Georges Bastin

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.

Structural properties and classification of kinematic and dynamic models of wheeled mobile robots

The structure of the kinematic and dynamic models of wheeled mobile robots is analyzed. It is shown that, for a large class of possible configurations, they can be classified into five types, characterized by generic structures of the model equations. For each type of model the following questions are addressed: (ir)reducibility and (non)holonomy, mobility and controllability, configuration of the motorization, and feedback equivalence.

Theory of Robot Control

Part 1 Rigid manipulators: modelling and identification joint space control task space control motion and force control. Part 2 Flexible manipulators: elastic joints flexible links. Part 3 Mobile robots: modelling and structural properties feedback linearization nonlinear feedback control. Appendix: control background.

A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws

We present a strict Lyapunov function for hyperbolic systems of conservation laws that can be diagonalized with Riemann invariants. The time derivative of this Lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions. It is shown that the derived boundary control allows to guarantee the local convergence of the state towards a desired set point. Furthermore, the control can be implemented as a feedback of the state only measured at the boundaries. The control design method is illustrated with an hydraulic application, namely the level and flow regulation in an horizontal open channel

Boundary feedback control in networks of open channels

This article deals with the regulation of water flow in open-channels modelled by Saint-Venant equations. By means of a Riemann invariants approach, we deduce stabilizing control laws for a single horizontal reach without friction. The stability condition is extended to a general class of hyperbolic systems which can describe canal networks with more general topologies. A control law design based on this condition is illustrated with a simple case study: two reaches in cascade. The proof of the main stability theorem is based on a previous result from Li Ta-tsien concerning the existence and decay of classical solutions of hyperbolic systems.

Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems

We give a new sufficient condition on the boundary conditions for the exponential stability of one-dimensional nonlinear hyperbolic systems on a bounded interval. Our proof relies on the construction of an explicit strict Lyapunov function. We compare our sufficient condition with other known sufficient conditions for nonlinear and linear one-dimensional hyperbolic systems.

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.

Optimizing bioreactors by extremum seeking

The optimization of the operation of biological reactors is an interesting non-linear problem whose solution offers potential economic benefit. We apply a peak seeking method to approach the maximum biomass production rate in a continuous stirred tank bioreactor. Two models, Monod and Haldane, are investigated and it is shown by simulation that the peak seeking scheme achieves optimization for both cases. A stabilizing feedback controller with a washout filter is designed to extend the operating range for the Haldane model. Copyright

Dynamic feedback linearization of nonholonomic wheeled mobile robots

Smooth time-varying laws can solve the stabilization problem of nonholonomic mechanical systems. The authors show that by means of dynamic state feedback, it is possible for three-wheeled mobile robots to track arbitrary fast trajectories not reduced to equilibrium points. Dynamical modeling of nonholonomic mechanical systems for the case of three-wheeled mobile robots is considered. Dynamic feedback allows solution of the tracking problem for an omnidirectional mobile robot with less motors than degrees of freedom. This is possible by choosing output functions depending on the mass repartition of the robot.<<ETX>>

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.