挠性卫星姿态动力学系统非线性控制新方法研究

The nonlinearity, flexibility and uncertainty are three major characteristics of the dynamical system of a satellite. Due to the lack of universal theory and effective methodology to cope with nonlinear problems, the approximate linearization technique is still a key method in both theoretical study and engineering design for a satellite attitude system. In recent years, the remarkable development in the positive polynomial theory, especially the sum of squares(SOS) techniques, has offered an effective way for the study of a nonlinear system. In view of the special structures of the attitude system of a satellite with flexible structures, heuristic approaches to the dynamics analysis, the nonlinear and the robust control of the satellite systems are proposed on the basis of SOS techniques, which probably provide a new way of attitude control for satellites with flexible structures. Therefore, the study is a valuable complement to the nonlinear control theory and related techniques. The attitude controller design for a satellite with flexible structures addressed in this study is performed on the original nonlinear model, which avoids the modeling error caused by the approximate linearization method. The SOS-based new theory and methods of dynamics analysis and nonlinear control for the flexible satellite systems are easily applicable because they can be verified by the convex programming. Furthermore, the corresponding controllers are of easy implementation because they are represented as some polynomial or rational functions of the systems outputs. Finally, the nonlinear control methods proposed in this project can improve the system performance and prevent the potential conflict of multi-performance objectives, which often appears in the linear control theory.

卫星姿态动力学系统具有明显的非线性、挠性和不确定性特征。由于缺乏有效的非线性设计理论和方法，姿态控制研究和工程实践多以线性化方法为主。近年来，正多项式特别是多项式平方和(SOS)理论取得重要进展，有力促进了非线性控制理论研究。挠性卫星姿态系统属一类有特定结构的多项式非线性系统，受此激励，本项目基于SOS方法，研究这类系统的动力学分析、非线性控制和鲁棒控制问题，为挠性卫星姿态控制设计提供新的途径。项目研究内容是对非线性控制理论和方法的有益补充。本项目直接针对挠性卫星姿态非线性系统模型的设计方案，可避免传统线性化方法引起的模型误差。由此建立的基于SOS的挠性卫星姿态系统动力学分析和非线性控制理论与方法，可借助于凸优化算法检验，且相应的非线性控制器仅是系统输出的多项式或有理式函数，不过分增加工程实现难度。另外，非线性控制方法避免了线性控制不能兼顾多性能指标相互冲突之固有不足，提高系统性能品质。

挠性卫星姿态动力学系统具有明显的非线性、挠性、不确定性和内外部干扰的特征，这些特征对高指向精度和高稳定度的姿态控制研究提出了挑战，是当前挠性卫星姿态控制领域的难点和热点问题。本项目直接以挠性卫星的非线性姿态动力学模型为对象，采用近期成熟的SOS 凸优化理论，主要围绕这类非线性系统的动力学分析、非线性控制以及鲁棒非线性控制的问题展开研究。首先，基于Lyapunov稳定性理论和SOS凸优化理论，建立了卫星非线性姿态系统的稳定性判据，并通过理论分析和数值仿真的手段，分析了挠性卫星参数变动、动态不确定性、外部扰动以及挠性附件对卫星本体姿态动力学行为的影响。其次，针对挠性模态的难以测量性，我们提出了基于挠性模态观测器的非线性姿态控制设计方案，给出了控制器的存在性条件，并证明了分离特性的成立，极大地降低了控制器设计的复杂性。在此基础上，针对航天工程实践中存在的主要不确定性因素，我们提出了鲁棒非线性姿态控制设计方案，给出了控制器的存在性条件，提高了卫星姿态系统适应参数变化、动态不确定性和外部干扰的能力。最后，基于以上研究方法，我们考虑了一般多项式非线性系统的输出反馈控制问题，给出了问题可解的凸优化条件，将本项目的工作一般化，完善了已有结果。项目中提出的控制方法，均通过数值仿真验证了其可行性和有效性，并建立了一个挠性卫星姿态仿真实验系统，用于比较线性控制和非线性控制方案各自的特点。