## 1 Introduction  
Solar energy has the advantages of large total volume, safety and economy, cleanness, and being pollution-free [1, 2]. A solar dish concentrator (SDC) system is one of the ways to realize the utilization of solar energy [3, 4], which has been widely used for its high concentration ratio and high light-electricity conversion efficiency (32%) [5, 6]. As shown in Figure 1a, a 38 kW solar dish Stirling thermal power (SDSP) generation system was developed by the authors [7]. The aperture radius \(R_{1}\) of the concentrator is 8.85 m, the focal length is 9.49 m, the unfilled angle \(\theta\) is 30 deg, and the unfilled radius \(R_{2}\) is 0.9 m. The SDC system is aimed at the sun in real time through the double-axis tracking device (DATD), gathers the solar radiation energy to the inner surface of the cavity receiver, heats the fluid working medium (usually hydrogen or helium) in the cavity receiver to drive the Stirling heat engine to do work, and, finally, drives the generator set to generate electricity [8]. When the SDC system cannot track the sun accurately, it will lead to the shift of the focus spot and the formation of high-temperature hot spots on the inner wall of the cavity receiver. This will lead to thermal deformation and burning damage to the cavity receiver, which will affect the safe operation of the SDC system [7]. The orthogonal relationship between elevation axis, azimuth axis, and concentrator focal axis of the SDC system is the key factor to ensure its tracking accuracy. Among these, the vertical relationship between the elevation axis and the azimuth axis can be ensured by controlling the machining accuracy of the DATD. The vertical relationship between the focal axis and the elevation axis can be ensured by adjusting the posture of the concentrator. However, due to its large windward area and heavy structural mass, the column (azimuth axis) may tilt under the action of wind loads and self-weight during the long-term service of the SDC system. Then, the azimuth axis becomes non-orthogonal with the horizontal ground, which will lead to the tracking error of the SDC system. Therefore, it is necessary to study the influence of the azimuth axis tilt error on the tracking performance of the SDC system. At present, many scholars have studied the influences of optical errors on the optical and photo-thermal performance of SDC systems, but fewer scholars have focused on the causes and influence laws of the generation of double-axis tracking errors. For example, in terms of optical and photo-thermal performance, [PERSON] et al. [10] developed a mathematical model of the dish/Stirling system and investigated the influence of the geometry of the concentrator and the receiver on the maximum and overall thermal efficiency of the system. [PERSON] et al. [9] investigated the influence of the geometric parameters of the dish concentrator on the optical performance of the solar dish/Stirling system. [PERSON] et al. [11] proposed a double-window pressurized volume receiver and studied, in detail, the influence of receiver parameters (cavity size, inner window thickness, distance between windows, and emissivity of inner surfaces) on its optical and thermal performance. [PERSON] et al. [12] established a PTC optical-thermal coupling model based on the Monte Carlo ray tracing method and finite volume method and studied the influence of the concentrator installation error on its optical-thermal performance. [PERSON] et al. [13] studied the influence of a tracking error caused by the DATD on the optical performance of the SDC system. In the aspect of tracking errors, [PERSON] [14] studied different tracking error distributions and their effects on the long-term operation performance of the dish concentrator system. He used four different tracking error distributions, three of which are bounded distributions and one of which is the widely used classical Gaussian distribution, to evaluate the interception factor, thermal efficiency, and engine efficiency.