## 5 Results and Discussion
### Vibration Synchronization and Control Synchronization
#### 5.1.2 Experimental Results  
Figure 11 shows the comparison between vibration synchronization and control synchronization of the vibration system driven by three ERs. Figures 12-14 are the high-speed photos for this experiment. The structural parameters are as follows: \(l_{1}=l_{2}=70\) mm, \(\beta_{1}=155^{\circ}\), \(\beta_{2}=25^{\circ}\), and \(\beta_{3}=270^{\circ}\). The experimental scheme is that three motors firstly operate without control, and the command of control synchronization is given by the phase controller after 20 s. The control strategy is that the master motor 2 and the slave motor 3 adopt the open-loop control, and the slave motor 1 adopts the closed-loop control. In the last 20 s, slave motor 3 adopts the closed-loop control. To facilitate observation of the motion states of the vibration system from start to steady-state, the data time is delayed for a few seconds during data processing. Figure 8: Motion state of three ERs using vibration synchronization: (**a**) one moment; (**b**) another moment. Figure 9: Motion state of two-thirds of ERs using control synchronization: (**a**) controlling motor 1 and 3; (**b**) controlling motor 1 and 2. Figure 11: Comparing vibration synchronization and control synchronization: (**a**) the velocities of three motors; (**b**) the phase differences; (**c**) acceleration amplitude of the mass center in \(y\)-direction; (**d**) acceleration amplitude of the mass center in \(x\)-direction; (**e**) acceleration amplitude of the edge position in \(y\)-direction; (**f**) acceleration amplitude of the edge position in \(x\)-direction. Figure 10: Stable phase differences of two-thirds of ERs using control synchronization. Figure 12: The phase difference of vibration synchronization of three ERs in the clockwise rotational direction. (**a**–**h**) are photos of continuous time intervals of 200 Hz. Figure 13: The phase difference of vibration synchronization of three ERs in the anticlockwise rotational direction. (**a**–**h**) are photos of continuous time intervals of 200 Hz. The velocities of three motors are shown in Figure 11a. It can be seen from velocity curves that the characteristic of the DC motor rapidly reaches the stable state value after power supply, which is different from that of the AC motor [34]. The synchronous velocity of three motors in the state of vibration synchronization is about 1538r/min. Since motor 1 and motor 2 are controlled by the same DSP, while motor 3 is controlled by another DSP, so the start times are not consistent. Figure 11b shows the phase difference curves of ERs. Because of \(2a_{3}=\varphi_{3}-\varphi_{1}=2\pi-2a_{1}-2a_{2}\), we do not give the curve of \(2a_{3}\) in Figure 11b in case there are too many curves in the graph to affect the observation. For the case of the clockwise rotational direction, the phase differences in vibration synchronization are \(2a_{1}\approx 96^{\circ}\) and \(2a_{2}\approx 140^{\circ}\), which proves the fact that motor 1 is the leading phase relative to motor 2. According to Figure 7, the change of the phase difference in Figure 11 proves that the theoretical analysis is correct and reasonable. At about 20 s, motor 2 performs control synchronization and begins to track the phase of motor 1. If three motors operate in the clockwise rotational direction, motor 1 is the leading phase ER affected by the self-adjusting of the vibration system. To hold on the synchronous motion of the zero phase difference, the motion tendency of motor 2 should track motor 1 according to Tables 2 and 3. As can be seen from Figure 11a, when motor 2 adopts the phase control, the synchronous velocity of three motors rapidly increases to about 1595 r/min and the velocity difference is about 57 r/min. The reason for this phenomenon is that the self-adjusting of the vibration system reduces the load on motor 1 and increases the load on motor 2 to keep the center of mass at rest. Of course, the load torque of the self-adjusting is smaller than the electromagnetic torque of the motor.