<p>In this work, we address the problem of online maximizing the hydrogen production rate of a continuous microbial electrolysis cell (MEC) by using the dilution rate as the optimizing control input. A discrete-time Super-Twisting-based extremum seeking control strategy is proposed to solve such an optimization problem online. To minimize hardware resources and power consumption, the floating point-based digital architecture related to the extremum seeking controller is designed and embedded in an FPGA device. Closed-loop simulations demonstrate the feasibility of the extremum seeking control strategy. The model of the MEC is implemented in a personal computer (PC), while the extremum seeking controller is embedded in a Cyclone II FPGA. The RS-232 interface is used to communicate between the FPGA and the PC. Results show that the digital architecture of the extremum seeking control uses <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1810_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$ 10.75 \% $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>10.75</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> of the total logic element, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1810_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">$ 2.34 \% $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2.34</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> of the dedicated logic registers, and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1810_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$ 20 \% $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>20</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> of the 8-bit multipliers of a Cyclone II FPGA and consumes only 126 mW.</p>

Microbial electrolysis cell optimization using a super-twisting-based extremum seeking control embedded in FPGA

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发表日期：

2025年8月22日

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Ixbalank Torres-Zúñiga,
José de Jesús Colín-Robles,
Fernando López-Caamal,
Glenda Cea-Barcia,
Víctor Alcaraz-González

摘要

In this work, we address the problem of online maximizing the hydrogen production rate of a continuous microbial electrolysis cell (MEC) by using the dilution rate as the optimizing control input. A discrete-time Super-Twisting-based extremum seeking control strategy is proposed to solve such an optimization problem online. To minimize hardware resources and power consumption, the floating point-based digital architecture related to the extremum seeking controller is designed and embedded in an FPGA device. Closed-loop simulations demonstrate the feasibility of the extremum seeking control strategy. The model of the MEC is implemented in a personal computer (PC), while the extremum seeking controller is embedded in a Cyclone II FPGA. The RS-232 interface is used to communicate between the FPGA and the PC. Results show that the digital architecture of the extremum seeking control uses $ 10.75 \% $ $10.75 %$ of the total logic element, $ 2.34 \% $ $2.34 %$ of the dedicated logic registers, and $ 20 \% $ $20 %$ of the 8-bit multipliers of a Cyclone II FPGA and consumes only 126 mW.