## 2 Dual-Axis Solar Tracking System Design and Construction  
After an analysis of the advantages and disadvantages of each configuration of the STSs, a decision was made to build a VPDAT based on a vertical pole-mounted tracker to transfer the load of the structure to the ground. To know the required STS movement limits, the annual Sun path in Aguascalientes, Mexico, was analyzed (latitude N 21\({}^{\circ}\)50\({}^{\prime}\)39\({}^{\prime\prime}\) and longitude W 102\({}^{\circ}\)20\({}^{\prime}\)38\({}^{\prime\prime}\)), as shown in Figure 1a [37]. Afterwards, we proceeded with the mechanical design of the STS, which comprises an actuator capable of moving in the azimuth and zenith axes. This system can rotate 324\({}^{\circ}\) on the azimuth axis, from 48\({}^{\circ}\) to 372\({}^{\circ}\) from the northern axis. In the zenith axis, the system can be moved from 10\({}^{\circ}\) to 92\({}^{\circ}\) from the surface plane; see Figure 1b. Figure 2a depicts the STS built. The steel pedestal is 2.3 m high and supports a commercial slew drive manufactured with a dual-axis motoreductor. This actuator moves a steel frame of 4 m\({}^{2}\), where the payload is placed. This system is anchored to the ground by a reinforced concrete isolated footing of 60 \(\times\) 50 \(\times\) 50 cm (height, weight and length). To easily assemble the payload, four aluminum profiles were placed on the steel frame. Since the solar tracker is designed for CSP and CPV applications, the desired solar tracking accuracy is <0.3\({}^{\circ}\), so a PDE3 H-Fang slew drive was selected. The slew drive has two main components: a precise dual-shaft close-turn drive with a 62:1 worm gear ratio, and two motoreductors of 24 V of direct current (VDC) and 2.8 A (one for each axis: azimuth and zenith), which has a transmission ratio of 236:1. Therefore, the total gear reductions of  
Figure 1: STS movement planning: (**a**) Sun path at the Optical Research Center A.C., in Aguascalientes, Mexico and (**b**) rotational axes of the STS. the slewing drive on the azimuth and zenith axes are 14,632:1 (62 times 236). Because of the high level of reduction, if the motor is de-energized, it maintains its position. Each motorector has an absolute encoder with 8 pulses per revolution. The slew drive accuracy reported by the supplier is \(<\)0.08\({}^{\circ}\); it has a small uncertainty due to the backlash. The rated output speed of the solar tracker is 0.12 revolutions per minute: it takes 4.16 min to rotate 180\({}^{\circ}\). It is fast enough, however, to track the Sun's apparent position during the day. In order to avoid overturning the slewing drive and to ensure a robust operation, the system has four limit switches, as seen in Figure 2b: clockwise (CWA) and counterclockwise (CCWA) sensors on the azimuth axis and upper (UZ) and lower (LZ) sensors on the zenith axis. The range of motion of the STS is defined by the limits' switches. Video 1 ([[https://youtu.be/GU-461](https://youtu.be/GU-461) boFCA]([https://youtu.be/GU-461](https://youtu.be/GU-461) boFCA), accessed on 20 January 2010) depicts a time-lapse video of the full motion of the system. For measuring the Sun's apparent position, the proposed solar tracker employs an analog solar sensor based on a micro-electromechanical system (ASS-MEMS) model ISS-A60, as seen in Figure 2b. This sensor has a low power consumption, an accuracy of 0.06\({}^{\circ}\), an IP65 protection, as well as a wide field of view (FOV) of \(\pm\)60\({}^{\circ}\), among other advantages [38]. The operating principle of the sensor is based on a four-quadrant array of photodetectors that generate voltages (\(V_{PH1}\), \(V_{PH2}\), \(V_{PH3}\) and \(V_{PH4}\)) depending on the angle of incidence of the Sun's rays through a window, as shown in Figure 3. The incidence angles of the Sun's rays with respect to the ASS-MEMS are obtained on \(\alpha\) and \(\beta\) by the set of Equations from (1) to (4) and from (5) to (8), respectively, where the \(C\) value is a geometric correction of the solar sensor model, \(C=1.889\).