库仑力与星间洛伦兹力复合力场卫星编队动力学与控制研究

Coulomb Formation Flying and Inter-Satellite Lorentz Force Formation are two representative techniques of the mass-cost-less satellite formation. Based on the fact that there are no equilibrium points within a three-craft triangular Coulomb Formation Flying, which may cause the chattering effect on the control inputs, this project proposes to incorporate the Lorentz force into the Coulomb Formation Flying. By this approach, the dynamics of the system may have multiple equilibrium points, which enables smoother control inputs while achieving stability. This yield the concept of the Coulomb-Lorentz Hybrid Formation Flying(CLHF). Coulomb Formation Flying and Lorentz Formation Flying are the most advanced approach to controlling a spacecraft formation. These two techniques are extraordinarily suitable to the long-term, tight-clustered space formation missions. Combining these two approaches can overcome the shortages of each one, such as introducing the equilibrium points into the Coulomb Formation. This approach may have a better performance while with increased control-ability. Based on our previous studies in this area, the applicant proposes this project to investigate the high-performance control for the three-craft CLHF reconfiguration and stable control problem. The objective is to develop a high-performance, high-reliability control strategy to achieve the reconfiguration maneuver of a three-craft CLHF virtual structure. The research would be launched following these steps: 1. Modeling of the hybrid force filed formation; 2. Dynamic analysis of the CLHF; 3. Maneuver orbit design and optimization; 4. Reconfiguration and stable control system design; 5. On ground testbed simulation. We are looking forward to achieving original academic accomplishments in the following aspects: 1. The properties of the equilibrium points and the algorithm to solve equilibrium point under the configuration constraint; 2. Patched transfer orbit design and optimization; 3. Under actuated control system design.

无工质消耗的卫星编队是卫星编队技术的前沿方向，库仑力卫星编队和星间洛伦兹力卫星编队是无工质卫星编队的两种代表性技术。本课题针对库仑力卫星编队中由于平衡点的缺失引起的稳定控制中的控制输入切换问题，提出在库仑力编队中引入星间洛伦兹力，形成库仑力与星间洛伦兹力复合力场编队的概念。藉此可以使原本无平衡点的系统转化为有平衡点的系统，从而使得平滑的控制输入成为可能。此复合力场编队飞行概念将编队飞行领域的两个前沿方向有机结合取长补短，对其开展研究有望获得一种性能更加优良且易于控制的编队方法。课题将从以下几个方面开展具体的研究：1.复合力场卫星编队建模；2.系统动力学分析；3.编队构形转移路径设计与优化；4.编队重构稳定控制系统设计；5.半物理仿真实验。通过攻关，争取在平衡点规律与目标构型解算、分段转移路径设计与优化、欠驱动系统稳定控制等问题上取得原创性学术成果。

库仑力与洛伦兹力复合力场卫星编队是一类无工质的卫星编队，采用星间静电力与洛伦兹力控制编队内卫星的相对运动，具有低功耗、清洁无羽流污染等优势，适合高轨或深空长周期卫星编队任务。本课题从地球同步轨道上三星库仑力编队静态平衡与控制问题、三星洛伦兹力与库仑力复合力场编队平衡点与控制问题着手，探讨此复合力场卫星编队的动力学与控制问题。课题的难点一方面在于三星编队系统是非仿射非线性的，另一方面在于需要保证平衡电荷解为实数解。前人在此领域上研究了一颗或两颗星固定于希尔坐标轴的GEO三卫星库仑力编队平衡解问题。本课题将前人的研究推广至指定平面上任意指向的GEO三卫星库仑力编队平衡解问题，并进一步探索了固定构形稳定控制问题。. 在希尔坐标系下建立以编队构形参数为自变量的动力学模型，然后在特定假设条件下求解平衡电荷解，通过数值仿真得到了当编队位于不同希尔坐标轴平面内时等腰三角形编队平衡电荷解与几何参数的关系。对于等腰三角形库仑力编队系统，在平衡点进行线性化后，对系统能控性进行分析。由于系统在仅受库仑力时是不可控的，因此将库仑力与常规推力结合，基于李雅普洛夫函数设计非线性反馈控制律，通过数值仿真对控制器效果进行了验证。对希尔系下洛伦兹力卫星编队的动力学与控制问题进行了分析。洛伦兹力是通过主动控制带有一个固定安装的电磁装置的副星上的电磁线圈电流与带电主星产生。在希尔系下建立动力学模型后，通过线性化确定了三组非平凡平衡点。在所有三组平衡点中，有两组不稳定但可控，而另一个是不稳定和不可控的。基于状态空间的线性规划设计了控制器来稳定结构达到平衡，通过多组数值仿真验证了控制算法的有效性。. 通过本课题的研究，明确了库仑力与洛伦兹力复合力场卫星编队概念的可行性，在原理上洛伦兹力的引入可以使得原本不存在平衡点的三星库仑力系统出现平衡点，从而为高性能的构型控制找到一条可行路径。

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