Fourier Optimization and Linear-Algebra-Based Combination of Controls to Improve Bioethanol Production

Abstract

The development of efficient strategies for optimizing and controlling nonlinear bioprocessesremains a significant challenge due to their complex dynamics and sensitivity tooperating conditions. This work addresses the problem by proposing a two-step methodologyapplied to a laboratory-scale fed-batch bioethanol process. The first step employsa dynamic optimization approach based on Fourier parameterization and orthonormalpolynomials, which generates smooth and continuous substrate-feed profiles using onlythree parameters instead of the ten required by piecewise approaches. The second stepintroduces a controller formulated through basic linear algebra operations, which ensuresaccurate trajectory tracking of the optimized state variables. Simulation results demonstratea 3.65% increase in ethanol concentration at the end of the process, together withan accumulated tracking error of only 0.0189 under nominal conditions. In addition, theclosed-loop strategy outperforms open-loop implementation when the initial conditionsdeviate from their nominal values. These findings highlight that the proposed methodologyreduces mathematical complexity and computational effort while producing continuouscontrol profiles suitable for practical application. The combination of optimization andalgebraic control thus provides a promising alternative for improving the efficiency ofbioethanol-production processes.