## 2 Methodology
### Proposed Tracking Strategy
Figure 5 shows the conventional algorithm used in the experiment, where \(t_{S}\) is the time constant required for each step calculated with the quotient of total time from sunrise to sunset, and the total number of steps obtained from path segmentation, and \(t_{s,k}\) is the time measurement at the \(k\)-point. The experimental setup is presented in Figure 6, where \(STS_{1}\) is configured to operate with the DMA and \(STS_{2}\) with the CA. The setup for both algorithms is described below:

* The location for the tests was in the Applied Dynamic Systems Laboratory of the UPIITA-IPN, in Mexico City, Mexico, with a latitude and longitude of 19.3014\({}^{\circ}\) and \(-\)99.0728\({}^{\circ}\), respectively. The day was 17 May 2024, when sunrise was at 05:59:00, noon \begin{table}
\begin{tabular}{c c c} \hline \hline
**Axis** & **\(\mathbf{N_{o}}\) [RPM]** & **\(\mathbf{T_{o}}\) [Nm]** \\ \hline Azimuth & 6.375 & 39.58 \\ Elevation & 0.865 & 343.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Rated output speed and torque of azimuth and elevation axis. at 12:32:00, and sunset at 19:06:00. The experimental tests began at 11:30:00 (UTC-6) and ended at 12:30:00 (UTC-6). * The experimentation was in mixed weather conditions with clear and partially cloudy conditions, where the periods of cloudiness were from 11:40:00 to 12:00:00 and from 12:05:00 to 12:22:00. * The solar path was calculated using the Solar Position Algorithm (SPA) and segmented in intervals of 4 min, resulting in 151 steps for both axes. * The power sensors calibration was using a Fluke 289 True RMS multimeter (Fluke Corporation, Everett, WA, USA), with a maximum error of 1.5%. The calibration procedure consisted of a zero adjustment to ensure the sensor reads zero when no current is flowing and a test with a constant electric load to compare the measured value with the multimeter value. * The acceleration and velocity profiles at the robot joints are the same for both algorithms; for this reason, they were not considered in the lifetime analysis. * The measurements of the monitoring device channels were configured to acquire 32 samples for each reading, considering an offset and measurement error correction factor. * Each monitoring device connects to a computer with a USB cable and wirelessly using the Bluetooth module for real-time data transmission and recording. In addition, when the monitoring process starts, a file with *.csv extension is created to continuously record the data on a Micro SD memory card configured with the exFAT file system. * Based on the results presented in [39], the selected control strategy for both systems is the PID controller due to a balanced relationship between the mixed tracking error and energy consumption, which ensures adequate performance for the case study. For more detail, in [39], a PID controller implementation in a two-axis solar tracker is presented. * According to the experimental tests in [29], the proposed energy-saving strategy includes the activation of the sleep mode of the tracker control hardware during idle times and the parallel activation of the axes until the desired position is reached. Figure 5: Flowchart of the conventional algorithm. ### Experimental Results

Figures 7 and 8 shows the tracking error results obtained for both strategies. The mean error in the azimuthal axis \(\bar{\epsilon}_{\beta}\) is 1.43\({}^{\circ}\) and 0.27\({}^{\circ}\) for the DMA and CA strategies, respectively. For the elevation axis, a mean error \(\bar{\epsilon}_{\gamma}\) of 4.39\({}^{\circ}\) and 1.00\({}^{\circ}\) for each strategy are measured. Therefore, a mixed tracking error is calculated using the Equation (2) obtaining a 4.61\({}^{\circ}\) for DMA and 2.04\({}^{\circ}\) for CA. The summarized results of the tracking error are presented in Table 2.

Figure 6: Experimental setup for the tracking strategy evaluation. Figure 7: Tracking error measurements of the DMA and the CA for the azimuth axis.