Globally stabilizing control of fed-batch processes with Haldane kinetics using growth rate estimation feedback q H. De Battista a, * , J. Pico ´ b , E. Pico ´ -Marco b a Faculty of Engineering, National University of La Plata, C.C. 91, 1900 La Plata, Argentina b Department of Systems Engineering and Control, Technical University of Valencia, Spain Received 30 June 2005; received in revised form 6 February 2006; accepted 8 February 2006 Abstract The regulation of the biomass specific growth rate is an important goal in many biotechnological applications. To achieve this goal in fed-batch processes, several control strategies have been developed employing a closed loop version of the exponential feeding law, an estimation of the controlled variable and some error feedback term. In the case of non-monotonic kinetics, the specified growth rate can be achieved at two different substrate concentration values. Because of the inherent unstable properties of the system in the decreasing portion of the kinetics function, stabilization becomes a crucial problem in this high-substrate operating region. In this context, the dynamic behavior of fed-batch processes with Haldane kinetics is further investigated. In particular, some conditions for global stability and performance improvement are derived. Then, a stabilizing control law based on a partial state feedback with gain dependent on the output error feedback and gain saturation is proposed. Although particular emphasis is put on the critical case of high-substrate oper- ation, low-substrate regulation is also treated. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Nonlinear control; Fed-batch processes; Haldane kinetics; Partial stability 1. Introduction Fed-batch processes are extensively used in the expand- ing biotechnological industry. The requirements for an efficient industrial production are encouraging the develop- ment of robust and reliable controllers. For this reason, fed-batch process control is receiving great attention by the research community. The control problem is character- ized by, e.g., modelling approximations, parameter uncer- tainties, nonlinear and non-minimum phase dynamics and scarce on-line measures. A large portion of biotechnological processes are char- acterized by pure cultures with one limiting substrate and with the metabolite of interest being formed in parallel to the microbial growth. These growth-linked reactions may be inhibited by the presence of the substrate or a certain product in excess [1,2]. A typical example of non-mono- tonic growth rate with substrate inhibition is the Haldane kinetics function depicted in Fig. 1. From a biological and production standpoint, an impor- tant goal is to force and keep microorganisms into a given physiological state [3–5]. This specification usually trans- lates into the following control task: the regulation of the biomass growth rate. In the case of Haldane-like kinetics, the specified growth rate can be achieved at two different substrate concentration values. Depending on the objective of the process, the desired growth rate should be accom- plished at one of these substrate equilibria. For instance, in baker yeast fermentation processes, the lowest setpoint 0959-1524/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jprocont.2006.02.001 q Research in this area is partially supported by ANPCyT (PICT2003 11-14111) and CONICET (Grant 691/04, PIP 5532/05) of Argentina and CICYT (DPI2002-00525) of Spain. * Corresponding author. Tel./fax: +54 221 425 9306. E-mail address: deba@ing.unlp.edu.ar (H. De Battista). www.elsevier.com/locate/jprocont Journal of Process Control 16 (2006) 865–875