Passivity-based nonlinear control of CSTR via asymptotic observers.

International audienceThis work makes use of a passivity-based approach (PBA) and tools from Lyapunov theory to design a nonlinear controller for the asymptotic stabilization of a class of non isothermal Continuous Stirred Tank Reactors (CSTR) around any desired stationary point. The convergence and stability proofs are derived in the port Hamiltonian framework. Asymptotic observers that do not require knowledge of reaction kinetics are also proposed for a system with incomplete state measurement. Numerical simulations are given to illustrate the application of the theoretical results to a CSTR with multiple steady states

Lyapunov-based control of non isothermal continuous stirred tank reactors using irreversible thermodynamics.

International audienceIn this paper, the thermodynamic availability function is used as a Lyapunov function for the practical derivation of non linear control laws for the stabilization of a large class of CSTRs far from the equilibrium. The strict convexity of the availability function is guaranteed as long as one of the extensive variables is fixed. In this study, we consider liquid mixture with constant volume, the constraint on the volume being insured by perfect regulation of the outlet flow of the CSTR. Several control laws are then derived which insure global asymptotic stability, exponential stability or simple asymptotic stability. These control laws are discussed regarding the magnitude and the dynamic variations of the control variable. It is shown that the availability function can be split into two parts: one corresponds to the mixing term and depends on mole numbers only and the other depends on both temperature and mole numbers. The two parts are positive and the second one is chosen as a new Lyapunov function. The use of this new Lyapunov function insures smooth variations of the control variable. An exothermal, first order chemical reaction leading to multiple steady-state operating points of the CSTR illustrates the proposed theory

Adaptive model predictive control

The problem of model predictive control (MPC) under parametric uncertainties for a class of nonlinear systems is addressed. An adaptive identi er is used to estimate the pa- rameters and the state variables simultaneously. The algorithm proposed guarantees the convergence of parameters and the state variables to their true value. The task is posed as an adaptive model predictive control problem in which the controller is required to steer the system to the system setpoint that optimizes a user-speci ed objective function. The technique of adaptive model predictive control is developed for two broad classes of systems. The rst class of system considered is a class of uncertain nonlinear systems with input to state stability property. Using a generalization of the set-based adaptive estimation technique, the estimates of the parameters and state are updated to guarantee convergence to a neighborhood of their true value. The second involves a method of determining appropriate excitation conditions for nonlin- ear systems. Since the identi cation of the true cost surface is paramount to the success of the integration scheme, novel parameter estimation techniques with better convergence properties are developed. The estimation routine allows exact reconstruction of the systems unknown parameters in nite-time. The applicability of the identi er to improve upon the performance of existing adaptive controllers is demonstrated. Then, an adaptive nonlinear model predictive controller strategy is integrated to this estimation algorithm in which ro- bustness features are incorporated to account for the e ect of the model uncertainty. To study the practical applicability of the developed method, the estimation of state vari- ables and unknown parameters in a stirred tank process has been performed. The results of the experimental application demonstrate the ability of the proposed techniques to estimate the state variables and parameters of an uncertain practical system.Departamento de Ingeniería de Sistemas y AutomáticaMáster en Investigación en Ingeniería de Procesos y Sistemas Industriale

Process Monitoring and Control of Microalgae Cultivation

Les bioprocédés jouent un rôle important dans la production de substances à haute valeur ajoutée. L’une des cultures les plus intéressantes parmi les biocultures sont les microalgues. Il s’agit d’organismes microscopiques vivant en milieu aquatique et dont la biomasse est une excellente source d’acide gras et de vitamines. De plus, la culture de microalgues pourrait être utilisée à grande échelle pour produire de l’énergie. Dans ce contexte, l’un des modèles les plus simples pour décrire son comportement dynamique est le modèle de Droop. Ce modèle largement utilisé a été choisi pour cette étude. L’estimation d’état est un domaine de l’ingénierie basé sur l’extraction des informations sur les variables inconnues à partir des informations connues. En génie biochimique, il est nécessaire de connaître les variables qui caractérisent l’état interne du procédé dans le but de produire de grandes quantités des substances d’intérêt. Cependant, l’un des problèmes les plus importants dans la conception de l’estimateur est de pouvoir garantir la convergence de l’erreur d’estimation. C’est pourquoi, en se basant sur les propriétés du modèle de Droop, un observateur de Lipschitz est proposé pour estimer les variables d’état à partir de la mesure. Par ailleurs, l'estimation des paramètres à l'aide de l'observateur est discutée en vue d'estimer certains des paramètres du modèle de Droop. Afin d’évaluer les performances de l’observateur dans le contexte de la commande avancée, le contrôle de la concentration de biomasse et de substrat sont introduits. Deux techniques de contrôle sont considérées en couplage avec l’observateur : le contrôle « backstepping » et le contrôle par linéarisation entrée/sortie. Le suivi de la consigne et le rejet de perturbation sont également étudiés pour ces stratégies. Pour terminer, une extension du modèle de Droop est étudiée pour la production de substances lipidiques. Une structure d’estimation de l’ensemble des variables d’état est ainsi démontrée. ---------- Bioprocesses play an important role to produce high-value products. One of the most interesting cultures among the biocultures is microalgae. It is a microscopic organism existing in aquatic environment. The biomass from this culture is a great source of fatty acids and vitamins. Large scale microalgae culture can be used to produce energy. One of the simplest models to describe the dynamic behaviour of the culture is the Droop model. This widely used model has been chosen for this study. State estimation is a field of control engineering that extracts information about unknown variables based on known information. In bioprocess engineering, in order to produce high amounts of valued product, it is necessary to know about internal state variables of the process. One of the most important problems in designing the estimator is to guarantee the stability of the error dynamics. Based on the properties of the Droop model, a Lipschitz observer is proposed to estimate the state variables from measurement. Moreover, the parameter estimation using the Lipschitz observer is discussed in order to estimate some of the parameters of the Droop model. In order to see the observer performance with advanced controller, the biomass and the substrate concentration control are introduced. Two observer- based controllers, input-output linearization and backstepping technique, are considered. The setpoint tracking and the load rejection problem are studied for both strategies. Finally, a lipid production model as an extension of the Droop model is introduced. The observability property of the model is explained. At the end, a structure for the estimation of all state variables using measurement is demonstrated

Regelungstheorie

The workshop “Regelungstheorie” (control theory) covered a broad variety of topics that were either concerned with fundamental mathematical aspects of control or with its strong impact in various fields of engineering