# An Improved Deviation Coupling Control Method for Speed Synchronization of Multi-Motor Systems
## 1 Introduction
Nonetheless, owing to inherent structural limitations, this configuration proves suboptimal as the number of motors increases gradually, with adjustment times extending excessively, thereby constraining its broader applicability. [PERSON] et al. [16] introduced a deviation coupling control strategy. This approach compensates for the speed of each motor based on the relationship between the speed difference and the speed deviation, resulting in improved synchronous performance and faster response speed. This synchronous structure not only capitalizes on the high synchronous accuracy of cross-coupling dual axes but also overcomes the limitation of the cross-coupling structure in multi-axis conditions. The deviation coupling control strategy exhibits excellent overall performance. To further enhance synchronization, researchers have integrated various synchronization control algorithms to make substantial improvements in multiple aspects. [PERSON] et al. [17] enhanced the speed compensator by integrating sliding mode control with a coupling matrix, thus advancing both the synchronization and robustness of the system. [PERSON] et al. [18] introduced a radial basis function (RBF) neural network into the conventional PID algorithm and utilized the gradient descent algorithm to mitigate errors, thereby enhancing the system's anti-interference capability and robustness. [PERSON] et al. [19] employed the space vector pulse width modulation (SVPWM) control technique as the inner loop, complemented by PI and sliding mode controllers serving as the outer loop within a four-motor control system. Their approach, augmented by a deviation coupling control strategy, ensured robust tracking performance in the face of sudden load variations. [PERSON] et al. [20] introduced a novel non-singular fast terminal sliding mode control (NSTSMC) method, integrating it with an improved deviation coupling control structure. This innovation bolstered the interconnection between multiple motors, thereby achieving precise position synchronization across the motor array. [PERSON] et al. [21] harnessed sliding mode control to enhance the dynamic response of motors within the deviation coupling control framework. Their proposed nonlinear function amalgamated various strategies to bolster synchronization and anti-interference capabilities within a four-motor control system, particularly in an independently driven electric vehicle setting. [PERSON] et al. [22] devised a self-adaptive integral sliding mode control (SAISMC) scheme alongside an improved sliding mode disturbance observer (SMDO). By integrating SAISMC and SMDO into the deviation coupling control framework for multiple permanent magnet synchronous motors (MPMSMs), their methodology substantially elevated the stability and control precision of the multi-motor system. [PERSON] et al. [PERSON] et al. (2019) proposed a tracking and synchronous control strategy for a vehicle two-motor SBW system using super-twisted second-order sliding mode control (SOSMC) and a mean deviation coupling structure (MDCS). This approach aimed to enhance the reliability and safety of conventional multi-motor systems. Meanwhile, [PERSON] et al. [PERSON] et al. (2019) adopted particle swarm optimization and an improved variable-speed integral, based on the mean coupled control (MCC) structure term, to optimize the regular compensation factors and parameters of the PI controller. This optimization was geared towards improving the tracking accuracy and stability of multi-motor systems. While the aforementioned method effectively optimizes the control system's performance, its complex structure leads to a significant increase in system arithmetic, particularly when dealing with additional control axes. To address these challenges, this study proposes an improved deviation coupling synchronous control approach. By incorporating average speed compensation, the structure of the multi-motor system is simplified, reducing system overhead during axis adjustments.