Modeling and Nonlinear State Estimation for Advanced Process Control of the Enzymatic Conversion of Lactose into Value-Added Products

Due to increased concerns over sustainability of chemical processes, significant research has been conducted to minimize the amount of process waste generated. Despite advances in efficiency, selectivity, and conversion, waste management is still a concern for all processes, especially biological. The most effective method for waste disposal would be its conversion into a value-added product through profitable means. Many industries are attempting to achieve this goal, but it is challenging to design a novel catalyst, enzyme, or process. In particular, recent advances in enzymatic process modeling have created an opportunity for small-scale cheese manufactures to convert their waste into value-added products. The manufacturing of cheese results in the formation of lactose rich whey permeate that cannot be easily utilized and thus is often disposed of at cost to manufacturers ^[1].

A recent advance in enzymatic modeling corresponds to a new kinetic model to convert lactose waste into value-added galactooligosaccharide (GOS) products using β-galactosidase ^[2]. This specific reaction has been studied by several researchers in the past, but each proposed model presented challenges such as mass balance issues and overfitting due to the excessive number of parameters ^[3]. The proposed kinetic model contains no mass balance errors, while minimizing the number of parameters to accurately depict the process characteristics. Furthermore, this model uniquely distinguishes between purely galactose derived disaccharides, trisaccharides, and tetrasaccharides and those containing a glucose saccharide group. Due to the similarity of glucose and galactose, there are no online measuring techniques that can discern between the specific di, tri, or tetrasaccharides stereoisomers. A High Performance Liquid Chromatography (HPLC) method coupled with an ion-exchange column and refractive index detector can distinguish between glucose and galactose, but has no resolution for other isomers such as disaccharide, trisaccharide, and tetrasaccharide stereoisomers. Without the ability to measure specific component concentrations, state estimation must be used to predict the individual states using the online measurements and the proposed kinetic model.

This work addresses the state estimation and advanced control employing the developed enzymatic model for the first time. Unique estimation challenges are posed and addressed, with the specific novelty of using nonlinear state estimation to find stereoisomer concentrations from available online measurements and the nonlinear kinetic model. Both an Extended Kalman Filter (EKF) and a Moving Horizon Estimator (MHE) are analyzed for process implementation. The EKF is an unconstrained estimator that allows for rapid estimation but does not guarantee feasible and optimal results. The MHE is a constrained estimator that guarantees feasibility at the cost of increased computational time ^{[4] [5]}. Using these estimation techniques, a Biologically-Inspired Optimal Control Strategy (BIO-CS) algorithm is applied to optimize the feeding of lactose and enzyme into a semi-batch reactor ^[6][7]. The proposed estimation and advanced control framework allows the feasibility of this process to be examined and provides a guide for other bioprocesses to follow.

References:

[1] Illanes, A. (2011). Whey Upgrading by Enzyme Biocatalysis. Electronic Journal of Biotechnology.

[2] Schultz, G., Alexander, R., Lima, F.V., Giordano, R., & Ribeiro, M. (2019). Kinetic Model for the Enzymatic Synthesis of Galacto-Oligosaccharides: Describing Galactobiose Formation. AIChE Annual Meeting.

[3] Vera, C., Guerrero, C., Illanes, A., & Conejeros, R. (2011). A Pseudo Steady-State Model for Galacto-Oligosaccharides Synthesis With ß-Galactosidase From Aspergillus oryzae. Biotechnology and Bioengineering.2270-2279.

[4] Campani, G., Ribeiro, M., Zangirolami, T., Lima, F.V. (2019). A Hierarchical State Estimation and Control Framework for Monitoring and Dissolved Oxygen Regulation in Bioprocesses. Bioprocess and Biosystems Engineering.1467-1481.

[5] Lima, F.V., Rawlings, J. (2011). Nonlinear Stochastic Modeling to Improve State Estimation in Process Monitoring and Control. Process Systems Engineering.996-1007.

[6] Mirlekar, G., Gebreslassie, B., Diwekar, U., Lima, F.V. (2018). Biomimetic Model-Based Advanced Control Strategy Integrated with Multi-Agent Optimization for Nonlinear Chemical Processes. Chemical Engineering Research and Design.229-240.

[7] Mirlekar, G., Al-Sinbol, G., Perhinschi, M., Lima, F.V. (2018). A Biologically-Inspired Approach for Adaptive Control of Advanced Energy Systems. Computers and Chemical Engineering.378-390.