# An Improved Deviation Coupling Control Method for Speed Synchronization of Multi-Motor Systems
## 3 Simulation Experiment and Result Analysis
### Analysis of Simulation Results  
Utilizing the established simulation model, the synchronization of the method is confirmed by evaluating motor speeds, speed synchronization errors between adjacent axes, and the adjustment time for synchronization errors when various control strategies are implemented. The simulation outcomes employing the PID controller are depicted in Figure 6, while the results utilizing the fuzzy PID controller are illustrated in Figure 7.  
Figure 6: Simulation results of the six-axis synchronous control model with PID.  
Table 2 presents a comparative analysis of different control strategies under the PID controller. Notably, the improved deviation coupling control strategy exhibits superior synchronization efficacy. The maximum synchronization error decreases from 28.82 rpm to 11.71 rpm, marking a significant 59% reduction compared to the without synchronization control strategy. Additionally, the synchronization error adjustment time decreases from 5.94 ms to 4.74 ms, reflecting a 20% improvement. During the initial phase, the motor achieves a steady state at 0.02773 s due to speed overshoot oscillation. Upon the abrupt load application at 0.05 s, motors 1 and 2 manifest noticeable speed fluctuations. With the incorporation of the deviation coupling control strategy, motor speeds interact, leading to more pronounced speed fluctuations in the remaining motors and an increase in synchronization error adjustment time. However, the maximum synchronization error diminishes significantly. On the contrary, the improved deviation coupling control strategy better facilitates synchronous motion among multiple motors. Post sudden load application, minor speed fluctuations occur in motors 1 and 2 with the improved deviation coupling control strategy, while the impact on other motors remains minimal, resulting in almost negligible speed fluctuations. The speed adjustment time for each motor shortens, and the maximum synchronization error experiences a notable reduction. Compared to the deviation coupling control strategy, the maximum synchronization error decreases from 19.19 rpm to 11.71 rpm, marking a 39% improvement, while the synchronization adjustment time decreases from 8.92 ms to 4.74 ms, signifying a 49% enhancement.  
Upon integrating fuzzy PID, depicted in Figure 7, it is evident that the phenomenon of speed overshoot oscillation during motor startup is notably mitigated. The motor achieves a steady state in a mere 0.01365 s, representing a remarkable 51% reduction in time. Additionally, under fuzzy PID control, the motor attains a steady state faster following a  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Without** & **Deviation Coupling** & **Improved** & **Compare** \\ \hline Maximum synchronization error & 28.82 rpm & 19.19 rpm & 11.71 rpm & \(-\)59\% \\ Synchronization error adjustment time & 5.94 ms & 8.92 ms & 4.74 ms & \(-\)20\% \\ \hline \end{tabular}
\end{table}
Table 2: Comparison of simulation data with PID.  
Figure 7: Simulation results of the six-axis synchronous control model with fuzzy PID.  
sudden load addition. Table 3 illustrates that compared to the deviation coupling control strategy, the improved deviation coupling control strategy can decrease the maximum synchronization error by 48%, from 18.88 rpm to 9.81 rpm, and reduce the synchronization error adjustment time by 32%, from 5.59 ms to 3.78 ms.  
In summary, the improved deviation coupling control method incorporating fuzzy PID, as proposed in this study, exhibits distinct advantages in reducing synchronization error and enhancing dynamic adjustment performance. Compared to without synchronization control, the maximum synchronization error can be reduced by 66%, and the synchronization error adjustment time can be diminished by 37% after implementing the improved deviation coupling control method. This method significantly improves the synchronous performance of the multi-axis control system.