## 5 Results and Discussion
### Vibration Synchronization and Control Synchronization
#### 5.1.2 Experimental Results
For the DC motor, the load decreases and the speed increases. Therefore, the synchronous velocity increases after motor 2 using the phase control. In the second stage, the vibration system seeks a new equilibrium because of the interference of motor 2, which is \(2a_{1}\approx 0^{\circ}\) and \(2a_{2}\approx-167^{\circ}\). According to Figures 9 and 10, the change of the phase difference in Figure 11 also proves that the theoretical analysis is  
Figure 14: The phase difference of control synchronization of three ERs in the clockwise rotational direction. (**a**–**h**) are photos of continuous time intervals of 200 Hz. correct and reasonable. Due to the accuracy of system modeling and parameter acquisition, although the values are not equal in theory and experiment, the trend is the same, which does not affect the qualitative analysis of the synchronous state. Furthermore, we can find that the self-adjusting reduces the load on the motor of the leading phase and increases the load on the motor of the lagging phase. In the last 20 s, motor 3 adopts the phase control. Since the phase difference \(2\alpha_{2}\approx-167^{\circ}\) in the second stage, the phase of motor 3 is the leading phase relative to motor 1. According to the control principle, motor 3 only needs to wait for motor 1 and motor 2 to track. Therefore, the synchronous velocity is not increased in the third stage. It is important to note that there is the overshoot phenomenon in these three stages, which is caused by the calculation method. We use a fixed time interval to calculate the velocity and the phase difference as shown in Figure 5, which is very susceptible to the collection method. Because of the timeliness and accuracy of the signal feedback, the function of the control method proposed in this paper is limited. By contrast, according to the results of the data, it is proved that the control scheme in this paper is feasible and effective. Furthermore, this set of data demonstrates the feasibility of the control scheme of controlling only the slave motors in the vibration system excited by three ERs. Comparing the overshoot in the second and third stages, it can be seen that the control synchronization is more difficult in the three-ERs system than in the two-ERs system because of the interference of the self-adjusting of the vibration system. Figure 11c,d are the acceleration amplitudes of the mass center (code AS1 in Figure 4) in both \(x\)- and \(y\)-directions. Similarly, Figure 11e,f are the acceleration amplitudes of the body edge (code AS2 in Figure 3) in both \(x\)- and \(y\)-directions. Comparing two measuring positions, the motion state is mainly the swing in the first stage when the vibration system operates in vibration synchronization because \(y\)-direction acceleration amplitude of the body edge is greater than that of the mass center. If the vibration system operates in control synchronization, the motion state in the third stage is mainly a circle according to the acceleration amplitude of the mass center. In Figure 11c,d, acceleration amplitudes of the mass center are close equal in the \(x\)- and \(y\)-directions, and \(y\)-direction is about \(90^{\circ}\) ahead of \(x\)-direction, which corresponds to the motion pattern of the clockwise circular motion. Furthermore, the acceleration amplitudes between the mass center and the body edge are close to equal in two directions, and there is not the phase difference between the acceleration amplitude curves of the two positions, which are in accordance with the motion pattern of the rigid body. To sum up, Figure 11c-f show the coupling characteristic that the phase difference affects the motion pattern of the vibration system. Figure 12 shows the high-speed photos of three ERs with the clockwise rotational directions in vibration synchronization, which is captured by a high-speed camera in 200 Hz. The data correctness of Figure 11 is verified according to eight images of the average time.