# Rotating Lorentz Force Magnetic Bearings' Dynamics Modeling and Adaptive Controller Design
## 1 Introduction  
Presently, space missions such as laser communication and high-score reconnaissance have increasingly high demands for rapid maneuverability and pointing accuracy of the payload. Both the satellite platforms are required to have ultra-stable pointing stability, ultra-sensitive attitude maneuverability, and ultra-precise load pointing accuracy [1; 2; 3]. In addition, compared to the world's top level, China's agile satellite attitude maneuver angular acceleration is small, and the accuracy and stability of the output torque are poor, resulting in the poor pointing accuracy and pointing stability of the load and a poor maneuvering capability. In order to solve the above problems, there are currently three solution ideas: one is the integrated design of the satellite platform and the load, which can effectively avoid the high-frequency vibration and high-order perturbation brought about by fuel shaking, the vibration of flexural parts, and measurement and control asynchrony. However, because the specialized nature is strong, the cost of a single star is high, which is not conducive to multi-satellite network work. The second is to develop high-precision control actuators, but the research and development cycle is long, which is not conducive to accelerating the use of space. The third is to use the stabilized platform to isolate the vibration transmission between the satellite platform and the payload, optimize the control algorithms, andimprove the stabilized platform's ability to control the payload's maneuvering and pointing. Therefore, under the current technical conditions, the use of stabilized platforms has more practical value for improving the performance of agile satellites [4; 5; 6; 7; 8; 9]. Stabilized platforms can be divided into mechanically stabilized platforms, mechanically and electromagnetically stabilized platforms, and electromagnetically stabilized platforms according to the difference in the force between the axis systems. Traditional mechanical stabilized platforms have friction moments between the axes, which affects the pointing accuracy and service life of the platform. Meanwhile, the magnetic levitation bearing has the characteristics of being frictionless, having a long life, having no displacement negative stiffness, and being actively controlled, which are why it is widely used. Therefore, the current mainstream stabilized platforms are mechanical electromagnetic platforms and electromagnetic stabilized platforms. The core idea of the mechanical electromagnetic platform is to use the magnetic levitation bearing to control the important degrees of freedom to ensure the accuracy, and use the mechanical bearing to ensure the stability, of the remaining degrees of freedom. This kind of idea is common in agile satellites: The French SPOT series of Earth observation satellites use the magnetic levitation flywheel as the attitude control system to achieve high-resolution Earth observation [10]. [PERSON]'s team at the Beijing University of Aeronautics and Astronautics (BUAA) has realized the high-precision attitude control of large remote-sensing satellites based on the magnetic levitation control moment gyroscope developed [11; 12; 13]. [PERSON]'s team at the University of Aerospace Engineering proposes a magnetic levitation control sensitive gyro that integrates moment output and attitude measurement to achieve attitude measurement and control of the deflected two degrees of freedom. In summary, the idea of the mechanical electromagnetic platform is to place one or more magnetic levitation components in the corresponding degrees of freedom of the satellite as actuators or measuring devices, to control the stable pointing and agile maneuvering of the satellite/payload. However, because the magnetic levitation only controls part of the degrees of freedom, it is easy to produce high-frequency micro-amplitude vibrations in the process of momentum exchange, which restricts the pointing accuracy of the payload.