# Rotating Lorentz Force Magnetic Bearings' Dynamics Modeling and Adaptive Controller Design
## 1 Introduction
Moreover, the control bandwidth is narrow, so it cannot deal with high-frequency and high-order perturbations, and it is necessary to additionally increase the band-pass filter, which, in turn, increases the complexity of the system [14; 15; 16; 17]. Electromagnetic stabilized platforms can well-solve the problems existing in mechanical electromagnetic platforms. As the full degrees of freedom of the load/platform are supported by magnetic levitation bearings, it is frictionless, requires no lubrication, and can be actively controlled, which can avoid friction torque and vibration transmission. The magnetic levitation rotary joint designed by the Beijing Institute of Control Engineering uses a magnetic levitation bearing to support a single-degree-of-freedom swing of the load, which can solve the imaging accuracy problem of the variable speed phase in the attitude maneuver of remote-sensing satellites [18]. In addition, the magnetic levitation airborne inertial stabilization platform designed by [PERSON]'s team from the University of National Defense Technology supports a two-degree-of-freedom deflection, which realizes the high-resolution airborne remote sensing of the Earth [19; 20]. The delicate high-frequency test satellite platform developed by the Shanghai Academy of Space Technology supports two-degree-of-freedom deflection and two-degree-of-freedom, which has the \"double super\" capability of an ultra-high pointing accuracy and ultra-high stability [21; 22]. However, the magnetic levitation stabilization platforms developed by the above units either use magnetoresistive magnetic bearings, whose nonlinear and strong coupling characteristics easily lead to low control accuracy, or they only have individual degrees of freedom movability and the rest of the degrees are freedom fixed. The new seven-degree-of-freedom Lorentz force magnetic levitation stabilization platform proposed in this paper adds a single degree of freedom for overall deflection on top of the six-degree-of-freedom motion of the load module, which can more effectively isolate the vibration transmission and high-frequency perturbation of satellites, and adopts the Lorentz force magnetic bearings in all the seven degrees of freedom, which ensuresthat the input current is linear with the output force/torque, and improves the pointing precision and pointing stability of the loads. The seven-degree-of-freedom novel Lorentz force stabilized platform consists of rotary magnetic bearings, linear magnetic bearings, and orthogonal magnetic bearings, in which the linear magnetic bearings and orthogonal magnetic bearings jointly control the two-degree-of-freedom deflection and three-degree-of-freedom translation to isolate the high-frequency vibration and higher-order perturbation between the load and the satellite; the rotary magnetic bearings act as the angular displacement actuators to improve the angular displacement, and they drive the load to achieve the fast maneuver and stable pointing. Therefore, the controller design of the rotary magnetic bearing in this paper is directly related to the pointing performance of the load. At present, the controllers of spacecraft actuators generally have PID controllers, robust sliding mode controllers, feedforward decoupling controllers based on perturbation state observers, and so on. Among them, PID controllers and feedforward decoupling controllers require accurate mathematical models and parameters, while the higher-order perturbations in space are difficult to be modeled accurately; robust sliding mode controllers need to give upper and lower bounds of the perturbations and improve the robustness of the system under the premise of sacrificing the accuracy; and the control method based on the state observer of the disturbance, although it can accurately estimate the perturbations and isolate the perturbations by the accompanying filters, will increase the complexity of the system greatly.