# An Improved Deviation Coupling Control Method for Speed Synchronization of Multi-Motor Systems
## 1 Introduction  
In recent years, propelled by the rapid advancements in intelligent manufacturing, the demand for welding robot arms has surged. They are extensively applied in aerospace, shipbuilding, automotive manufacturing, and other sectors due to their capability to operate in challenging and intricate environments, delivering high welding efficiency and consistent weld quality [1; 2; 3; 4; 5]. However, during welding operations, the synchronization of multiple axes within the robot arm can significantly impact welding quality. Consequently, achieving high-precision welding necessitates a heightened focus on synchronous joint control of robot arm movements. The synchronization control of multiple axes in welding robot arms is commonly categorized into several approaches, including master command control, master-slave control, cross-coupling control, virtual shaft control, adjacent cross-coupling control, and deviation coupling control [6; 7; 8]. Among these, the master-slave control method stands out due to its simplicity and ease of implementation. Additionally, it employs a parallel processing strategy where each axis receives identical signals, thus eliminating delays in signal transmission caused by inter-axis factors. In the master-slave control strategy, one motor is designated as the master motor while the other motor acts as the slave motor. The output speed signal from the master motor is utilized as the input speed signal for the slave motor. Both master command control and master-slave control fall under the category of uncoupled control, meaning there is no coupling relationship between the axes during motion, leading to significant synchronization errors [9]. The cross-coupling control strategy, initially introduced by [PERSON] [10], offers an effective resolution to the challenge of two-axis synchronous motion coupling. This strategy involves utilizing the speed disparitybetween two motors as a compensatory signal fed into the controller. [PERSON] [11] presented a friction-compensated multi-motor cross-coupling synchronous control method to achieve synchronous control of multi-servo motors. This method relied on friction compensation and incorporated a virtual shaft as its primary strategy, along with the design of a fuzzy PID compensation controller. By implementing this approach, a significant reduction in multi-servo motor synchronization error was achieved, resulting in high synchronization control accuracy. Nonetheless, it is imperative to note that while effective for certain applications, the cross-coupling control strategy may not be universally applicable to multi-motor systems. The concept of virtual shaft control was originally introduced by [PERSON] [12], aiming to emulate the traction properties of mechanical shafts for achieving synchronous control across multiple motors. This approach involves providing feedback on the actual operating torque from the multiple motors to the virtual shaft, which then adjusts its output to drive the slave shafts back to a synchronized state. [PERSON] et al. [13] adopted a non-singular terminal sliding-mode control technique to refine the virtual shaft control strategy. They integrated this with the dynamic sliding film control method specific to switched reluctance motors (SRMs) to enhance speed synchronization in dual SRM systems. However, challenges persist with this method, including inherent signal delays and the complexity of determining virtual shaft inertia. The concept of adjacent cross-coupling strategy was introduced by [PERSON] et al. [14], facilitating synchronous control of more than three motors. [PERSON] et al. [15] augmented this approach by integrating adjacent cross-coupling control with master-slave control. Their devised controller, employing a convergence law algorithm and global sliding mode control, notably enhances the synchronicity of multi-motor oscillating systems.