Cybernetic Model Predictive Control of a Continuous Bioreactor with Cell Recycle Kapil G. Gadkar and Francis J. Doyle III* Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106 Timothy J. Crowley † Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Jeffrey D. Varner ‡ Institute of Biotechnology, ETH-Zu ¨ rich, Zu ¨ rich CH 8093, Switzerland The control of poly--hydroxybutyrate (PHB) productivity in a continuous bioreactor with cell recycle is studied by simulation. A cybernetic model of PHB synthesis in Alcaligenes eutrophus is developed. Model parameters are identified using experimental data, and simulation results are presented. The model is interfaced to a multirate model predictive control (MPC) algorithm. PHB productivity and concentration are controlled by manipulating dilution rate and recycle ratio. Unmeasured time varying disturbances are imposed to study regulatory control performance, including unreach- able setpoints. With proper controller tuning, the nonlinear MPC algorithm can track productivity and concentration setpoints despite a change in the sign of PHB productivity gain with respect to dilution rate. It is shown that the nonlinear MPC algorithm is able to track the maximum achievable productivity for unreachable setpoints under significant process/model mismatch. The impact of model uncertainty upon controller performance is explored. The multirate MPC algorithm is tested using three controllers employing models that vary in complexity of regulation. It is shown that controller performance deteriorates as a function of decreasing biological complexity. 1. Introduction Continuous bioprocesses are theoretically attractive because of greater potential efficiency relative to batch and fed-batch operation. Practically, however, continuous processes require significantly more engineering for viability. Challenges encountered include genetic insta- bility, time varying system parameters, complex dynamic behavior, and lack of on-line measurements. Recent work in model-based continuous bioreactor control has attempted to address the practical operational difficulties of continuous operation. Several authors have studied the impact of segregated population models on bioreactor dynamics and control (20, 27, 38). Zhang et al. developed a cell mass distribution population balance model for continuous cultures of Saccharomyces cerevisiae to study the control of sustained cell population oscilla- tions (38). Andersen et al. experimentally studied the control of a continuous Saccharomyces cerevisiae biore- actor at near-optimal biomass productivity under aerobic, glucose-limited conditions (1). Thatipamala et al. con- ducted experimental control studies of continuous ethanol production in Saccharomyces cerevisiae using a state space model and on-line state estimation (30). Lee et al. used nonsingular transformation along with state esti- mates to determine optimal feed profiles of glucose and ammonium chloride to maximize PHB concentrations in a fed-batch bioreactor, where a low order Luedeking- Piret type model was used to simulate the PHB produc- tion (25). Recent developments in metabolic modeling may pro- vide control relevant nonlinear models capable of captur- ing complex metabolic regulation and control. Reuss et al. have developed a dynamic model of central carbon metabolism in Escherichia coli that employs a detailed kinetic description and has been directly validated using transient pulse experiments (4). However, this class of kinetic model represents the exception rather than the rule because of parametric and biological uncertainty. Attempts have been made to cope with uncertainty in dynamic metabolic models. Liao et al. employed fuzzy logic to cope with parametric uncertainty in a model of Escherichia coli (22). Page et al. employed piecewise- linear models to simulate sporulation control in Bacillus subtilis where qualitative information is used in the form of algebraic inequalities among the parameters to get a course grain picture of dynamics (6). The cybernetic approach of Ramkrishna and co-workers approximates missing or incomplete knowledge of metabolic regulation * To whom correspondence should be addressed. Phone: 805- 893-8133. Fax: 805-893-4731. Email: doyle@engineering.ucsb.edu. † Current address: United Technologies, International Fuel Cells Division. ‡ Current address: Genencor International, 925 Page Mill Rd, Palo Alto, CA. 1487 Biotechnol. Prog. 2003, 19, 1487-1497 10.1021/bp025776d CCC: $25.00 © 2003 American Chemical Society and American Institute of Chemical Engineers Published on Web 08/06/2003