# A High-Precision Active Vibration Isolation Control System: Experimental Study
## 4 Experimental Study
### Experimental Results and Discussions  
The experiments are conducted in four systems: the passive system, the AVIS with the PD controller, the AVIS with the robust feedback controller only, and the system with the proposed controller. Three scenarios are considered where an impact force is applied at a certain point in the top platform in the \(x_{t}\)-, \(y_{t}\)-, and \(z_{t}\)-direction, respectively. Each scenario is conducted in two cases: with and without a 2.8 [kg] device mounted on the top platform. A loadcell CSBA-1 LS is used to measure the impact force. Due to the similarity of the results in the \(x_{t}\)- and \(y_{t}\)-directions, only the former is shown in this paper. Figures 4 and 5 show the impact forces in the \(x_{t}\)- and \(z_{t}\)-directions. The impact forces are approximately the same in each case and each scenario for valid comparisons. Figure 6 shows the vibration suppression performances in the first case. An impact force is applied along the \(z_{t}\)-direction to the top platform at 137.5 [mm] away from the right edge and 97.5 [mm] away from the rear edge. The peak force is about 4.5 [N], as seen in Figure 4. Such an eccentric vertical force will transmit three direct disturbances in the \(z_{t}\)-, \(\theta_{xt}\)-, and \(\theta_{yt}\)-directions to the top platform. Of these, the motion in the \(z_{t}\)-direction is most affected. This results in damped oscillations of the top platform if there is no control intervention. The results show that, in this passive system, the \(z_{t}\)-direction  
Figure 3: Experiment setup. motion needs about 5 [8] to reach the zero steady state again after the impact. With the operation of the VCMs, the proposed controller only needs 0.9 [s], whereas the robust controller and the PD controller need approximately 1.3 [s] and 1.5 [s]. The peak amplitude of the resulting velocity in the controlled cases is also smaller. The maximum is only 5 [mm/s] in the proposed AVIS compared to 7.7 [mm/s], 9 [mm/s], and 15 [mm/s] of the robust control, the PD control, and the passive system, respectively. However, in the other directions, the PD-controlled system has the least efficiency among the three, where the top platform's oscillations last from the smallest 1.2 [s] (\(\dot{\theta}_{xt}\)) to the largest 1.5 [s] (\(\dot{\theta}_{xt}\)). The robust controller performs better since it only needs 0.9 [s] (\(\dot{\theta}_{xt}\)) up to 1.3 [s] (\(\dot{\theta}_{xt}\)). The most impressive of all is the robust decoupling controller, with mostly around 0.7 [s]. In terms of maximum amplitude, the PD controller has the least efficiency, from the smallest translational velocity of 2.4 [mm/s] (\(\dot{x}_{t}\)) to the largest rotational velocity of 0.07 [rad/s] (\(\dot{\theta}_{xt}\)), while the robust controller is from 2.0 [mm/s] (\(\dot{x}_{t}\)) to 0.06 [rad/s] (\(\dot{\theta}_{xt}\)). The most impressive is the robust decoupling controller, which is from 1.9 [mm/s] (\(\dot{x}_{t}\)) to 0.038 [rad/s] (\(\dot{\theta}_{xt}\)). The control efforts in Figure 6b are the 6-DoF forces/torques computed from the eight actuators and show that the proposed controller reacts with the interactions better than the robust controller, and that the PD controller is the worst. In some cases, such as in the \(\dot{\theta}_{xt}\)-direction, the PD controller requires the most torque but cannot maintain a good vibration suppression. Figure 4: Impact forces in experimental cases with no payload. (**a**) Case 1: impact force in the \(z_{t}\)-direction; (**b**) case 2: impact force in the \(x_{t}\)-direction. Figure 5: Impact forces in experiment cases with payload. (**a**) Case 3: impact force in the \(z_{t}\)-direction; (**b**) case 4: impact force in the \(x_{t}\)-direction. Figure 7 shows the performances in case of applying an impact force to the top platform without a payload in the \(x_{t}\)-direction. The impact force is 37.5 [mm] away from  
Figure 6: Experimental results in case 1: (**a**) velocities at the center of the top platform; (**b**) control efforts.