ScienceDirect IFAC-PapersOnLine 48-1 (2015) 586–591 Available online at www.sciencedirect.com 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2015.05.094 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. * BioSys, University of Mons, 7000 Mons, Belgium, (e-mail: micaela.benavides@umons.ac.be). † Dept. of Chemical Engineering, KU Leuven, 3001 Leuven, Belgium (e-mail: Dries.Telen@cit.kuleuven.be,Joost.Lauwers@cit.kuleuven.be Filip.Logist@cit.kuleuven.be, Jan.VanImpe@cit.kuleuven.be) ‡ BioSys, University of Mons, 7000 Mons, Belgium, (e-mail: alain.vandewouwer@umons.ac.be) Abstract: The Droop model is a classical model used to describe substrate limitation in cultures of micro- algae in photobioreactors. In this study, we address the questions of structural identifiability as well as practical identifiability. Optimal experiment design based on the M-criterion is used to determine a small set of experiments that would allow an accurate estimation of the model parameters. Direct and cross-validation results are presented and discussed in the framework of a simulation study. As a result, all parameters are found to be structurally identifiable and two continuous experiments are proposed that target either the estimation of the maximum substrate uptake rate and maximum growth rate, or the half saturation constant of the uptake rate, respectively. Parameter Identification of the Droop Model using Optimal Experiment Design Micaela Benavides * Dries Telen, Joost Lauwers, Filip Logist, Jan Van Impe † Alain Vande Wouwer ‡ Keywords: Mathematical modeling; parameter estimation; identifiability; microalgae culture. 1. INTRODUCTION Research and applications of microalgae cultivation have experienced a fantastic boom in the last two decades due to a renewed interest in alternative energy sources, and the potential of microalgae to produce large quantities of lipids. Besides, microalgae have a large spectrum of applications ranging from pigments, cosmetics, food to wastewater treatment (Becker (1993); Chisti (2007)). Kinetic modeling of microalgal photosynthesis and growth allows the prediction of the process performance and op- timization of operating conditions (Becker (1993)). In the literature, there are numerous models that describe micro- algal growth as a function of the environmental variables, such as nutrients and light (Geider et al. (1998); Flynn (2001)). In this work, we consider one of the earliest and most famous models, i.e., the Droop model (Droop (1968)). This model describes the ability of microalgae to store nutrients and the decoupling between substrate uptake and biomass growth. The nutrient storage is repre- sented by an intracellular variable, called quota Q, which is defined as the concentration of internal nutrient per concentration of biomass. This model could serve as a good basis to develop soft- ware sensors or controllers for the photobioreactor (PBR). However, it contains a set of parameters that have to be inferred from experimental data, which raises the ques- tion of structural and practical identifiability (Chis et al., 2011b). In this connection, it is important to ensure that the experimental data contains sufficiently rich informa- tion so as to estimate accurate parameter values. Optimal experiment design (OED) allow the selection of a reduced number of experiments to achieve this objective. OED can classically be achieved using the Fisher infor- mation matrix that contains information on the parame- ter sensitivities and the measurement errors (Pukelsheim (2006)). Various criteria can be used, based, for instance, on the determinant (D-criterion) or the eigenvalues (E- criterion) of this matrix. OED for microalgae cultures has been studied, e.g., in (Mu˜ noz-Tamayo et al., 2014), where a simplification of a model developed in (Bernard, 2011) is used. In this model, the temperature and light are considered as time- varying inputs. Since the authors aim at improving the accuracy of all parameters, they propose the use of a D- criterion, which maximizes the determinant of the Fisher information matrix. The objective of the present study is to first investigate structural identifiability of the Droop model using differen- tial algebra, as implemented in the software DAISY (Bellu et al., 2007). Then, practical identifiability is assessed using OED with the dilution rate of a limiting nutrient as manipulated input, and the M-criterion (parameters with maximum variance). In this approach, ”target” parameters are selected, which will mostly benefit from the OED, and a compromise has to be met between the number of target parameters, and their accuracy. The methodo-