## 5 Regulation Test of Facility  
### Adjustment Test of Motion Control System  
After the installation adjustment of hardware and software, the velocity control of the moving carriage in the constant-speed stage was tested and examined. A total of 10 set velocity values, 0.1 m/s, 0.2 m/s, 0.3 m/s, 0.4 m/s, 0.5 m/s, 0.6 m/s, 0.7 m/s, 0.8 m/s, 0.9 m/s, and 1.0 m/s, were selected. At each set velocity, the data acquisition lasted 6 s with a frequency of 1000 Hz and a total number of acquisition times of 6000, where the velocity values were averaged every 60 ms, and a total of 100 velocity data were obtained. Figure 10 shows the velocity variation (100 sequential values) with time under the control of the motion control system within constant-speed stage at each set velocity. The fluctuation in velocity is seen to be small and is all less than 0.0005 m/s, except at velocity 0.7 m/s at which the initial fluctuation reaches a maximum value of 0.000989 m/s, which is also the maximum under all the set velocities. Figure 10: Variation of velocity value with time in constant-speed stage under each set velocity. By processing the 100 velocity values \(V_{i}\) (\(i\) = 1, 2, 3, \(\ldots\), 100) at each set velocity, the average velocity \(V_{\rm avg}\), the root mean square error of the velocity\(\sigma_{V}\), the maximum of all the deviations of the measured (i.e., controlled by the motion control system) velocity values from the average value \(\mid V_{i}-V_{\rm avg}\mid_{\rm max}\), the maximum of all the deviations of the measured (controlled) velocity values from the set value \(\mid V_{i}-V_{\rm set}\mid_{\rm max}\), and the absolute difference between the average velocity and the set velocity \(\mid V_{\rm avg}-V_{\rm set}\mid\) can be obtained:  
\[-V_{\rm avg}=\frac{\sum\limits_{i=1}^{n}V_{i}}{n}, \tag{7}\]  
\[\sigma_{V}=\sqrt{\frac{\sum\limits_{i=1}^{n}\left(V_{i}-V_{\rm avg}\right)^{2 }}{n-1}}, \tag{8}\]  
\[\left|V_{i}-V_{\rm avg}\right|_{\rm max}=\max_{i}(\left|V_{i}-V_{\rm avg} \right|), \tag{9}\]  
\[\left|V_{i}-V_{\rm set}\right|_{\rm max}=\max_{i}(\left|V_{i}-V_{\rm set} \right|). \tag{10}\]  
The corresponding relative errors are \(\sigma_{V}/V_{\rm avg}\), \(\mid V_{i}-V_{\rm avg}\mid_{\rm max}/V_{\rm avg}\), and \(\mid V_{i}-V_{\rm set}\mid_{\rm max}/V_{\rm set}\), \(\mid V_{\rm avg}-V_{\rm set}\mid/V_{\rm set}\). The calculated absolute errors yielded from data processing at each of 10 set velocities are shown in Table 4, while the corresponding relative errors are listed in Table 5. Table 4 reveals that within the whole calibration velocity range of 0.1 m/s to 1.0 m/s, the maximum value of \(\sigma_{V}\) is 0.000175 m/s and the maximum value of \(\mid V_{i}-V_{\rm avg}\mid_{\rm max}\) is 0.0009778 m/s, indicating that the velocity distribution in time direction at each set velocity has good uniformity. Among all the 10 set velocities, the maximum of \(\mid V_{i}-V_{\rm set}\mid_{\rm max}\) is 0.000989 m/s, which satisfies the velocity control target accuracy 0.003 m/s. In the whole calibration range of velocity, the relative root mean square error of the velocity \(\sigma_{V}/V_{\rm avg}\) ranges from 0.012% to 0.108% (Table 5) with a maximum of 0.108%. The maximum relative deviation of the controlled real velocity from the set velocity is 0.241% which occurs at velocity 0.1 m/s and is one order higher in magnitude than 0.0141%, the estimated error in Section 3.3.2. Obviously, the conditions for error estimation are more idealized, not counting in random errors. The maximum relative error 0.241% meets the design target accuracy 0.4%.