously weakened due to the disturbance both the atmospheric drag and electromagnetic force. The divergent trend of the in-plane motion of the system is substantially reduced because of the increasing of satellite orbit height because the atmospheric drag is decreased.
(4) The current feedback control method is introduced to the two-dimensional model of the EDT system. The control results show that this control method is effective.
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