## 1 Introduction
As shown in Figure 1, the system compensates 5/6 of the CLRV's weight over a square test field of 80 \(\times\) 20 square meters. As shown in Figure 1, the primary research of this paper is the track-following servo subsystem in the LGCF, consisting of an overhead moving crane and a trolley. The crane moves on the bridge, tracking the real-time position of the CLRV in the \(X\) direction, and the trolley moves along the crane girder to follow the real-time \(Y\) position of the CLRV. The servo motors drive the crane and trolley. The paper introduces the vector control of the PMSM to the track-following servo subsystem, enabling high-precision and rapid tracking control. In servo motors, the permanent-magnet synchronous motor (PMSM) has many outstanding advantages compared with other motors. The PMSM vector control system can achieve high precision, high dynamic performance, and an extensive range of speed regulation, tracking, and control, attracting wide attention and research from scholars worldwide [15; 16; 17]. This track-following servo subsystem includes the position servo closed-loop and closed-loop control of the motor speed and current. In the simulation model of the speed and current closed-loop control, the surface-mounted PMSM (SPMSM) vector control system based on the Space Vector Pulse Width Modulation (SVPWM) method was used in the paper [18], which highly simulated the actual system. The PI method was used for the PMSM vector control system. In the position servo closed-loop, there are constraints on the movement speed and acceleration of the crane and trolley to avoid motor idling [19] or over-speed. Moreover, the motion ranges of the crane and trolley are also constrained by the size of the facility. The traditional PID control cannot meet the control requirements, due to multi-variable constraints in the position servo closed-loop. In particular, this paper employs the explicit model predictive controller (EMPC) [20] in the position servo closed-loop so that the overhead moving crane and the trolley follow the motion of the CLRV in the \(X\) and \(Y\) directions, respectively. The MPC is a new computer optimization control algorithm that can effectively deal with multi-variable constraint systems [21]. It has become a standard optimization method for complex constraint systems. In recent years, the MPC has received significant attention in path tracking and fast tracking [22; 23]. The main reason is that the MPC can better handle the constraints of concern to physical and safety systems, which benefits system control performance and component protection. Despite the advantages of the MPC mentioned above, its substantial computational complexity resulting from online optimization at each sampling time poses a significant drawback and limits its applicability to relatively small and slow systems. To address this challenge, [PERSON] and [PERSON] et al. proposed a novel approach based on an MPC scheme that moves all computational efforts offline, enabling the scheme to overcome the aforementioned limitation [24; 25], and the method is the EMPC. Overall, this study provides an innovative and promising design proposal for a track-following servo subsystem of an LGCS suitable for the CLRV ground test. The vector control of the PMSM based on SVPWM is used in this paper to achieve a fast response of the track-following servo control. Notably, this paper adopts an EMPC in the position servo closed-loop to obtain good control performance. The EMPC controller can be applied to multi-constrained systems, ensuring a fast response while reducing overshoot. Finally, simulation models of the subsystem are built, and the simulation results are presented and discussed to evaluate the proposed system design and control scheme. The study provides a significant contribution to the field of the LGCS and serves as a valuable reference for future research. The paper is organized as follows.