## 1 Introduction
Compared with the electromagnetic joint proposed in this paper, the SMA wire actuator has the advantages of a simpler structure, smaller volume, lighter weight and lower power supply, but its disadvantage is the lower response speed. [PERSON] et al. [24] developed a Levi-type analytical solution to describe the static and dynamic deformation response of smart laminated piezoelectric composite plates. Compared with only considering the bending deformation of the plate under low-frequency excitation below 1 Hz in this paper, their method considers not only the bending behavior of the plate, but also the torsional behavior of the plate, thus it has the advantage of accurately predicting the vibration response of the plate under arbitrary excitations. The above active methods adopt the intelligent piezoelectric structure and then combine them with modern control theory to control vibration. Although smart materials are beneficial for the micro-amplitude drive, they have a limited drive and control in large strokes. For example, the integrated intelligent piezoelectric structure on the surface of solar panels can efficiently suppress low-frequency and small-amplitude vibration. However, because of its limited control output ability, it is only suitable for small-amplitude vibration suppression. Additionally, the multi-body structure, rigid-flexible coupling, and combined bending-torsion vibration lead to a higher dimensional system and challenging controller design. This method also needs numerous sensors on the structure to obtain the system's information. However, the surface of the solar array is covered with solar cells, and it does not allow the arbitrary installation of intelligent structures on the surface. To summarize, due to the special limitations of volume, weight and installation requirements in aerospace applications, this method is difficult to popularize and apply to spacecraft [25; 26; 27; 28; 29; 30; 31]. Semi-active control is a parameter control technology. The stiffness, inertia, and damping characteristics of specific links in the system can be regulated in real time according to their input change and output requirement. Semi-active control provides excellent vibration characteristics. The required actuator consumes less energy and has a low price. Generally, both its volume and weight are easy to accept [32; 33; 34]. [PERSON] et al. [35] proposed a rotating magneto-rheological damper, which was installed between the driving mechanism and support frame of solar array, to suppress the driving disturbance caused by a solar array subject to drive fluctuation. By adjusting the coil current and damping torque and changing the magnetic field strength, semi-active vibration control of the system was realized. In addition, [PERSON] et al. [36] proposed an active joint mechanism and semi-active vibration control method for low-frequency vibration control, and preliminarily studied the influence of joint torsional stiffness on the low-frequency vibration characteristics of two flexible beams. In the current study, a flexible solar panel system with magnetic joints is proposed. The magnetic joint has the characteristics of the integration of structure and function. As a structural member, it provides rigid support for adjacent solar panels. As a functional element, its stiffness/damping can be actively adjusted, which can solve the frontier problem of low-frequency and large-amplitude vibration control of flexible space solar panels. The magnetic joints work based on the idea of the electromagnetic direct drive. The joint output shaft is coupled directly with the load for the driving output, which omits the traditional intermediate transmission link (gear reducer, etc. ), thereby eliminating the errors in the driving process, such as elastic deformation, transmission clearance, friction vibration, etc. Therefore, the accurate and rapid adjustment of joint stiffness/damping can be realized.