Optimal periodic switching strategy for self-cycling bioprocesses: Fliess series-based parameter design and ethanol fermentation case

Wenliang Li; Chi  Zhai

doi:10.59400/adecp3659

Optimal periodic switching strategy for self-cycling bioprocesses: Fliess series-based parameter design and ethanol fermentation case

Wenliang Li Faculty of chemical engineering, Kunming University of Science and Technology, Kunming 650500, China
Chi Zhai Faculty of chemical engineering, Kunming University of Science and Technology, Kunming 650500, China

Article ID: 3659

Keywords: Fliess series expansion; periodic optimal control; self-cycling fermentation; bang-bang control; successive batch bioreactors

Abstract

This study proposes a framework for optimizing cyclic discharge-reload operations in successive batch bioreactors under integral input constraints (e.g., total substrate consumption, cumulative energy use). Prior research has shown that candidates for optimal fed-batch and periodic on/off operation, formulated in an input-affine system, can be derived from bang-bang form. However, the practical application of these results to successive batch configurations requires a prior knowledge of operational periodicity, which limits flexibility and adaptability to variability. To address this limitation, we reformulate the switching strategy into an algebraic form using the Fliess series expansion. This expansion explicitly embeds periodicity constraints, enabling direct computation of switching parameters from predefined boundary conditions. The overall performance, defined as the over-yield relative to steady-state operations, is quantified via integrated integrals. For practical implementation, we leverage self-cycling fermentation as a foundational framework to determine required periodicity, and design optimal trajectories. Analytical results are derived to clarify the quantitative relationship between boundary conditions and switching parameters for any arbitrary anchor point (i.e., reference state for cycle initialization). The proposed framework is validated using an experimentally calibrated ethanol fermentation model. Simulation results demonstrate that the optimized cyclic strategy achieve a 25.58% relative increase in ethanol yield compared to traditional batch operations. This method enables the seamless integration of on/off operation with optimal periodicity, addressing critical gaps between theoretical periodic switching strategy and industrial bioprocess implementation.

Published

2025-10-08

How to Cite

Li, W., & Zhai, C. (2025). Optimal periodic switching strategy for self-cycling bioprocesses: Fliess series-based parameter design and ethanol fermentation case. Advances in Differential Equations and Control Processes, 32(4). https://doi.org/10.59400/adecp3659

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Vol. 32 No. 4 (2025)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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