This paper proposes a discrete-time Extremum-Seeking Control (ESC) strategy based on the Super-Twisting algorithm to optimize online a microbial electrolysis cell (MEC) for green hydrogen production. Besides, the digital architecture of the ESC strategy is designed and embedded in an FPGA to minimize hardware and energy consumption. Closed-loop simulations on the MEC model demonstrate the feasibility of the discrete-time ESC strategy. Results show that hydrogen production is correctly maximized for different inlet substrate concentrations, and the FPGA requires an estimate of only 122mW.

In this paper, a very simple discrete-time extremum-seeking control strategy is proposed from the classical direct search gradient-based optimization algorithm. First, the optimization problem to solve and solvability conditions are presented. Then, the discrete-time extremum-seeking strategy is developed and its convergence is assured by demonstrating that the optimization error dynamics is globally asymptotically stable. Finally, the feasibility of the proposed extremum-seeking algorithm is demonstrated by simulations on a fermentation reactor for bioethanol production.