## 4 Results and Discussion
### Tracking Performance of an SDC System in a Whole Year Operation Cycle under Azimuth Axis Tilt Error  
This section focuses on the tracking performance variation law of an SDC system in a typical region (Dunhuang) during a whole year operation cycle under the azimuth axis tilt error. Figure 11 shows the annual average effective tracking factor \(\overline{\sigma}_{y}\) and \(\mathrm{SD}_{y}\) variation of an SDC system with different azimuth axis tilt errors. From Figure 11, it can be seen that the annual average effective tracking factor of the SDC system achieves the maximum value when the azimuth axis tangential angle \(\phi_{1}=0^{\circ}\) (due south) or \(\phi_{1}=180^{\circ}\) (due north), i.e., the tracking performance is optimal. When the azimuth axis tangential angle \(\phi_{1}=75^{\circ}\) (i.e., \(75^{\circ}\) south by west), the annual average effective tracking factor achieves the minimum value, i.e., the worst tracking performance. It can be seen from Figure 11 that when the azimuth axis tangential angle \(\phi_{1}=0^{\circ}\) (due south), \(90^{\circ}\) (due west), \(180^{\circ}\) (due north), or \(270^{\circ}\) (due east), the \(\mathrm{SD}_{y}\) value is relatively small, i.e., the tracking performance stability is relatively better. Since the tangential angle of azimuth axis is symmetrical about the origin, its tracking error is the same. Therefore, only some of the data are listed. Figure 12 shows the variation of the monthly average effective tracking factor \(\overline{\sigma}_{\mathrm{m}}\) of an SDC system for different azimuth axis tilt errors. It can be seen that when the azimuth axis tangential angle \(\phi_{1}=(0^{\circ},\,90^{\circ})\), the monthly average effective tracking factor first increases and then decreases, i.e., the tracking performance first increases and then decreases. When the azimuth axis tangential angle \(\phi_{1}=(90^{\circ},\,180^{\circ})\), the monthly average effective tracking factor first decreases and then increases, i.e., the tracking performance first decreases and then increases. When the azimuth axis tangential angle \(\phi_{1}=0^{\circ}\) (due south) or \(90^{\circ}\), this is the turning point of the effective tracking factor variation rule of an SDC system. In particular, when the azimuth axis tangential angle \(\phi_{1}=0^{\circ}\), the monthly average effective tracking factor varies in a \"wavy\" pattern. Figure 11: Variation of the annual average effective tracking factor \(\overline{\sigma}_{y}\) and \(\mathrm{SD}_{y}\) of an SDC system under different azimuth axis tilt errors: (**a**) annual average effective tracking factor \(\overline{\sigma}_{y}\); and (**b**) \(\mathrm{SD}_{y}\). Figure 13 shows the variation of the monthly average effective tracking factor \(\overline{\sigma}_{\rm m}\) and \(\rm SD_{m}\) of an SDC system. It can be seen that the monthly average effective tracking factor and \(\rm SD_{m}\) of the SDC system gradually decrease from January to June, and gradually increase from July to December, i.e., in June and July, the tracking performance of the SDC system is worse, but the tracking performance is more stable. We have counted the extreme values of effective tracking factors and corresponding dates of the SDC system at different azimuth axis tangential angles when the azimuth axis radial angle is 0.1\({}^{\circ}\) in the whole year operation cycle, as shown in Table 3. Obviously, when the azimuth axis tangential angle is \(\phi_{1}=0^{\circ}\) (due south), the minimum effective tracking factor of SDC system is larger than the maximum effective tracking factors with its tangential angles of 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), 75\({}^{\circ}\), 90\({}^{\circ}\), and 105\({}^{\circ}\). Figure 12: Variation of the monthly average effective tracking factor \(\overline{\sigma}_{\rm m}\) of an SDC system under different azimuth axis tilt errors. Figure 13: Variation of the monthly average effective tracking factor \(\overline{\sigma}_{\rm m}\) and \(\rm SD_{m}\) of an SDC system.