Model Predictive Control of dissolved oxygen level in an intermittent fed-batch process – Simulation & Application

Bioprocess engineering tries to create the ideal physiological conditions for the organisms inside of a bioreactor to avoid byproduct formation, unwanted metabolic shifts or cell death. The dissolved oxygen (DO) level in the broth is a key process parameter here and manipulated by the stirring speed, the aeration flow rate and partial pressure of oxygen. Commonly, simple cascaded PID control loops are deployed that act on the DO signal falling underneath a set threshold. But the inherent non-linear process dynamics of microbial cultivations poses difficulties for these control algorithms, even when extended through feedback linearization or gain scheduling (Babuška et al. 2003). In the face of abrupt changes in nutrient additions the DO signal will suddenly drop and eventually the purely reactive controller will not be able to avoid phases of oxygen limitation, as described by Kim et al. (2023). These problems can be observed in high throughput small scale multi-reactor system, where a scheduled pipetting robot adds the nutrients in form of bolus shots to the individual cultivations. The resulting oxygen limitations can affect the health and productivity of the organism, which calls for a more advanced control scheme.

Model Predictive Control (MPC) emerges as a promising alternative to account for the non-linear process dynamics directly within the control loop. To enable this algorithm a process model is constructed by combining first principal mass balances, a simple cell growth kinetic and the kLA correlation proposed by Van’t Riet (1979) to estimate the oxygen demand as well as the oxygen transfer rate in the reactor. The latter directly implements the stirring speed and the air gas flow, the two actuators of the control loop. The resulting process model is parameterized with laboratory scale experiments combining online and offline signals. The MPC algorithm is then tested in-silico with different configurations for the objective function and compared to the performance of a tuned PID control.