# A High-Precision Active Vibration Isolation Control System: Experimental Study
## 4 Experimental Study
### System Implementation
\begin{table}
\begin{tabular}{c c c c} \hline \multicolumn{1}{c}{**Parameter**} & **Description** & **Unit** & **Value** \\ \hline \multirow{8}{*}{\
\begin{tabular}{c} Mechanical components \\ \end{tabular} } & \(m\) & Total mass of the top platform & kg & 9.085 \\  & \(l_{0x}\), \(J_{0y}\), \(J_{0z}\) & Moment of inertia of the top platform & kg\(\cdot\)m\({}^{2}\) & 0.1218, 0.1656, 0.2838 \\  & \(l,w,h\) & Length, width, and height of the top platform & mm & 465, 366, 12 \\  & \(k_{x}\), \(k_{y}\), \(k_{z}\) & Identified stiffness of the spring & N/m & 12683, 12683, 22526.2 \\  & \(c_{x}\), \(c_{y}\), \(c_{z}\) & Identified damping ratio of the spring & Ns/m & 9.087, 9.087, 26.64 \\  & \(l_{z}\) & Vertical distance from \(O_{t}\) to the top surface & mm & 1.5 \\ \cline{2-4}  & \(l_{xi}\), \(l_{yi}\) & Distance from spring \(i\), ( \(i=1\,\sim\,4\)) & mm & 161.3, 161.3, 170.7, 170.7, \\  & \(l_{xi}\), \(l_{yi}\) & to \(O_{t}\) in the \(x_{t}\)- and \(y_{t}\)-directions & mm & 215.5, 215.5, 215.5, 215.5, 215.5 \\ \hline \multirow{8}{*}{VCMs} & \(l_{yxxi}\), \(l_{yxi}\) & Distance from VCM \(Z_{i^{\prime}}\) ( \(i=1\,\sim\,4\)) & mm & 146.7, 146.7, 156.3, 156.3, \\  & \(l_{0}\), \(l_{t}\) in the \(x_{t}\)- and \(y_{t}\)-directions & mm & 146.6, 146.6, 146.6, 146.6 \\ \cline{2-4}  & \(l_{yxxi}\), \(l_{yxi}\), \(l_{yxi}\) & Distance from VCM \(X_{i^{\prime}}\) ( \(i=1\,\sim\,2\)) & 69.8, 69.8, \\  & \(l_{0}\), \(l_{t}\) in the \(x_{t}\)-, \(y_{t}\)- and \(z_{t}\)-directions & mm & 199.9, 199.9, \\  & \(l_{3}\), \(l_{yxi}\), \(l_{yxi}\), \(l_{yxi}\) & Distance from VCM \(Y_{i^{\prime}}\) ( \(i=1\,\sim\,2\)) & 145.8, 155.2, \\  & \(l_{0}\), \(l_{t}\) in the \(x_{t}\)-, \(y_{t}\)- and \(z_{t}\)-directions & mm & 0, 0, \\ \hline \multirow{8}{*}{
\begin{tabular}{c} Geophones \\ \end{tabular} } & \(l_{gxixi}\), \(l_{gxi}\), \(l_{gxi}\) & Distance from sensor \(X_{i^{\prime}}\) ( \(i=1\,\sim\,2\)) & 151.3, 151.3, 160.7, 160.7, \\  & \(l_{0}\), \(l_{t}\) in the \(x_{t}\)-, \(y_{t}\)- and \(z_{t}\)-directions & mm & 112.9, 112.9, 112.9, 112.9 \\ \cline{1-1}  & \(l_{gxi}\), \(l_{gxi}\), \(l_{gxi}\), \(l_{gxi}\) & Distance from sensor \(X_{i^{\prime}}\) ( \(i=1\,\sim\,2\)) & 20.9, 20.9, 20.9, 20.9, \\ \cline{1-1} \cline{2-4}  & \(l_{gxi}\), \(l_{gxi}\), \(l_{gxi}\), \(l_{gxi}\) & Distance from sensor \(X_{i^{\prime}}\) ( \(i=1\,\sim\,2\)) & 70.3, 70.3, \\ \cline{1-1}  & \(l_{gxi}\), \(l_{g}\), \(l_{gxi}\), \(l_{gxi}\) & Distance from sensor \(Y_{i^{\prime}}\) ( \(i=1\,\sim\,2\)) & 109.3, 118.7, \\ \cline{1-1}  & \(l_{gxi}\), \(l_{g}\), \(l_{g}\), \(l_{gxi}\) & Distance to \(O_{t}\) in the \(x_{t}\)-, \(y_{t}\)- and \(z_{t}\)-directions & mm & 53.1, 52.8, \\ \cline{1-1} \cline{2-4}  & \(l_{gxi}\), \(l_{g}\), \(l_{g}\), \(l_{gxi}\) & Distance from sensor \(Y_{i^{\prime}}\) ( \(i=1\,\sim\,2\)) & 11.3, 11.3 \\ \hline \end{tabular} (16)  
\end{table} 
Table 1: Parameters of the 6-DoF AVIS. \(\mathbf{K_{P}}\) and \(\mathbf{K_{D}}\) are the diagonal matrices of parameters of the PD controller for each DoF. The parameters are selected by a trial-and-error method with the assistance of the PID Tuner app in Mathworks MATLAB. They are listed as follows:  
\[ \begin{array}{l}\mathbf{K_{P}}=diag\{100,\ 80,\ 700,\ 10,\ 10,\ 10\},\\ \mathbf{K_{D}}=diag\{0.3,\ 0.3,\ 0.3,\ 0.3,\ 0.3\}\end{array}  \tag{17}\]  
The system without control, i.e., PVIS, and the AVIS controlled only by the robust feedback control law \(\mathbf{U_{k}}\) are also taken into comparison. The setup of the experiments is shown in Figure 3. The system consists of the AVIS (two platforms, mechanical springs, feedback sensors, actuators), amplifiers, data acquisition (DAQ), and the power source. The sensors, LGT Seismic Geophones 4.5 (LGT-4.5), are used to detect and measure the motion of the system. The actuators, VCMs, produce controlled movement. The amplifiers regulate the control signals sent from the DAQ device--dSPACE DS6101--to the actuator. The DAQ processes the data and then controls the actuators through the amplifiers.