## 1 Introduction  
The plate-type PM-EDS system is mainly composed of PMs and nonnegative conductive plates. By the relative motion between the PMs and the conductive plates, induction eddy currents are formed in the conductive plates, which interact with the source of the magnetic field to generate the electromagnetic force to suspend the PMs [1]. PM-EDS system has the advantages of no friction, low power consumption, large levitation air gap and simple structure. Typical PM-EDS systems include the Magplane system [2; 3], the InductrackII system [4] and the Skytran system [5; 6]. The design speed of the Magplane vehicle is 250 km/h, its conductive plate is approximately arc-shaped, and the on-board Halbach PM arrays are used as the magnetic excitation sources as shown in Figure 1, which has low cost and high reliability, but the drag force is too large and the lift-to-drag ratio is low at low speed. As shown in Figure 2, the characteristic of the InductrackII system is that there are a set of Halbach PM arrays on the upper and lower sides of the conductive plate, respectively, which makes the drag force smaller at low speed, but it is not suitable for high-speed operation. As shown in Figure 3, the Skytran system places the conductive plate vertically, and the levitation force is generated by the angle between the PM and the conductive plate. The structure of Skytran mainly includes four parts: on-board PMs, propulsion system, ground track system and vehicle cabin. The linear propulsion motor pulls the train along the track, and suspension force is generated between the PMs and the conductive plates; the support wheels provide support when the train is not suspended. Although the PM-EDS system can be self-stabilizing, the system damping is weak and even exhibits a negative damping state under certain conditions. Therefore, the active damping or passive damping scheme is necessary. To improve the damping, the Magplane system adopts the active control of adjusting the magnet position by a set of hydraulic systems [7]. The InductrackII system uses a hybrid magnetic array with PMs and electromagnetic coils to realize the active control of the levitation force of the train by dynamically adjusting the current in the coil. The PM of the Skytran system can be driven by a motor to rotate around the shaft, and the levitation force can be dynamically adjusted by adjusting the angle between the PM and the conductive plate. The Skytran system, with adjustable angles of PMs, provides more flexibility. However, compared with Magplane and InductrackII systems, the angle adjustment mechanism will lead to increased weight  
Figure 1: Structure of Magplane. Figure 3: Structure of Skytran. Figure 2: Structure of InductrackII. and fatigue wear of the suspension system. At the same time, the problem of a small lift-to-drag ratio and lift-to-weight ratio of the PM-EDS system cannot be ignored [8]. The structure of Skytran is introduced in detail in articles [5; 6]. However, there is no article that calculates the electromagnetic forces and magnetic fields of Skytran system. The innovation of this paper is that the analytical calculation of electromagnetic forces and magnetic fields of the PM-EDS structure with an adjustable angle of PM is derived in detail, and the size of the PM is optimized by using the MOPSO method. First, the electromagnetic field analytical model of the system is established by introducing the SOVP, and the analytical solutions of the electromagnetic forces and the magnetic fields are obtained from the boundary conditions. Secondly, the FEA simulation model of the PM-EDS structure is established, and the calculation results of the analytical solution are verified. The results show that the calculation results of the two methods are consistent. Finally, the length, width and thickness of the PM are optimized to maximize the lift-to-drag ratio and lift-to-weight ratio by using the MOPSO algorithm.