Adaptive data-driven controller based on fractional calculus for solid oxide fuel cell

In the realm of fuel cell technologies, solid oxide fuel cells are distinguished by their efficiency and potential for sustainable energy conversion. However, controlling these cells poses significant challenges due to the inherent nonlinearity of their output voltage characteristics. The current study introduces an improved model-free control strategy, designed to enhance the performance of fuel cell output voltage without reliance on traditional model-dependent control. Central to this strategy is developing a beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} variable model-free control mechanism, leveraging online estimation based on the forgotten recursive least square method to obtain better dynamic regulation. Furthermore, the integration of a fractional-order PI control, underpinned by extended state observer, estimates effectively unknown dynamics and optimizes the tracking process. The control structure is further augmented by the incorporation of a fractional-order adaptive sliding mode control to reduce observer estimation errors and bolster robustness across all operational scenarios. The stability of the proposed closed-loop system is validated using the Lyapunov stability theorem. Simulation results demonstrate the controller's efficacy in accurately tracking the output voltage, outperforming the conventional regulators. Notable achievements include considerable enhancements in the system's response characteristics, such as achieving a precise response without any overshoot, a rapid settling time, and a negligible steady-state error.