# NPS6D200--A Long Range Nanopositioning Stage with 6D Closed Loop Control
## 4 Positioning Characteristics in 6D Closed Loop Control  
With the stage mechanics and control system as described in the previous chapters, the NPS6D200 was put into operation and now operates as a nanopositioning platform ready for the implementation of versatile tools or probes, depending on the advised application. Toward this end, it is important to investigate the positioning capabilities in order to assess the suitability for a specific task. In this chapter, we give an overview of the positioning \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Specifications** & \(x\)**-axis** & \(y\)**-axis** & \(\varphi_{z}\)**-axis** & \(z\)**-axis** & \(\varphi_{x}\)**-axis** & \(\varphi_{y}\)**-axis** \\ \hline Gain margin & 11.5 dB & 11.8 dB & 16.1 dB & 14.7 dB & 15.4 dB & 15.2 dB \\ Phase margin & 39.1\({}^{\circ}\) & 37.5\({}^{\circ}\) & 41.8\({}^{\circ}\) & 39.5\({}^{\circ}\) & 40.6\({}^{\circ}\) & 40.9\({}^{\circ}\) \\ Bandwidth & 85.5 Hz & 88.4 Hz & 72.8 Hz & 95.1 Hz & 76.7 Hz & 75.2 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Robustness and performance parameters for all six closed loops. Figure 8: Bode response of the \(x\)-axis. Figure 7: Control scheme for individual axis controller, where \(y_{sp}\) is the commanded setpoint, \(y\) is the measured output, and \(u\) is the control effort. scenarios that were considered and the respective positioning performance that is achieved with the NPS6D200. The first important characteristic is the remaining servo error at a constant setpoint. Figure 9 shows the time signals of the six DOFs measured with the internal feedback system with the stage fully activated and at a constant setpoint in the center of the travel range. At this point, the conceptual benefits mentioned above pay off, and a remaining RMS servo error below 1 nm for \(x\), \(y\), and \(z\) is achieved with the developed controller. When the slider changes its position within the planar and vertical travel range, the mechanical conditions of the force transfer change, and accordingly, a change in control behavior is expected. In corresponding investigations, we find that the servo errors vary slightly within the lateral travel range of \(\diameter 200\,\mathrm{mm}\), but nonetheless, they remain in the range below 1.5 nm (RMS), as depicted in Figure 10. Also, concerning the vertical slider position, only a minor servo error variation below 1 nm is observed, as shown in Figure 11. This performance in static setpoint operation opens the path for deterministic motion at the nanometer level, which is demonstrated by the illustrative staircase exercise shown in Figure 12.  
Figure 10: RMS servo error variation within planar travel range. In a second set of experiments the tracking performance was evaluated by means of 3D positioning exercises that require simultaneous and synchronized movements in the different axes. Such exercises reveal remaining parasitic cross-coupling effects between the DOFs and are well suited as a performance test for complex 3D motion paths. To analyze the occurence and extend of these effects we execute a stage movement along a helix with varying dimensions from the nanometer (\(\diameter 40\,\mathrm{nm}\)\(\times\) 20\(\,\mathrm{nm}\)) to the millimeter (\(\diameter 40\,\mathrm{mm}\)\(\times\) 5\(\,\mathrm{mm}\)) range. The stage velocity is adapted accordingly and ranges from \(7\,\mathrm{nm}\,\mathrm{s}^{-1}\) up to \(7\,\mathrm{mm}\,\mathrm{s}^{-1}\). Together with the tracking errors, the control effort and the power loss in the actuators are analyzed because of their great importance for any future application scenario. Exemplarily, Figure 13 shows the result of positioning a helix with \(\diameter 40\,\mathrm{nm}\) and a path velocity of \(7\,\mathrm{nm}\,\mathrm{s}^{-1}\) while Table 7 summarizes the achieved tracking errors and current consumptions connected to the different helix positioning exercises. As can be seen from the table, we obtained servo errors in the low nanometer range together with currents in the range of only milliamperes.