## 1 Introduction  
In recent decades, permanent magnet synchronous motors (PMSMs) have been widely used in drive systems in industries such as aircraft and electric vehicles, due to their high power density, simple structure, and high efficiency. However, as the power requirements for drive systems continue to increase, single-motor systems are increasingly unable to meet the high-performance demands. As a result, dual-motor drive systems have gradually become a research hotspot in recent years. Compared to single-motor drives, dual-motor drives can effectively compensate for the shortcomings of single-motor systems in terms of load-bearing capacity and power output, showing significant advantages. Although the parameters of the two motors in a dual-motor system are typically kept consistent during the design process, they may still be influenced by external disturbances such as load variations, friction, and vibrations during actual operation. These disturbances can cause inconsistencies in the motor speeds or system imbalances, thereby affecting overall drive performance and stability. Therefore, improving the synchronization accuracy of dual-motor systems has become a key issue in enhancing production efficiency and ensuring the reliability of the production process. Improving the disturbance rejection capability and dynamic performance of a single motor is fundamental to enhancing the synchronization accuracy of a dual-motor system. The stronger the dynamic performance and disturbance rejection capability of the single motor, the smaller the speed synchronization error of the dual-motor system. Due to the nonlinear, multivariable, and strongly coupled characteristics of PMSMs, traditional PID control methods are difficult to meet the high-precision control requirements. When the system is subjected to load disturbances, the control parameters of the PI controller cannot be adjusted online, resulting in a significant degradation of system performance under the original control parameters. Therefore, many advanced control methods, such as model predictive control (MPC) [1; 2; 3], adaptive control [4; 5], and sliding mode control (SMC) [6; 7], have been proposed to improve the performance of single-motor systems. Among these advanced control methods, sliding mode control is effective in addressing disturbances and uncertainties in motor systems, enabling high-performance control. As a result, the application of sliding mode control in PMSM servo systems has not only significantly enhanced the system's robustness but has also become a major research focus in academia [8; 9; 10; 11; 12; 13]. Second-order sliding mode control (2-SMC), a commonly used method in higher-order sliding mode control, effectively reduces chattering phenomena compared to traditional first-order sliding mode control by introducing higher-order sliding surfaces [14]. Building on this, the control strategy based on second-order global fast terminal sliding mode control (2-GFTSMC) can further enhance the control performance of the motor, especially under the influence of external load disturbances, significantly improving the system's robustness and stability [15]. However, when either of the motors is disturbed, the synchronization of the dual-motor system will be affected, causing the two motors to fail to maintain the same speed. Therefore, extensive research has been conducted by scholars both domestically and internationally on synchronization control strategies for dual-motor systems, leading to the proposal of various advanced synchronization control methods to further reduce synchronization errors. Commonly used synchronization control strategies include parallel control, master-slave control, and cross-coupling control [16]. Currently, research remains focused on cross-coupling control strategies, particularly the improvement of cross-coupling control based on disturbance compensation, which can effectively enhance the system's disturbance rejection capability and suppress dynamic errors [17].