Denis Dochain

On-line estimation and adaptive control of bioreactors

Chapter 1. Dynamical Models of Bioreactors. Introduction. The basic dynamics of microbial growth in stirred tank reactors. Extensions to the basic dynamics. Models of the specific growth rate. The reaction scheme of a biotechnological process. General dynamical model of bioreactors. Examples of state space models. A basic structural property of the general dynamical model. Reduction of the general dynamical model. Stability analysis. Extending the general dynamical model. References and bibliography. Chapter 2. Kinetic Modelling, Estimation and Control in Bioreactors: An Overview. Introduction. Difficulties in modelling the reactor kinetics. Minimal modelling of reaction kinetics. Software sensors for bioreactors. Adaptive control of bioreactors. Conclusions and perspectives. References and bibliography. Chapter 3. State and Parameter Estimation with Known Yield coefficients. Introduction. On state observation in bioreactors. Extended Luenberger and Kalman observers. Asymptotic observers for state estimation when the reaction rates are unknown. On-line estimation of reaction rates. References and bibliography. Chapter 4. State and Parameter Estimation with unknown yield coefficients. Introduction. On-line estimation of the specific reaction rates. Joint estimation of yield coefficients and specific reaction rates. Adaptive observers. Estimation of yield coefficients. Other parameter estimation issues in bioreactors. References and bibliography. Chapter 5. Adaptive Control of Bioreactors. Introduction. Principle of linearizing control and remarks on closed loop stability. Singular perturbation design of linearizing controllers. Adaptive linearizing control (known yield coefficients). A general solution to the linearizing control problem for a class of CST bioreactors. Adaptive linearizing control (unknown yield coefficients). Practical aspects of implementation. Case study: Adaptive linearizing control of fed-batch reactors. Case study: Adaptive control of the gaseous production rate of a synthesis product. References and bibliography. Appendix 1. Models of the Specific Growth Rate. Appendix 2. Elements of Stability Theory. Appendix 3. Persistence of excitation. Convergence of Adaptive Estimators. Nomenclature. Index.

State and parameter estimation in chemical and biochemical processes: a tutorial

This paper aims at giving an overview of available results of state and parameter approaches for chemical and biochemical processes. It is largely organized as a tutorial and starts with a brief reminder concerning the design of extended Luenberger (ELO) and Kalman (EKO) observers, followed by an illustrative nonlinear observer algorithm. Evaluation of the performance of classical observers in presence of model uncertainties will serve as a basis for the motivation of designing asymptotic and interval observers, that do not require the knowledge of the process kinetics. The design of state observers with known kinetic models but uncertain kinetic parameters will then be considered via suggestions of improvements of the EKO and the introduction of two other types of observers (observers where the unknown parameters are used as design parameters; adaptive observers). Finally, the design of online parameter estimation schemes will be introduced. One of the objectives of the present survey is also to suggest new research directions

Dynamical modelling and estimation in wastewater treatment processes.

Dynamical Modelling Dynamical Mass Balance Model Building and Analysis Structure Characterisation (SC) Structural Identifiability Practical Identifiability and Optimal Experiment Design for Parameter Estimation (OED/PE) Estimation of Model Parameters Recursive State and Parameter Estimation Glossary Nomenclature

Practical Identifiability of a Biokinetic Model of Activated-sludge Respiration

This paper deals with the estimation of the parameters of the Monod model for the activated sludge process on the basis of oxygen uptake rate data only. The objective of the paper is to concentrate on the practical identifiability properties of the model and on the design of informative experiments for parameter estimation. The results are illustrated by experimental data. Improvements in parameter estimation accuracy with a factor 2 can be obtained by small extensions of the respirometric experiments. The optimal experimental design procedure for parameter estimation (OED/PE) can be implemented in the respirographic sensor.

Paper: Adaptive identification and control algorithms for nonlinear bacterial growth systems

This paper suggests how nonlinear adaptive control of nonlinear bacterial growth systems could be performed. The process is described by a time-varying nonlinear model obtained from material balance equations. Two different control problems are considered: substrate concentration control and production rate control. For each of these cases, an adaptive minimum variance control algorithm is proposed and its effectiveness is shown by simulation experiments. A theoretical proof of convergence of the substrate control algorithm is given. A further advantage of the nonlinear approach of this paper is that the identified parameters (namely the growth rate and a yield coefficient) have a clear physical meaning and can give, in real time, a useful information on the state of the biomass.

Structural Identifiability of Biokinetic Models of Activated-sludge Respiration

This paper deals with the identifiability of parameters of kinetic models describing the activated sludge process. The main concern of the paper is to present important aspects of the structural identifiability properties. The identifiability analysis is based on the availability of only on-line oxygen uptake rate data (given by a novel respirographic biosensor). Four model candidates (exponential, Monod, double Monod and modified IAWQ No. 1) are considered. Two different methods (Taylor series expansion, and transformation of the nonlinear model into a model linear-in-the-parameters) are considered, their advantages and drawbacks are illustrated with the four kinetic models. For each model it is found that only a smaller set of the original parameters are structurally identifiable on the basis of oxygen uptake rate data only.

Modelling and adaptive control of nonlinear distributed parameter bioreactors via orthogonal collocation

This paper deals with the control of fixed bed bioreactors. The dynamics of these processes are described by a nonlinear distributed parameter model. In a first step, the partial differential equations of the model are reduced to ordinary differential equations by using an orthogonal collocation method. A nonlinear adpative controller is then designed, which is based on the nonlinear discretized model. Its performance is illustrated by simulation results on a fixed bed anaerobic waste water treatment process.

Dynamical analysis of distributed parameter tubular reactors

This paper is dedicated to the dynamical analysis of tubular reactor models, namely plug-flow and axial dispersion reactors involving sequential reactions for which the kinetics only depends on the concentrations of the reactants involved in the reaction. This analysis is performed by describing these models as infinite-dimensional state-space systems, with bounded observation and control operators. It is shown that these systems are exponentially stable, and that (a) the plug-flow reactor model is observable when the component concentrations are measured at the reactor output and observable with respect to its physical domain when only the product concentration is measured, and it is reachable with respect to its physical domain when it is controlled at the reactor input; and (b) any finite set of dominant modes of the axial dispersion reactor model is observable, when either all the component concentrations or only the product concentration are measured, and reachable, by using appropriate sensors and actuators. The dynamical properties of related finite-dimensional models are also discussed.

Adaptive extremum seeking control of continuous stirred tank bioreactors with unknown growth kinetics

In this paper, we present an adaptive extremum seeking control scheme for continuous stirred tank bioreactors. We assume limited knowledge of the growth kinetics. An adaptive learning technique is introduced to construct a seeking algorithm that drives the system states to the desired set-points that maximize the value of an objective function. Lyapunovs stability theorem is used in the design of the extremum seeking controller structure and the development of the parameter learning laws. Simulation results are given to show the effectiveness of the proposed approach.

On-line estimation of microbial specific growth rates

Abstract Continuous time algorithms for the on-line estimation of microbial specific growth rates of fermentation processes are proposed. An important feature of the proposed algorithm is that they do not require any kind of analytical description of the specific growth rate which is simply considered as an unknown bounded time varying parameter. Four different input-output configurations are considered. In each case, the stability and convergence properties of the algorithms are described and their feasibility is illustrated by real life experiments.