The present research develops the parametric estimation of a second-order transfer function in its standard form, employing metaheuristic algorithms. For the estimation, the step response with a known amplitude is used. The main contribution of this research is a general method for obtaining a second-order transfer function for any order stable systems via metaheuristic algorithms. Additionally, the Final Value Theorem is used as a restriction to improve the velocity search. The tests show three advantages in using the method proposed in this work concerning similar research and the exact estimation method. The first advantage is that using the Final Value Theorem accelerates the convergence of the metaheuristic algorithms, reducing the error by up to 10 times in the first iterations. The second advantage is that, unlike the analytical method, it is unnecessary to estimate the type of damping that the system has. Finally, the proposed method is adapted to systems of different orders, managing to calculate second-order transfer functions equivalent to higher and lower orders. Response signals to the step of systems of an electrical, mechanical and electromechanical nature were used. In addition, tests were carried out with simulated signals and real signals to observe the behavior of the proposed method. In all cases, transfer functions were obtained to estimate the behavior of the system in a precise way before changes in the input. In all tests, it was shown that the use of the Final Value Theorem presents advantages compared to the use of algorithms without restrictions. Finally, it was revealed that the Gray Wolf Algorithm has a better performance for parametric estimation compared to the Jaya algorithm with an error up to 50% lower.

Cannabidiol (CBD) and its derivatives show interesting therapeutic potential, including antioxidant, anti-inflammatory, and anticancer properties; however, their clinical translation remains a complex task due to physicochemical restrictions such as low water solubility, high lipophilicity, and instability under light, oxygen, and high temperatures. Polymeric encapsulation has emerged as a promising strategy to overcome these challenges, offering protection against environmental degradation, improved bioavailability, and controlled release. Natural and synthetic polymers, both biocompatible and biodegradable, provide versatile matrices for CBD delivery, enabling nanoparticle formation, targeted transport, and enhanced pharmacokinetics. This review highlights the structural characteristics of CBD, its interaction mechanisms with polymeric matrices such as hydrogels, electrospun nanofibers, biodegradable microparticles, thin films, and lipid-polymer hybrid systems, and the principal encapsulation techniques, such as emulsion solvent evaporation, electrospinning, and supercritical fluid technologies, that facilitate stability and scalability. Furthermore, material characterization approaches, including microscopy, thermal, and degradation analyses, are discussed as tools for optimizing encapsulation systems. While notable advances have been made, key challenges remain in achieving reproducible large-scale production, ensuring regulatory compliance, and designing smart polymeric carriers personalized for specific therapeutic contexts. By addressing these gaps, polymer-based encapsulation may unlock new opportunities for CBD in pharmaceutical, nutraceutical, and therapeutic applications, providing a guide for future innovation and translation into effective patient-centered products.

The study of dynamic models and their parameterization remains a relevant topic in research. Motors and their models have been extensively analyzed, studied, and parameterized using various techniques due to their broad applicability in motorering and industrial settings. However, most methods for obtaining model parameters require at least two averaged signals from the motor, such as torque, current, speed, position, or acceleration. In this work, we propose the parameterization of a motor’s dynamic model using only the speed signal and the steady-state values of the variables. Through evolutionary computation, the mechanical and electrical equations of the motor are reconstructed based on this signal. This approach offers a significant advantage, as it enables parameter estimation without requiring the instrumentation needed for full current signal measurement or, alternatively, torque measurement. To achieve this, the transfer function representing the motor’s speed is utilized. The function reconstruction is performed with a Root Mean Square Error (RMSE) of less than 1% for both the speed and current signals. Since the original current signal is not required for this estimation, this work presents an innovative approach to estimating a system of dynamic equations using only a single measured variable and the dynamic relationships of its step-input response.

Proton exchange membrane fuel cell (PEMFC) durability under dynamic operation remains a major challenge because the observed voltage decay may combine persistent and transient performance changes. This study presents a condition-aware and data-driven analysis of PEMFC degradation under a dynamic fuel cell load cycle (FC-DLC). A public single-cell PEMFC dataset was reconstructed into 3076 dynamic cycles over 1008.24 h of operation and complemented with polarization curves measured directly after dynamic operation and after 12 h of shutdown rest. Load-resolved voltage indicators, polarization descriptors, direct-to-after-rest difference metrics, hysteresis indices, and uncertainty-evaluated short-horizon forecasting models were developed. The dynamic analysis showed that voltage degradation was strongly current-dependent, with the early-to-late voltage drop increasing from 23.09 mV at 0 A to more than 76 mV at the highest current levels. Over the common 100–1000 h comparison window, maximum power decreased by 9.31% in the direct condition and by 12.00% in the after-rest condition, whereas the voltage–current area decreased by 11.79% and 10.40%, respectively. Therefore, the after-rest temporal losses were not uniformly smaller and depended on the selected indicator and current region. The comparison between direct and after-rest curves revealed persistent after-rest minus direct voltage differences of 30–45 mV in medium- and high-current regions even after 1000 h. A sensitivity analysis showed that the voltage-cleaning threshold had no measurable effect on the reported dynamic indicators. For high-load voltage forecasting, Ridge regression achieved RMSE values of 0.00936 V and 0.01134 V at 50- and 100-cycle horizons, improving upon the persistence baseline by 29.7% and 23.5%, respectively. These error reductions were statistically significant, although the corresponding $R^2$ values remained negative on the late-life temporal holdout. The ablation analysis further showed that the complete feature set was not systematically optimal, and the best-performing feature group depended on the target and forecasting horizon. Nominal 90% conformal coverage was adequate at 50 cycles (91.25%) but decreased to 55.03% at 100 cycles, indicating loss of calibration under the longer temporal horizon. Overall, the proposed framework integrates load-dependent voltage-loss characterization, direct and after-rest measurement conditions, feature-group ablation, persistence benchmarking, and uncertainty evaluation without assigning the observed measurement-condition difference to a unique reversible or irreversible mechanism or claiming a validated remaining-useful-life or maintenance-decision system.