## 2 Methodology
### Proposed Tracking Strategy
* The analysis is carried out for the elevation axis because it is the critical element due to the configuration of the tracking robot, and the loads applied to the azimuthal axis are neglected since they are axial with a minimum impact on the bearing. * The angular velocity is considered identical for each strategy, with an average value of 0.1067 RPM, which allows the service life calculation to focus on the impact on the operating time. * The output torque for each step is calculated through the dynamic analysis of the system for each step in the trajectory, where the dynamic model is described by: \[D(q)\ddot{q}+C(q,\dot{q})+g(q)\ =\ \tau\] (14) where \(q\), \(\dot{q}\), and \(\ddot{q}\in\mathbb{R}^{2}\) are the angular position, the velocity and acceleration of the azimuthal and elevation axis, respectively. The matrix \(D(q)\in\mathbb{R}^{2\times 2}\) represents the effective inertia matrix for the axis motors, \(C(q,\dot{q})\in\mathbb{R}^{2\times 2}\) is the Coriolis matrix, \(g(q)\in\mathbb{R}^{2}\) is the gravitational vector, and \(\tau\in\mathbb{R}^{2}\) is the torque of each axis. The explicit model is defined as follows: \[D(q)\ =\ \begin{bmatrix}m_{2}l_{2}^{2}C_{2}^{2}+I_{y_{1}}+I_{x_{2}}S_{2}^{2}+ I_{y_{2}}C_{2}^{2}&0\\ 0&m_{2}l_{2}^{2}+I_{z_{2}}\end{bmatrix} \] (15) \[C(q,\dot{q})\ =\ \begin{bmatrix}(I_{x_{2}}-I_{y_{2}}-m_{2}l_{2}^{2})C_{ 2}S_{2}q_{2}&(I_{x_{2}}-I_{y_{2}}-m_{2}l_{2}^{2})C_{2}S_{2}q_{1}\\ (-I_{x_{2}}+I_{y_{2}}+m_{2}l_{2}^{2})C_{2}S_{2}q_{1}&0\end{bmatrix} \] (16) \[g(q)\ =\ \begin{bmatrix}0\\ m_{2}g_{2}l_{2}C_{2}\end{bmatrix} \] (17) where \(I_{x_{2}},I_{y_{1}},I_{y_{2}},I_{z_{2}}\) are the tensor of inertia, \(m_{2}\) is the PV module and link structure mass, \(l_{2}\) is the distance of the elevation link, \(g\) is the gravity constant, and \(C_{2}\) and \(S_{2}\) stand for \(\cos(q_{2})\) and \(\sin(q_{2})\), respectively. For more detail, the dynamic model using the Euler-Lagrange procedure is presented in [40]. Since the load on the azimuth axis is absorbed by the bearing, the dynamic model is simplified and focused on the elevation axis, where the torque is expressed as follows: \[T_{m}\ =\ m_{2}\cdot l_{2}\cdot g\cdot\sin(q_{2})\] (18) where \(m_{2}\) is equal to 4.081 kg, \(l_{2}\) is 0.08 m, and \(q_{2}\) is the angular position of the elevation axis with the horizon as reference for each step in the strategies path. * The rated service life \(K\) of the system was defined as 60,000 h according to supplier recommendations for industrial robotic systems presented in [41]. Table 3 shows the torque and angular position data for each step and the strategy used for the calculation, where step 0 is the initial position for the experimental test and is calculated by the Solar Position Algorithm. Finally, based on experimental results and considering the Equations (4)-(6), the calculated service life for CA is \(3.34\times 10^{6}\) h and \(22.77\times 10^{6}\) h for DMA, representing an improvement of 682.10% of the lifetime with the proposed strategy (see Table 4). ## 4 Conclusions and Future Work

A novel tracking strategy for dual-axis solar trackers is presented, which increases the useful life of the mechanisms considering the required tracking precision and without affecting energy productivity. The algorithm significantly reduces the tracking operation time due to the reduction of the path steps without affecting energy productivity depending on decisions made during the real-time monitoring process. The proposed methodology was experimentally tested, comparing the decision-making algorithm with a conventional strategy under the same weather conditions and with identical tracking systems, reducing the energy consumption by 14.18% due to the tracking action while maintaining identical energy productivity between both strategies.