## 5 Experimental Test
A modal hammer was utilized to apply impulse forces at the actuation points along the two axes, respectively. The dynamic response of the terminal platform was captured by the length gauges and the spectral analyses on the experimental results have been given in Figure 24. The first two natural frequencies of the CPM were obtained as 793 Hz and 799 Hz, which are close to the simulated values. The step response of the CPM was tested where only the piezoelectric actuators adopted the closed-loop control. The result of the 1 \(\upmu\)m step response test of the \(x\)-axis is shown in Figure 25. The rising time was 8 ms without overshoot. Similar results in the \(y\)-axis were obtained, but are not shown herein. The results show that the CPM has a rapid response performance. The positioning resolution of the CPM was tested in the closed-loop control. A consecutive-step positioning with a step size of 2 nm was carried out for each axis; results are shown in Figure 26. The steps can be clearly identified, which indicates that the positioning resolution of the CPM is better than 2 nm. Moreover, the resolution can be improved by filtering the measurement noise. The output decoupling performance of the 2-DOF CPM was evaluated by actuating one axis and measuring the displacement output of the terminal platform along the other axis. The CPM's maximum output motion ranges along the two axes were both set as 40 \(\upmu\)m. Figure 27 shows the coupled motions along the two axes when the preload force along the \(x\)-axis changed from 240 N to 320 N while the preload force along the \(y\)-axis remained unchanged. It can be seen that the coupling motions along the \(y\)-axis varied significantly as the preload force changed. However, the variation of the coupling motions along the \(x\)-axis was slight. Figure 24: Natural frequency test of the CPM. Figure 25: Step response test of the \(x\)-axis of the stage. The coupling motions along the two axes when the preload force along the \(y\)-axis changed from 240 N to 320 N are shown in Figure 28, and a similar conclusion can be obtained. The cases shown in Figures 27 and 28 may come from manufacturing errors in the flatness of the measuring datum planes. Figure 29 provides an explanation for the tested results of the coupling motions when the preload force along the \(x\)-axis changes. It can be seen that the variation of the preload load force along the \(x\)-axis will alter the initial measuring point on the terminal platform while testing the coupling motions along the \(y\)-axis. The initial measuring point, however, remains the same when testing the coupling motions along the \(x\)-axis. Therefore, the flatness of the measuring datum planes will influence the test of the coupling motions along the \(y\)-axis when the preload force along the \(x\)-axis varies. Figure 20:0 Coupling motions along the two axes when the preload force along the \(y\)-axis changes. (**a**) Coupling motion along the \(x\)-axis. (**b**) Coupling motion along the \(y\)-axis. Figure 20:1 Coupling motions along the two axes when the preload force along the \(x\)-axis changes. (**a**) Coupling motion along the \(x\)-axis. (**b**) Coupling motion along the \(y\)-axis. Figure 20:2 Positioning resolution test of the stage. (**a**) Positioning resolution of the \(x\)-axis. (**b**) Positioning resolution of the \(y\)-axis. Because the preload forces affect the coupling motions of the CPM, we can adjust the preload forces to minimize the cross-axis outputs. Through trial and error, the preload forces along the \(x\)- and \(y\)-axes, respectively, were chosen as 250 N and 270 N. The test for the two axes' output coupling was performed and the results are shown in Figure 20:3 It can be seen that the maximum output couplings between the two axes are less than 0.5%. Since the flatness of the measuring datum planes has a negative effect on the output decoupling performance of the CPM, the direct way of reducing its output coupling is to improve the manufacturing accuracy of the measuring base.