This research focuses on the design and implementation of a movement strategy for a photovoltaic (PV) system, presented through four phases: First came the design of the mechanical part and the selection of geared motors with high torque and low power consumption, while having a solid mechanical structure that supports the panel. An open-loop control was selected using solar positioning equations, with the inputs defined as solar equations. The Intel Edison development board was chosen for programming the solar equations in Python. Two linear potentiometers served as sensing elements, where analog–digital characterization was conducted for each movement. The plant started with the static panel at a latitude of 7° south, oriented toward the equator, achieving a performance of 177.62 kWh. With the solar tracker, a performance of 232.38 kWh was obtained, resulting in an efficiency increase of 27%. Given the aim of enhancing PV efficiency through increased utilization, satisfactory results were achieved. Another advantage of the unit is that it is designed to support more than one panel.

This research project focuses on developing a mathematical model that allows us to understand the behavior of the balancing loops in system dynamics in greater detail and precision. Currently, simulations give us an understanding of the behavior of these loops, but under the premise of an ideal scenario. In practice, however, accurate models often operate with varying efficiencies due to various irregularities and particularities. This discrepancy is the primary motivation behind our research proposal, which seeks to provide a more realistic understanding of the behavior of the loops, including their different levels of efficiency. To achieve this goal, we propose the introduction of fractional calculus in system dynamics models, focusing specifically on the balancing loops. This innovative approach offers a new perspective on the state of the art, offering new possibilities for understanding and optimizing complex systems.

Control engineering and state-space representation are valuable tools in the analysis and design of dynamic systems. In this research, a methodology is proposed that uses these approaches to transform a system-dynamics simulation model into a mathematical model. This is achieved by expressing input, output and state variables as input, output and state vectors, respectively, allowing the representation of the model in matrix form. The resulting model is linear and time-invariant, facilitating its analysis and design. Through the use of this methodology, the system transfer matrix is obtained, which allows the analysis and design of the optimal control of the simulation model. The Ackermann gain-control technique is used to determine the optimal control of the system, which results in a shorter settlement time. This research proposal seeks to mathematically strengthen simulation models and provide an analytical alternative through modern control engineering in SD simulation models. This would allow more informed and effective decisions in the implementation of dynamic systems.

In this study, we introduced a unified family of fractional-order derivatives of the error function, bridging classical error function ($ \alpha = 0 $) and Gaussian ($ \alpha = 1 $) through Maclaurin expansion and Lacroix's fractional calculus. The adaptive model was validated against cubic spline and Gaussian baselines using six days of real photovoltaic measurements from a tropical environment. Moving-window optimization achieved competitive accuracy (Root Mean Squared Error (RMSE): 0.0083–0.0104; Mean Absolute Error (MAE) 0.0068–0.0086) while preserving physical interpretability via the fractional order $ \alpha $. Comparative analysis demonstrated significant improvement over Gaussian fitting, with an average 14.17% reduction in RMSE across all test days. The fractional approach also delivered more consistent daily performance and better captured asymmetric transitions, despite spline's occasional marginal RMSE advantages. Graphical analysis revealed persistent diurnal $ \alpha $ patterns: from 0.50 at sunrise, peaking at 0.90–0.91 near noon, declining to 0.37 afternoon, with sunset rebound. Our results confirmed the model effectively captures photovoltaic memory effects while offering superior interpretability and dynamic adaptation versus traditional methods. The framework enables accurate energy forecasting and condition-based maintenance, with future work focusing on real-time $ \alpha $ tuning and machine learning integration.

This study identifies motivational profiles among high school students regarding access to the University of Guanajuato, Yuriria Campus, within the framework of Sustainable Development Goal 4 (SDG 4). Using a survey of 306 students from diverse public and private institutions in southern Guanajuato, we applied K-means clustering analysis with validation techniques (elbow method, silhouette, bootstrap) to examine five key dimensions: family support, university interest, academic perception, transport accessibility, and self-efficacy. The analysis revealed three distinct profiles: (1) “Privileged and committed” (21%), with high scores in all variables and predominantly from private schools; (2) “Supported but not captivated” (65%), with moderate resources but low specific interest in the institution; and (3) “Vulnerable and disconnected” (14%), facing multiple barriers including low family support, economic constraints, and rural origin. ANOVA confirmed significant differences between clusters (p < 0.001). The inclusion of socioeconomic variables allowed for a deeper characterization of equity gaps. These findings provide evidence-based insights for designing targeted recruitment and retention strategies aligned with SDG 4, demonstrating how educational data analytics can inform sustainable higher education policies in regional contexts.