(528b) An Integrated State Estimation, Covariance Estimation, and Optimal Control Framework of a Semi-Batch Reactor for Bioprocess Applications

Despite improvements in process model development regarding high-fidelity first-principles models and machine learning-based advances, it is still extremely challenging to accurately model real chemical and biochemical processes. Unmodeled disturbances such as fouling, environmental heat losses, pH variations, or even poor storage of enzymes can influence reaction rates, chemical equilibrium, and other critical process variables. Ultimately, such unmodelled and unaccounted disturbances can cause significant departure between the available plant model and the true process states, which makes it difficult to solely rely on the developed process models for process systems engineering (PSE) applications. Although real-time and delayed process measurements are available to track an ongoing process, these measurements are often corrupted by significant amounts of noise, poor calibration, or are unable to directly quantify key process states such as concentrations [1]. Traditionally, state estimation approaches such as the Extended Kalman Filter (EKF) or Moving Horizon Estimation (MHE) have been implemented to blend these process models and measurements together to derive more robust approximations of the true process states. However, the performance of these estimation techniques is highly dependent on the correct selection of the noise covariance matrices, which is a challenging endeavor that is typically solved via trial-and-error procedures in real process applications. These challenges hinder the implementation of other PSE methods such as advanced control as reliable insight into the true process states is required for optimal trajectory tracking and model predictive control (MPC).

In this work, an integrated state estimation, covariance estimation, and optimal control framework is proposed. Such framework provides robust state estimates that can be used by the optimal control algorithm to improve process performance and remediate noise effects. Due to the complex estimation challenges and increasing market demand, this framework is applied to a batch lactose to galacto-oligosaccharide (GOS) system utilizing β-galactosidase [2]. GOS typically refers to a class of lactose derived products ranging in the size of 2-5 units of galactose sometimes attached to a glucose residue. These products have important prebiotic and health positive properties and can be used in many food products such as infant formula [3]. In this framework, state estimation is handled using various EKF and MHE formulations that are selected based upon the specific needs of the process. The noise covariance matrices are defined using the autocovariance least-squares (ALS) technique that has previously exhibited excellent performance on both continuous and batch process applications [4]. These two techniques provide accurate values of the process states and allow the optimal control algorithm implementation. By combining these three parts into a single framework, it is possible to overcome plant-model mismatch, measurement and process noises.

To challenge this framework, various sources of noises are introduced into the GOS system by varying kinetic parameter values, changing feedstock concentrations, and applying white noises to the process measurements. Overall, these sources of noise provide a simulation of real process disturbances and allow this framework to be applied to a more realistic system. Furthermore, due to the flexibility of this noise generation approach and the combined framework proposed, this ultimately provides a customizable solution to addressing process monitoring and control challenges faced by the modern chemical and biochemical industry.

References

[1] Alexander, R., Campani, G., Dinh, S., Lima, F.V. (2020). Challenges and Opportunities on Nonlinear State Estimation of Chemical and Biochemical Processes. Processes, 8, 1462.

[2] Schultz, G., Alexander, R., Lima, F. V., Giordano, R. C., Ribeiro, M. P. A. (2021). Kinetic Modeling of the Enzymatic Synthesis of Galacto-Oligosaccharides: Describing Galactobiose Formation. Food and Bioproducts Processing, 127, 1-13.

[3] Lamsal, B. (2012). Production, health aspects and potential food uses of dairy prebiotic galactooligosaccharides. J Sci Food Agric, 92, 2020-2028.

[4] Rinćon, F., Roux, G.A., Lima, F. V. (2014). The Autocovariance Least-Squares Method for Batch Processes: Application to Experimental Chemical Systems. Ind. Eng. Chem. Res., 2014, 18005-18015.