## 4 Experiment
### Synchronized Motion Experiments
#### 4.2.2 Synchronization Accuracy Verification  
To further verify the correctness of the calculation for the proposed adaptive fractional-order anti-saturation synchronous control method and its effectiveness in improving the synchronization accuracy of the dual-motor system, the cubic curve shown in Equation (43) was selected to perform the high-speed high-acceleration motion experiments. According to the above analysis and experiments of the FDC-UM, the parameters of the PID feedback controller selected in the experiments are shown in Equation (38), and those of the friction compensator are shown in Equations (40) and (41). When the dual-motor system was controlled by the proposed synchronous control method, the AFOAM analyzed the spectrum of the input signal and the FDC of the control system and then used Equation (36) to calculate the order of the FOLLC as 1.3190. According to Equations (31)-(33), \(\omega_{j}\) = 7.1740, \(K_{C}\) = 1, \(x\) = 0.8055, and \(\lambda\) = 0.1381. Therefore, using Equation (26), the transfer function of the AFOAM was calculated as Equation (45). According to Equation (45), we could draw the adjustment curve of the voltage amplitude characteristic realized by the AFO-AM, as shown in Figure 12a. An FDC comparison of the motor system with and without the designed AFO-AM is shown in Figure 12b. The anti-saturation module can avoid synchronization errors owing to the voltage limitation; therefore, compared with the force compensation cross-coupling synchronous control method, the proposed synchronous control method can avoid the artificial secondary parameter adjustment of the control system to achieve high-synchronization accuracy under different motion plannings. Figure 13 shows the experimental results of the synchronous motion of the dual-motor system. Under force compensation cross-coupling synchronous control, both motor systems were affected by long-term saturation, which led to a large synchronization error. However, there was no control voltage saturation under the proposed synchronous control, as shown in Figure 13b, so the synchronization error was reduced obviously, as shown in Figure 13c. Table 2 shows the comparison results of experimental data under three different motion plannings, in which we use the commonly used indicators, such as absolute maximum value (\(|\)MAX\(|\)), mean absolute error (MAE), and root mean square error (RMSE) to compare the synchronization error under different control methods. Under the proposed adaptive fractional-order anti-saturation synchronous control, the root-mean-square synchronization error of the dual-motor system can be reduced by more than 77.580% compared with that under the force compensation synchronous control. The comparison results of the three sets of experimental data verify that the proposed adaptive fractional-order anti-saturation synchronous control method has obvious advantages in improving the synchronization accuracy of the dual-motor system. \[T_{a}(s)=\frac{1+0.1112\mathrm{s}^{1.3190}}{0.0269\mathrm{s}^{1.3190}\left( \frac{25.17\mathrm{s}^{5}+521.1\mathrm{s}^{4}+2.479\mathrm{e}05\mathrm{s}^{3} +3.714\mathrm{e}06\mathrm{s}^{2}+3.311\mathrm{e}06\mathrm{s}+8924}{s^{6}+16.92 \mathrm{s}^{5}+10610\mathrm{s}^{4}+79160\mathrm{s}^{3}+54480\mathrm{s}^{2}} \right)+0.1381\mathrm{s}^{1.3190}+1}. \tag{45}\]