# Air-Based Contactless Wafer Precision Positioning System
## 3 Flowerbed
### Flowbed Actuation  
In 2016, [PERSON] designed a reluctance actuator to actuate the movable plate of the Flowerbed [14; 15]. Reluctance actuators can provide a high force, but they also have a high mass. With the use of fractional order control, this resulted in a control bandwidth for the Flowerbed of 100 Hz. The bandwidth was limited by the eigenmodes caused by the actuator as shown in Figure 7. Figure 8 shows the flapping mode of the actuators that was limiting the bandwidth. The position of the wafer is measured using optical sensors. This required that gratings are attached to the wafer. The position of the wafer is controlled with a bandwidth of 60 Hz.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Property** & \multicolumn{2}{c}{**Value**} \\ \hline Translational stiffness & \(k_{eq}\) & 200 kN/m \\ Rotational stiffness & \(k_{\theta}\) & 2.1 kNm/rad \\ Equivalent mass & \(m_{eq}\) & 1.9 kg \\ Equivalent inertia & \(I_{eq}\) & \(5.2\times 10^{-3}\) kg m\({}^{2}\) \\ Translational eigenmode & \(f_{0,d}\) & 51.6 Hz \\ Rotational eigenmode & \(f_{0,\theta}\) & 101 Hz \\ \hline \hline \end{tabular}
\end{table}
Table 1: Flowerbed properties.  
Figure 6: Schematic of the flowerbed during (**a**) translation and (**b**) rotation [13].  
To increase the bandwidth of the system, [PERSON] redesigned the actuator in 2018. The new actuator was designed with special care for dynamic performance. Instead of traditional hinges, a design with notch flexures is chosen. The flexures provide a high stiffness in the out of the plane direction and work without backlash. The reluctance actuators have been replaced with Lorentz actuators, because they have a linear force current relation. Furthermore, the permanent magnets were placed on the stationary frame, and the coils on the mover, resulting in a minimal moving mass.  
Figure 9 shows the chosen guidance for the movable plate. In the figure, the application point of the force and sensor are shown, as well as the notch flexure and guide linkages. The sensors that measure the actuator displacement are placed close to the actuator.  
Figure 8: Flapping modeshape of the actuators at 1080 Hz (measured) [14].  
Figure 7: The simulated and measured frequency response function of the Flowerbed with the reluctance actuator [14].  
Figure 10 shows the Flowerbed including the realized actuator. From top to bottom it shows the connection between the actuator and movable plate. The coil is used to generate the force on the movable plate. The sensor is placed directly behind the actuator. The actuators have a relatively small motion range thus the wires running from the coil to the base plane are no problem. Furthermore, the stiffness is small compared to the stiffness of the movable plate [13].  
Figure 10: Photograph of the Flowerbed with the compliant mechanism and Lorentz actuator design [13].  
Figure 9: Compliant mechanism design used to house the Lorentz actuators. Adapted from [13].  
The position of the actuators is measured using Micro-Epsilon CapaNCDT CS08 capacitive sensors, which have a range of 800 um. With the 16 bits ADC this resulted in a resolution of 24.4 nm. The noise is measured at 0.6 um peak-to-peak, with an RMS value of 72 nm.