## 5 Discussion  
Synchronization error of a dual-motor system will usually lead to degradation of equipment performance. Several researchers focused on the cross-coupling synchronous  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Experiment**} & \multicolumn{4}{c}{**Motion Planning**} & \multicolumn{4}{c}{**Synchronization Error (\(\mu\)m)**} & \multirow{2}{*}{**RMSE**} \\ \cline{2-2} \cline{4-9}  & **Displacement** & **Velocity** & **Acceleration** & **(m/s)** & **Control Method** & **1 MAX1** & **MAE** & **RMSE** & **Reduction (\%)** \\ \hline \multirow{2}{*}{1} & \multirow{2}{*}{0.05} & \multirow{2}{*}{0.35} & \multirow{2}{*}{30} & Method 2 & 584.500 & 117.259 & 221.443 & - \\  & & & Proposed method & 89.800 & 36.987 & 42.132 & 80.974 \\ \hline \multirow{2}{*}{2} & \multirow{2}{*}{0.05} & \multirow{2}{*}{0.5} & \multirow{2}{*}{30} & Method 2 & 561.600 & 80.388 & 161.193 & - \\  & & & Proposed method & 52.900 & 31.436 & 32.338 & 79.938 \\ \hline \multirow{2}{*}{3} & \multirow{2}{*}{0.05} & \multirow{2}{*}{0.5} & \multirow{2}{*}{50} & Method 2 & 769.000 & 106.681 & 220.616 & - \\  & & & Proposed method & 141.400 & 40.019 & 49.454 & 77.580 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental data comparison results of the synchronous motion experiments.  
Figure 12: FDC adjustment of the proposed adaptive fractional-order anti-saturation method: (**a**) fractional-order FDC planning target for the voltage amplitude characteristic; (**b**) FDC comparison of the two motor systems with and without the proposed method.  
Figure 13: Synchronous motion experimental results of the dual-motor system under different synchronous control methods: (**a**) displacement comparison; (**b**) control voltage comparison (\(\,|\,u_{max}\,|\,=\,10\text{V}\)); (**c**) synchronization error comparison.  
control method, by reducing the synchronization error from the aspects of the compensation method and the control parameter tunning method, to improve the synchronous motion performance of a dual-motor system [19; 30]. However, the cross-coupling synchronous control method is usually used to compensate the control voltage after the synchronization error occurred, so there is a time delay between the generation and the compensation of the synchronization error. As shown in Figure 3, under the control of the chirp signal, although the cross-coupling synchronous control method could greatly reduce the synchronization error of the dual-motor system, it was difficult to eliminate the synchronization error completely due to the constant changes in the amplitude and frequency of the input signal and the inconsistent response characteristics of the dual-motor system. The experimental results showed the relationship between the dynamic response characteristics and the FDC of the motor systems. With the proposed adaptive fractional-order anti-saturation synchronous control method, the FDC of the dual-motor system was adjusted to be consistent to guarantee the same dynamic response output of the dual-motor system. Compared with the cross-coupling synchronous control method, our method can suppress the generation of the synchronization errors of the dual-motor system and eliminate the influence of the saturation effect and thus can achieve a better synchronous-motion control performance, as shown in Table 2. It can be seen from the experimental results in Figure 13 that our method can effectively avoid the non-linear phenomenon of control voltage saturation and ensure the high-precision synchronization accuracy of the dual-motor system. Considering the problem of the hysteresis nonlinearity and gap nonlinearity of the dual-motor system, the synchronous control performance of the proposed method may be affected. Next, we will tackle this problem to further improve the synchronous control method for the dual-motor system.