A. Vande Wouwer

Adaptive Method of Lines

Introduction Application of the Adaptive Method of Lines to Nonlinear Wave Propagation Problems Adaptive MOL for Magneto-Hydrodynamic PDE Models Development of a 1-D Error-Minimizing Moving Adaptive Grid Method An Adaptive Method of Lines Approach for Modelling Flow and Transport in Rivers An Adaptive Mesh Algorithm for Free Surface Flows in General Geometries, M. Sussman The Solution of Steady PDEs on Adjustable Meshes in Multidimensions Using Local Descent Methods Adaptive Linearly Implicit Methods for Heat and Mass Transfer Problems Linearly Implicit Adaptive Schemes for Singular Reaction-Diffusion Equations Unstructured Mesh MOL Solvers for Reacting Flow Problems Two-Dimensional Model of a Reaction Bonded Aluminum Oxide Cylinder Method of Lines within the Simulation Environment DIVA for Chemical Processes.

Robust adaptive control of yeast fed-batch cultures

Abstract Model-based control of bioprocesses is a difficult task due to the challenges associated with biological system modeling and the lack of on-line measurements. In this study, two robust controllers using minimal a priori process knowledge and minimal measurement information are designed to maximize biomass productivity in aerobic cultures of Saccharomyces cerevisiae . This latter objective can be achieved through the regulation of the ethanol concentration at a low constant value. The linearization of Sonnleitner’s model allows simple transfer function models to be derived, which describe the relation between the ethanol concentration, the substrate feed and an exponential disturbance – image of the substrate demand for cell growth – in the different operating (respirative and respiro-fermentative) regimes. The two controllers are based on these linear models and use a RST structure, but differ in the way the exponential growth disturbance is handled. In the first controller, the disturbance is represented by a linear model, whereas in the second controller, the disturbance is measured on-line via the oxygen transfer rate signal and a feedforward control action is used to cancel the disturbance effect on the ethanol concentration. Particular attention is paid to the robustification of the controllers to measurement noise, neglected high frequency dynamics and uncertain stoichiometry coefficients using the observer polynomial. Tests in simulation show the controller performance.

Software sensors for bioprocesses.

State estimation is a significant problem in biotechnological processes, due to the general lack of hardware sensor measurements of the variables describing the process dynamics. The objective of this paper is to review a number of software sensor design methods, including extended Kalman filters, receding-horizon observers, asymptotic observers, and hybrid observers, which can be efficiently applied to bioprocesses. These several methods are illustrated with simulation and real-life case studies.

Practical issues in distributed parameter estimation: Gradient computation and optimal experiment design

Abstract Parameter estimation in nonlinear distributed-parameter systems is usually accomplished by minimizing an output least-square criterion, which is defined implicitly through the solution of the model equations. This paper addresses itself to two important practical issues of the parameter-estimation procedure, i.e., the numerical procedure used to compute the gradient of the criterion with respect to the unknown parameters, and the selection of experimental conditions, i.e., sensor locations and input signals. An experiment design procedure based on the sensitivity matrix is presented. The methods for gradient computation and experiment design have been successfully applied to several process models, and are illustrated in this paper with a simple heat-conduction problem and a more complex model of a catalytic fixed-bed reactor.

Nonlinear model predictive control of fed-batch cultures of micro-organisms exhibiting overflow metabolism: Assessment and robustness

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.

Modeling and simulation of a SMB chromatographic process designed for enantioseparation

Abstract This paper focuses on modeling of a simulated moving bed process (SMB) dedicated to the separation of racemic mixtures. In the first approach, a true moving bed model is derived, which assumes an equivalent counter-current movement of the solid phase. The good agreement between the model and the real system is demonstrated with experimental results. Then, a more rigorous approach is developed, which considers the system as an arrangement of static chromatographic columns and takes into account periodic switching. Attention is focused on model formulation and numerical solution techniques in order to develop efficient dynamic simulation programs.

Dynamic metabolic models of CHO cell cultures through minimal sets of elementary flux modes

The concept of Elementary Flux Modes (EFMs) has been of central importance in a number of studies involving the analysis of metabolism. In Provost and Bastin (2007) this concept is used to translate the metabolic networks of the different phases of CHO cell cultures into macroscopic bioreactions linking extracellular substrates to products. However, a critical issue concerns the calculation of these elementary flux vectors, as their number combinatorially increases with the size of the metabolic network. In this study, a detailed metabolic network of CHO cells is considered, where the above-mentioned combinatorial explosion makes the computation of the elementary flux modes impossible. To alleviate this problem, a methodology proposed in Jungers et al. (2011) is used to compute a decomposition of admissible flux vectors in a minimal number of elementary flux modes without explicitly enumerating all of them. As a result, a set of macroscopic bioreactions linking the extracellular measured species is obtained at a very low computational expense. The procedure is repeated for the several cell culture phases and a global model is built using a multi-model approach, which is able to successfully predict the evolution of experimental data.

Macroscopic modelling and identification of an anaerobic waste treatment process

Abstract Anaerobic fermentation is an important process used for recycling solid organic waste, which leads to a significant reduction of the waste volume with the production of biogas as a positive side effect. For state observation and control purposes, a mathematical representation of the process is required. However, anaerobic fermentation is far too complex to be described in full metabolic details, due to the variety of responsible microorganisms and the unknown and time-varying waste composition. The level of complexity of the description is limited by the amount and quality of available experimental data, which can be used for model identification. In practice, the derivation of a dynamic process model involves the following steps: (i) the selection of suitable macroscopic reaction schemes and kinetic structures, (ii) the estimation of the unknown model parameters from experimental data by minimizing a maximum-likelihood criterion, (iii) the estimation of the unknown measurement variances, (iv) the estimation of the covariance matrix of the parameter estimates and (v) the validation of the obtained model. In this study, attention is focused on these several steps, and a dynamic model of a complex anaerobic process is inferred from infrequent measurements of global variables. The experimental data are obtained from six experiments carried out in a small-scale continuous bioreactor under different feed and (controlled) acidity conditions.

Systematic Generation of Identifiable Macroscopic Reaction Schemes

Abstract Mathematical modelling of bioprocesses is very useful for building simulators, software sensors, con trollers, etc. Th ese tools are generally based on simple models consisting of the system of mass balances for the macroscopic species involved in a reaction scheme. Although this reaction scheme plays a key role in bioprocess modelling, its determination usually relyon intuition, process knowledge and trials and errors. This paper focuses on a metho d to genera te and to co mpare, in a syste matic way, all the identifiable schemes given a set of components for which concentration measurements are available. “Identifiable schemes” means that the pseudo-stoichiometric coefficients can be (uniquely) identified, independently of the kinetics which are unknown. The method is illustrated on a case study.

Continuous - discrete interval observers for monitoring microalgae cultures

Algorithms estimating unmeasured component concentrations play a key role in bioprocess applications where only a few on‐line measurements are usually available. In this article, interval observers are designed to provide guaranteed intervals for the key components involved in cultures of microalgae. In contrast with most of the published studies focusing on continuous‐time measurements, this study considers discrete‐time measurements with possibly long and irregular sampling and defines predictors based on model equations and state transformations to ensure the enclosure of the state variables between two measurement times. The methods are validated with experimental data where the remaining inorganic nitrogen and the microalgal internal quota are estimated.