## 3 Magnetic Levitation Control System
### Experimental Evaluation
#### 3.3.2 Magnetic Levitation under Driving Conditions  
An experiment was conducted to observe the control performance of the magnetic levitation while the system maintained magnetic levitation and moved in the \(y\)-axis driven by the LSM. Figure 10 shows the 5-DOF fluctuation of the magnetic levitation wafer transfer system when it travels a distance of \(D=1100\) mm with an S-curve motion profile [25; 26] under a maximum speed of \(V_{\text{max}}=1500\) mm/s and a maximum acceleration of \(A_{\text{max}}=3060\) mm/s. During the driving process, the maximum fluctuations in the \(x\), \(z\), \(\theta_{x}\), \(\theta_{y}\), and \(\theta_{z}\)-directions were \(\pm 0.097\) mm, \(\pm 0.101\) mm, \(\pm 6.37\times 10^{-4}\) rad, \(\pm 2.97\times 10^{-4}\) rad,  
Figure 9: Experimental results related to the transient response from the landing state to the magnetic levitation state: (a) 5-DOF fluctuations; (b) Control inputs.  
and \(\pm 7.48\times 10^{-4}\) rad, respectively. These results represent a very satisfactory control performance. In this system, during the acceleration and deceleration periods, inertial moments are generated due to the height difference (\(h\)) between the point in which the thrust force is generated and the center of gravity, as shown in Figure 11. This leads to significant oscillations in the \(\theta_{x}\)-direction of the magnetic levitation wafer transfer system, and these oscillations are considered external disturbances. To overcome these external disturbances, we attached an accelerometer to the moving base as shown in Figure 4, to measure the actual acceleration in the \(y\)-axis. Furthermore, we took into account the height difference between the point at which the thrust force is generated and the center of gravity, which we know in advance. By multiplying the actually measured acceleration and height difference, external disturbances were roughly predicted to minimize the effects of external disturbances. Thanks to this, it was experimentally confirmed that control performance was significantly improved.  
Table 3 summarizes the maximum fluctuations in the 5-DOF of the magnetic levitation wafer transfer system. Through these experimental results, it was confirmed that the developed magnetic levitation wafer transfer system with a robust feedback control design can achieve a high-accuracy magnetic levitation control performance during the state transition initial takeoff from the landing state and high-speed operation conditions.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Description** & **Standstill** & **Driving Condition** \\ \hline Max. fluctuation in the \(x\)-axis & \(\pm 0.0048\) mm & \(\pm 0.097\) mm \\ Max. fluctuation in the \(z\)-axis & \(\pm 0.0072\) mm & \(\pm 0.101\) mm \\ Max. fluctuation in the \(\theta_{x}\)-axis & \(\pm 1.29\times 10^{-5}\) rad & \(\pm 6.37\times 10^{-4}\) rad \\ Max. fluctuation in the \(\theta_{y}\)-axis & \(\pm 1.40\times 10^{-5}\) rad & \(\pm 2.97\times 10^{-4}\) rad \\ Max. fluctuation in the \(\theta_{z}\)-axis & \(\pm 8.54\times 10^{-6}\) rad & \(\pm 7.48\times 10^{-4}\) rad \\ \hline \hline \end{tabular}
\end{table}
Table 3: Maximum fluctuations in the 5 DOF of the magnetic levitation wafer transfer system.  
Figure 10: Experimental results of the magnetic levitation wafer transfer system under driving conditions.