## 5 Experiments
### Discussions  
Signals including square waves, triangle waves, and sine waves were applied to two piezoelectric actuators. The input signal diagram is shown in Appendix D, (Figures 13-18). The two pieces of capacitive sensors were respectively installed on the fixed bracket and the center of the output stage, as shown in Figure 17 (1) Y-direction, 2 X-direction, 3 the fixed bracket). The fixed bracket was fixed to the air floating platform. When the signal was input, the distance between the two pieces of the capacitive sensor would change, and the capacitance detection module was used to achieve output signal acquisition and convert the signal. The response curves of the output stage in the X- and Y-directions are shown in Figures 18-20. Theoretically, the response curves were the same as the input signal curves. However, it can be seen that the actual output signal tended to be flat after 0.02 s, as shown in Figure 18a. Through the analysis of the stage and experiment system, the piezoelectric system itself had a return response and the return response of the stage was lagging. A period of each of the square wave, triangle wave, sine wave was extracted and put together for comparative analysis. (1) In Figure 18, when the square wave was used as the input signal, the actual output had obvious hysteresis. In the X-direction, after 0.0224 s, the actual output of the stage reached the value of the theoretical output. In the Y-direction, after 0.0205 s, the actual output of the stage reached the value of the theoretical output. (2) In Figure 19, when the triangle wave was used as the input signal, the sharp point became smooth. The output signal amplitude fluctuated around the ideal output signal. (3) In Figure 20, when the sine wave was used as the input signal, the actual output and the ideal output were almost consistent. To sum up, the system had a better tracking effect for sine wave signals, and it was worse for triangular wave signals with sharp points but better than square wave signals. Corresponding experiments were carried out under different initial position conditions (pre-tensioning,  
Figure 17: Experiment test system. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **P-842.60** & **Unit** & **Tolerance** \\ \hline Travel range at 0 to 100 V & 90 & \(\mu\)m & \(\pm\)20\% \\ Resolution & 0.9 & nm & \\ Static large-signal stiffness & 10 & N/\(\mu\)m & \(\pm\)20\% \\ Push force capacity & 800 & N & max. \\ Pull force capacity & 300 & N & max. \\ Torque on tip & 0.35 & Nm & max. \\ Electrical capacitance & 9 & \(\mu\)F & \(\pm\)20\% \\ Resonant frequency f\({}_{0}\) (no load) & 6 & kHz & \(\pm\)20\% \\ Operating temperature range & \(-\)40 to 80 & \({}^{\circ}\)C & \\ Mass without cable & 86 & g & \(\pm\)5\% \\ Length L & 127 & mm & \(\pm\)0.2 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The parameters of the PZT (PI-842.60). According to the analysis of the motion curve due to the hysteresis of the piezoelectric ceramics and the return response of the mechanism itself, the stage could not return to the initial position immediately during the movement, and the center of the stage was shifted. Herein, (1) the displacement characteristic curve for the \(X\)-axis is shown in Figure 21 (when the input signal was a 20 V sine signal with a phase difference of 180 degrees). The error of the rising and descending process was analyzed and calculated to draw the error graph in Figure 22. The response speed of the stage was the main cause of the error. The initial position offset of the \(X\)-axis was approximately 0.084 \(\upmu\)m (initial position difference of the repeated movement), while the maximum displacement difference caused by hysteresis was 1.11 \(\upmu\)m. The error may have been from an installation error or the inconsistent piezoelectric preloads. The experiments showed that the stage had good motion performance along the \(X\)-axis.