无拖曳卫星在卫星导航、地球重力场测量、空间广义相对论验证和引力波探测等领域具有重要应用。无拖曳卫星的卫星本体和检验质量都有很高的微重力水平，能为各种空间科学实验提供条件。近年来，随着我国空间科学的发展，科学家提出了我国自己的空间引力波探测、重力场测量任务，无拖曳卫星在这些任务中占有重要地位，因此，无拖曳控制研究对推动我国空间科学的发展具有重要的意义。

本研究以抗扰为无拖曳控制研究的核心，引入自抗扰控制这一控制器设计框架，来统一解决无拖曳控制中所涉及到的问题。另外，我们在地面搭建了无拖曳半物理仿真平台来实现地面闭环无拖曳控制。具体工作如下：

（1）研究了单检验质量无拖曳卫星的自抗扰控制器设计问题。首先，我们导出了无拖曳卫星的动力学模型。利用扰动解耦控制方法，将无拖曳控制回路和悬浮控制回路解耦，由此，检验质量上的残余加速度性能指标可以分解为无拖曳控制回路和悬浮控制回路的性能指标。另外，我们导出了基于降阶扩张状态观测器的自抗扰控制器的两自由度内模控制结构，用来验证每一个控制回路的鲁棒稳定性。根据系统稳定性和性能指标要求，设计搜索程序，得到满足条件的控制器，分析无拖曳控制器回路和悬浮控制回路的频域性能，我们发现，控制器对系统的摄动具有很好的鲁棒性，并且具有很好的扰动抑制性能。最后，为了确认控制器能满足性能指标要求，进行全系统的数值仿真模拟，结果表明自抗扰控制方法设计的控制器可以满足性能指标要求。

（2）研究了双检验质量无拖曳卫星的自抗扰控制器设计问题，首先，我们导出了双检验质量无拖曳卫星的动力学模型，确定了控制器的结构，在这种控制策略作用下，无拖曳系统实现解耦，另外，我们定义了作用在双检验质量无拖曳系统上的扰动，包括系统的测量噪声和作用在卫星本体和检验质量上的扰动。而后，我们定义了无拖曳控制的性能指标要求，将性能指标要求转化为对各回路的灵敏度函数和补灵敏度函数的约束。我们引入自抗扰控制方法来设计各控制回路的控制器，为了使控制器在低频段有更好的扰动抑制性能，引入了高阶扩张状态观测器。对于无拖曳控制回路的延迟，将其作为模型信息在控制器设计中予以考虑，设计基于模型信息的自抗扰控制器。最后，我们分析了各回路的闭环灵敏度函数和补灵敏度函数的频域特性，发现设计的控制器在低频段有很好的扰动抑制性能，在此基础上进行全系统的数值仿真模拟，结果表明，设计的控制器能满足性能指标要求。

（3）研究了双检验质量无拖曳系统的辨识问题，我们根据自抗扰控制原理，设计了扩张状态观测器估计系统不同控制回路的扰动和状态，基于状态和扰动估计值设计控制器使系统稳定。提出了基于扩张状态观测器（ESO）的多输入多输出系统闭环参数辨识方法。为了提高实际应用中的辨识效果，通过引入积分型滤波器对观测状态中的噪声进行抑制，并从理论上说明了其噪声抑制机理。最后，我们把这种方法应用于类似于LISA Pathfinder的单轴无拖曳模型，对系统动力学参数进行估计，通过数值仿真实验验证所提出的辨识方法的有效性和实用性。

（4）以近地轨道地球重力场测量卫星为研究对象，研究无拖曳控制中典型的状态估计问题，卫星本地轨道参考坐标系的估计。首先，我们导出了系统的动力学方程，定义了系统的输出。采用扩张状态卡尔曼滤波器来估计卫星本地轨道坐标系的状态参数。扩张状态卡尔曼滤波器（ESKF）是由扩张状态观测器发展而来，根据测量噪声的信息、被观测系统中存在的不确定动态、以及离散化误差，我们改进扩张状态观测器的结构，最优化扩张状态观测器的增益参数就可以得到扩张状态的卡尔曼滤波器，最后对提出的状态估计方法进行数值仿真模拟，并和扩展卡尔曼滤波器和无迹卡尔曼滤波（UKF）的仿真结果进行了对比。

（5）针对目前无拖曳卫星仿真研究和实际在轨运行无拖曳卫星之间的鸿沟，提出了无拖曳技术验证卫星的地面无拖曳半物理仿真方案。按照物理量等效的原则，将技术验证星沿无拖曳控制敏感轴的平动等效为地面悬挂扭摆的转动，惯性传感器等效为地面的倒立摆和附属在悬挂摆上的电容感测和驱动极板。在此基础上，设计无拖曳悬挂摆和倒立摆，搭建半物理仿真系统，并采用自抗扰控制方法初步设计了控制器，并进行模拟仿真。

研究结果表明，在本文中确定的扰动和噪声输入情况下，设计的无拖曳控制器可以满足性能指标要求，设计的参数辨识方法对参数估计的误差优于2.5%，设计的扩张状态卡尔曼滤波器可以满足性能指标要求。地面1-D无拖曳半物理仿真实验方案具有可实现性。

Drag-free satellites have important applications in satellite navigation, Earth gravity field measurement, spatial general relativity verification, and gravitational wave detection. The satellite and the test mass have high microgravity levels, which can provide conditions for various space science experiments. In recent years, with the development of China's space science, scientists have proposed China's own space gravitational wave detection and gravity field measurement projects. Drag-free satellites play an important role in these projects. Therefore, the study of drag-free control is of great significance to promote the development of space science in China.

In this thesis, disturbance rejection is the core of the drag-free control, and the controller design framework of active disturbance rejection control is introduced to solve the problems involved in the drag-free control. In addition, we built a drag-free semi-physical simulation platform on the ground to achieve closed-loop drag free control. The specific work is as follows:

(1) The problem of designing an active disturbance rejection controller for drag-free satellite with single test mass is studied. By using the disturbance decoupling control method, the drag-free control loop and the suspension control loop are decoupled. Thus, the residual acceleration performance requirements on the test mass can be decomposed into the performance requirements on the drag-free control loop and the suspension control loop. In addition, we derive a two-degree-of-freedom internal model control structure for the ADRC based on the reduced-order extended state observer to verify the robust stability of each control loop. According to the system stability and performance requirements, a search program is designed to obtain the controller that meets the conditions, and the frequency domain performance of the drag free controller loop and the suspension control loop is analyzed. We found that the controller is robust to the perturbation of the system and has good performance on disturbance rejection. Finally, in order to confirm that the controller can meet the performance requirements, the whole system numerical simulation is carried out. The results show that the controller designed by the active disturbance rejection control method can meet the performance requirements.

（2）The problem of designing an active disturbance rejection controller for drag-free satellite with double test mass is studied. First, we derive the dynamic model of the drag-free satellite with double test mass, and determine the structure of the controller. Under this control strategy, the drag-free system can be decoupled. In addition, we define disturbances acting on the system, including the measurement noise of the system and the disturbances acting on the satellite and the test mass. Then, we defined the performance requirements for drag-free control, and converted the performance requirements into constraints on the sensitivity function and the complementary sensitivity function of each loop. We introduce active disturbance rejection control method to design the controllers of each control loop. In order to make the controller have better disturbance rejection performance in the low frequency band, a high-order extended state observer is introduced. For the delay of the drag-free control loop, it is considered as the model information in the controller design, and the active disturbance rejection controller based on the model information is designed. Finally, we analyze the frequency domain characteristics of the closed-loop sensitivity function and the complementary sensitivity function of each loop. It is found that the designed controller has good disturbance rejection performance in the low frequency band. Based on this, the whole system numerical simulation is performed. The results show that The designed controller can meet the performance requirements.

（3）The identification problem of drag-free satellite with double test mass is studied. Based on the principle of active disturbance rejection control, we design the extended state observer to estimate the disturbance and state of different control loops of the system. Based on the state and disturbance estimation, the controller is designed to make the system stable. A closed-loop parameter identification method for multi-input and multi-output systems based on extended state observer (ESO) is proposed. In order to improve the identification effect in practical applications, the noise in the observed state is suppressed by introducing an integral filter, and the noise suppression mechanism is theoretically explained. Finally, we apply this method to a single-axis drag-free model similar to LISA Pathfinder, estimate the system dynamics parameters, and verify the validity and practicability of the proposed identification method through numerical simulation experiments.

(4) Taking Earth gravity field measurement satellite as the research object, the typical state estimation problem in the drag-free control and the estimation of the satellite local orbit reference coordinate system is studied. First, we derived the dynamic equations of the system and defined the output of the system. An extended state Kalman filter is used to estimate the state parameters of the satellite's local orbital coordinate system. The extended state Kalman filter (ESKF) is developed from an extended state observer. Based on the information of the measured noise, the uncertain dynamics present in the observed system, and the discretization error, we improve the structure of the extended state observer. The Kalman filter of the extended state can be obtained by optimizing the gain parameters of the extended state observer. Finally, the proposed state estimation method is numerically simulated and simulated with the extended Kalman filter and the unscented Kalman filter (UKF). A comparison was made.

(5) Aiming at the gap between the current drag-free satellite simulation research and the actual on-orbit operation drag-free satellites, a ground drag-free semi-physical simulation project of drag-free technology verification satellite is proposed. According to the principle of physical quantity equivalent, the translation of drag-free technology verification satellite along the drag-free control sensitive axis is equivalent to the rotation of the ground suspension torsion pendulum. The inertial sensor is equivalent to the ground inverted pendulum and the capacitive sensing and driving plate attached to the suspension pendulum. On this basis, design suspension pendulum and inverted pendulum to build a semi-physical simulation system, and the controller is preliminarily designed and simulated by the active disturbance rejection control method.

The research results show that under the disturbance and noise input conditions determined in this paper, the designed drag-free controller can meet the performance requirements, and the designed parameter identification method has better error than 2.5% for the parameter estimation. The designed extended state Kalman filter can meet the performance requirements. The ground 1-D drag-free semi-physical simulation experimental scheme is achievable.