## 5 Results and Discussion
### Control Synchronization of Two Control Schemes  
In Figure 11, we adopt motor 3 as the object using the open-loop control and as slave motor using the closed-loop control. Then, Figure 15 selects motor 2 to study the coupling of the vibration system, which is used to further verify the feasibility of control synchronization. The control strategy of the master motor 1 and the slave motors 2 and 3 is selected in this experiment. The experiment is divided into four stages: first, motor 1 chooses the open-loop control and motor 2 and motor 3 choose the closed-loop control. Second, motor 2 chooses the open-loop control and others remain unchanged. Third, motor 2 chooses the closed-loop control again and others remain unchanged. Lastly, motor 1 chooses the closed-loop control of the velocity and others remain unchanged. Figure 15: Comparing different slave motor in 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 15a shows the velocities of three motors, which is similar to Figure 11a. However, there is a different phenomenon that the velocities of three motors appear over control at the ascending stage. The reason is that due to the master motor adopting the open-loop control, and it being tracked by slave motors, these reduce its load torque result in increasing its velocity, which conforms to the property of the vibration system. In fact, the self-adjustment of the vibration system is effective only when the velocities of motors are close. Therefore, the overshoot phenomenon of the vibration motor after reaching the rated speed is caused by the self-adjustment of the vibration system. In Figure 15a, motor 2 performs the phase control and begins to track the phase of motor 1. According to the coupling characteristic of the vibration system, motor 2 is the lagging phase ER rotating in the clockwise direction. To achieve the zero phase difference, the motion pattern of motor 2 should increase velocity to track the phase of motor 1. The synchronous velocity of the first stage in Figure 15a equals that of the third stage in Figure 11a. However, the synchronous velocity of the second stage in Figure 11a does not equal that of the second stage in Figure 11a. Since motor 2 is a lagging phase ER, in order to achieve the zero phase difference, motor 2 only has to increase the velocity so that the synchronous velocity of motors will rise. However, motor 3 is a leading phase ER and it only decreases the velocity to wait for motor 1, which causes the synchronous velocity to decrease. Comparing the synchronous velocity in two stages, it has a downward change when motor 2 is not controlled. At this time, the synchronous velocity is about 1500r/min, and it decreases by about 95r/min. In the third stage, the synchronous velocity equals that in the first stage again. When the vibration system runs into the fourth stage, the master motor adopts the velocity control. Although there are some fluctuations at the beginning of each stage, it does not mean that the controllers are not stable enough, but because of the limit of calculating velocity signal. In Figure 5, it is known from the introduction to the calculating velocity method of vibration motor that obtaining its average velocity requires multiple motor rotational periods to ensure the accuracy of velocity value, which will affect the timeliness of velocity closed-loop control. To verify the effectiveness of the velocity controller, the velocity value is set higher than the synchronous velocity in the first stage, which is set as 1680r/min.