Computers and Chemical Engineering 39 (2012) 143–151 Contents lists available at SciVerse ScienceDirect Computers and Chemical Engineering jo u rn al hom epa ge : www.elsevier.com/locate/compchemeng Nonlinear model predictive control of fed-batch cultures of micro-organisms exhibiting overflow metabolism: Assessment and robustness L.O. Santos a , L. Dewasme c,∗ , D. Coutinho b , A. Vande Wouwer c a CIEPQPF, Department of Chemical Engineering, Faculty of Sciences and Technology, University of Coimbra, Portugal b Department of Automation and Systems, Federal University of Santa Catarina, 476 Florianopolis, 88040-900, Brazil c Service d’Automatique, Université de Mons (UMONS), Boulevard Dolez 31, B-7000 Mons, Belgium a r t i c l e i n f o Article history: Received 19 July 2011 Received in revised form 23 November 2011 Accepted 13 December 2011 Available online 29 December 2011 Keywords: Predictive control Min–max optimization Overflow metabolism Fermentation Biotechnology a b s t r a c t Overflow metabolism characterizes cells strains that are likely to produce metabolites as, for instance, ethanol for yeasts or acetate for bacteria, resulting from an excess of substrate feeding and inhibiting the cell respiratory capacity. The critical substrate level separating the two different metabolic pathways is generally not well defined. This occurs for instance in Escherichia coli cultures with aerobic acetate formation. This work addresses the control of a lab-scale fed-batch culture of E. coli with a nonlinear model predictive controller (NMPC) to determine the optimal feed flow rate of substrate. The objective function is formulated in terms of the kinetics of the main metabolic pathways, and aims at maximizing glucose oxidation, while minimizing glucose fermentation. As bioprocess models are usually uncertain, a robust formulation of the NMPC scheme is proposed using a min–max optimization problem. The potentials of this approach are demonstrated in simulation using a Monte-Carlo analysis. © 2011 Elsevier Ltd. All rights reserved. 1. Introduction Industrial vaccine production is usually achieved using fed- batch cultures of genetically modified yeast or bacteria strains, which can express different kinds of recombinant proteins. From an operational point of view, the main goal is to maximize the recombinant protein production and, consequently, the biomass production, all in a minimum of time (i.e., to maximize the biomass productivity). This requires the determination of an optimal feed- ing strategy, that is, the optimal time evolution of the input flow rate to the fed-batch culture. The main problem encountered comes from the metabolic changes of such strains in the presence of feeding overflow. This “overflow metabolism”, also called “short-term Crabtree effect” (Crabtree, 1929), is a metabolic phenomenon that is induced when the rate of glycolysis exceeds a critical value, leading to a by-product formation from pyruvate, inhibiting the oxidative capacity and, then, the cell growth. It occurs for instance in Saccharomyces cere- visiae cultures with aerobic ethanol formation, in Pichia pastoris with aerobic methanol formation, in Escherichia coli cultures with ∗ Corresponding author. Tel.: +32 65374135. E-mail addresses: lino@eq.uc.pt (L.O. Santos), Laurent.Dewasme@umons.ac.be (L. Dewasme), Coutinho@das.ufsc.br (D. Coutinho), Alain.VandeWouwer@umons.ac.be (A.V. Wouwer). aerobic acetate formation or in mammalian cell cultures with the aerobic lactate formation. To avoid this undesirable effect, a closed- loop optimizing strategy is required, which could take various forms including nonlinear closed-loop strategies based on predic- tive control (Akesson, 1999; Chen, Bastin, & van Breusegem, 1995; Dewasme et al., 2010; Hafidi, 2008; Pomerleau, 1990). Potentiali- ties of application of conventional PID controllers are unfortunately limited since the feeding trajectory should follow the biomass exponential growth. Indeed, in Axelsson (1988, 1989), the tuning of a PID controller regulating the ethanol concentration (i.e., in yeast cultures) is investigated. Despite the integral part of the controller, an exponentially growing error is observed, showing that this type of controllers is inappropriate. Moreover the derivative action, which usually improves the stability margin, has bad robustness with respect to the process parameters (Axelsson, 1989). Nonlinear model predictive control (NMPC) is suitable especially for nonlinear unsteady batch processes where a trajectory needs to be followed from the prediction of a nonlinear model. In addition, it is use- ful for processes operating at or near singular points (e.g., singular control trajectory, sign changes in process gain and input multi- plicities) that cannot be captured by linear controllers (as PID) and for processes with wide swings in operation, beyond the ranges of a local linearization. These characteristics are observed in many process problems including changeovers in continuous processes, tracking problems in startup and batch processes and the control of nonlinear reactors. For these processes NMPC uses the nonlinear 0098-1354/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2011.12.010