With the development of heavy machinery, there is often a need to machine large integral parts and workpieces with complex geometries. Traditional gantry milling machines have a fixed gantry column, with the worktable carrying the workpiece fed longitudinally along the guide rails. Due to the large weight of the moving parts, it is difficult to achieve high acceleration; at the same time, due to limitations in worktable length and the need to save workplace space, the fixed-column structure of the gantry milling machine is far from meeting the requirements for high-speed machining of large workpieces. High-speed gantry milling machines, while meeting dynamic and static stiffness requirements, keep the worktable and workpiece stationary, allowing the gantry column to feed longitudinally along the guide rails. Because the moving mass of the column is relatively small, high acceleration characteristics can be achieved. However, because the large moving components, including the crossbeam and its matching tool post, the gantry and its matching parts, do not always form a symmetrical structure and symmetrical force distribution, and various uncertainties and disturbances occur during operation, even if both sides of the gantry column use identical transmission mechanisms, the consistency of movement of the columns on both sides of the gantry frame cannot be guaranteed. This inconsistency and the resulting mechanical coupling can damage the gantry frame drive components and the machined workpiece. Therefore, synchronous transmission of the two columns is a key technology for eliminating mechanical coupling, avoiding mechanical damage, and ensuring machining accuracy in this type of machine tool. To address the issue of changes in the equivalent inertia of the columns caused by the change in the tool holder's position on the crossbeam disrupting the dynamic synchronization performance of the output, a load dynamic compensation method is used to adjust the proportional gain, ensuring the two motors remain synchronized. In recent years, intelligent control has developed rapidly, especially fuzzy control, which does not completely rely on the mathematical model of the object. It is suitable for controlling systems with uncertainties and nonlinear systems, and is beneficial for solving many problems that classical control struggles with. This paper introduces a fuzzy PID controller as a speed regulator, effectively utilizing the advantages of fuzzy control to improve the accuracy of synchronous control. Structure and Coupling of a Gantry Moving Milling Machine Figure 1 shows the structure of a gantry milling machine driven by linear motors. Two linear motors drive two columns respectively. The input of one control loop affects the output of the other control loop through mechanical coupling. Interference in any single loop not only affects the output of its own loop but also affects the output of the other loop through the crossbeam; that is, interference is mutually coupled, and there is mechanical coupling at the output ends of the two drive motors. The mathematical model of the linear permanent magnet servo motor (LPMSM) is as follows: The voltage equation and flux linkage equation of the dq axis model of the LPMSM are: [align=left][img=133,106]http://www.ca800.com/uploadfile/maga/servo2007-1/____wm13.jpg[/img]（1） Where rs is the motor resistance; ud, uq, id, iq, ld, lq, [img=36,21]http://www.ca800.com/uploadfile/maga/servo2007-1/____wm14.jpg[/img] are the d and q axis motor voltage, current, inductance and flux linkage respectively; [img=13,15]http://www.ca800.com/uploadfile/maga/servo2007-1/____wm15.jpg[/img] are the motor velocity; [img=25,18]http://www.ca800.com/uploadfile/maga/servo2007-1/____wm16.jpg[/img] represents the pole pitch; represents the excitation flux linkage of the stator permanent magnet. Vector control is applied to lpmsm so that the mover current vector is orthogonal to the stator permanent magnet magnetic field in space. Even if id=0, then: [/align][align=left][img=127,38]http://www.ca800.com/uploadfile/maga/servo2007-1/___wmf81.jpg[/img]（2） Where kt is the thrust coefficient [font=黑体]Equation of motion[/font][/align][align=left][img=157,30]http://www.ca800.com/uploadfile/maga/servo2007-1/___wmf82.jpg[/img]（3） Where fl is the load resistance; fe is the equivalent resistance generated by the end effect; d is the viscous friction coefficient; m is the mass of the mover and its load. [align][font=黑体][color=#008284][/color][/font] System Control Structure In the synchronous servo system of a gantry milling machine, two servo subsystems move according to the same speed given signal. One servo system is defined as the driving axis, and the other as the driven axis, thus forming an independent master-slave drive mode. The two axes are kept synchronized by thrust control of the linear motor. This paper adopts a master-slave control structure, using position control only for the driving motor. The output of the driving motor's position controller is used as the speed command signal for the driven motor. When the driving motor experiences external disturbances and changes its position feedback, the reference speed of the driven motor changes accordingly, just like the reference speed of the driving motor. This improves the safety factor of the coupled structure of the control system. The schematic diagram of the synchronous control system is shown in Figure 2. Here, p2 is the position feedforward controller; p1 is the position proportional controller; the fuzzy PID controller is the speed controller to achieve a fast and accurate response to the input signal; the PI controller compensates for dynamic deformation force to prevent excessive dual-axis synchronization errors from harming the system under high-speed operation. Figure 2. Schematic diagram of synchronous control system structure and dynamic load compensation design. When a gantry-type moving boring and milling machining center implements two-dimensional motion control, the change in the position of the tool holder driven by the y-axis linear motor often leads to a change in the equivalent inertia of the x-axis linear motor. The driven motor, lacking independent positioning control, is easily affected by changes in its equivalent inertia, thus impacting the output synchronization of the two x-axis outputs. This necessitates the use of dynamic load compensation to adjust the proportional gain and provide control compensation to the x-axis driven motor, enabling the system to maintain synchronous operation. When the equivalent inertia of the motor increases, the transfer function between its current input and speed output will change, i.e., [img=107,17]http://www.ca800.com/uploadfile/maga/servo2007-1/___wmf83.jpg[/img]. The principle of load dynamic compensation is to use a weighted adjustment of the transfer function between the current input and the speed output to maintain a constant relationship. This is the load dynamic modulation gain. Here, w is just a proportional value, which can be defined as 1. Designing w' only requires obtaining Δm. As shown in Figure 3, define lengths e, f, g, h, and the centers of mass m1, m2, m3, and points a and b. Using the torque balance principle, the equivalent mass Δm of the structure (including m1 and m2) borne by point b can be calculated. Through the compensation of load dynamic modulation gain, even if the equivalent inertia of the driven motor changes, its speed output will not be affected, so that the system still maintains good synchronous response. Figure 3 Torque balance schematic diagram Design of fuzzy PID controller The fuzzy controller is designed according to the fuzzy control theory. Define the system error |e| and the rate of change of error |ec| as the input of the fuzzy controller, where e=yd-y (4) [img=50,17]http://www.ca800.com/uploadfile/maga/servo2007-1/___wmf88.jpg[/img] (5) kp, ki, kd are the outputs, that is, this fuzzy controller is a two-input three-output form. The universe of discourse for the input linguistic variables is {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}, and the universe of discourse for the output linguistic variables kp, ki, and kd is {0, 1, 2, 3, 4, 5, 6}. Based on past practical engineering experience, the membership functions of e and ec, and the control rule tables for the PID parameters kp, ki, and kd are obtained. A fuzzy PID controller is then designed. The control rules for kp, ki, and kd are shown in Table 1-3: [img=203,426]http://www.ca800.com/uploadfile/maga/servo2007-1/zxmb123.jpg[/img] System Simulation Two linear motors with identical parameters were used for simulation. The parameters are as follows: m=11.0kg, d=2.0ns/m, kt=27.5n/a, fe=200n. Controller parameters: p1=12, p2=1, pi=0.0583+0.213/s. When the time is 0.5s, a step signal with an amplitude of 0.4m is input on the x-axis as the position signal. Regarding the change in the load center of gravity on the y-axis, this study uses dynamic load compensation to eliminate the influence of the driven motor caused by the change in equivalent inertia, and adds a fuzzy PID controller for adjustment. Figure 4 shows the position error response curve of the system without load dynamic compensation and fuzzy PID control. Figure 5 shows the position error response curve after adding load dynamic compensation and fuzzy PID control. It can be seen that the addition of fuzzy PID control and load dynamic compensation greatly improves the synchronization accuracy of the two linear motors. Figure 4: Position error response curve without load dynamic compensation and fuzzy PID control. Figure 5: Position error response curve with load dynamic compensation and fuzzy PID control. Conclusion This paper, based on the analysis of the main reasons for the asynchrony between the two linear motors driven by dual linear motors on the x-axis in a gantry milling machine, proposes a control method using fuzzy PID and load dynamic compensation. Simulation curves show that the addition of fuzzy PID control and load dynamic compensation greatly improves the synchronization accuracy of the two linear motors.