<p>This thesis considers the problem of making dynamic models for industrial processes by combining physical modelling with experimental data. The focus is on distributed parameter systems, that is, systems for which the model structure involves partial differential equations (PDE). Distributed parameter systems are important in many applications, e.g., in chemical process systems and in intracellular biochemical processes, and involve for instance all forms of transport and transfer phenomena. For such systems, the postulated model structure usually requires a finite dimensional approximation to enable identification and validation using experimental data. The finite dimensional approximation involves translating the PDE model into a set of ordinary differential equations, and is termed model reduction.</p><p>The objective of the thesis is two-fold. First, general PDE model reduction methods which are efficient in terms of model order for a given level of accuracy are studied. The focus here is on a class of methods called moving mesh methods, in which the discretization mesh is considered a dynamic degree of freedom that can be used for reducing the model reduction error. These methods are potentially highly efficient for model reduction of PDEs, but often suffer from stability and robustness problems. In this thesis it is shown that moving mesh methods can be cast as standard feedback control problems. Existing moving mesh methods are analyzed based on tools and results available from control theory, and plausible explanations to the robustness problems and parametric sensitivity experienced with these methods are provided. Possible remedies to these problems are also proposed. A novel moving finite element method, Orthogonal Collocation on Moving Finite Elements (OCMFE), is proposed based on a simple estimate of the model reduction error combined with a low order linear feedback controller. The method is demonstrated to be robust, and hence puts only small demands on the user.</p><p>In the second part of the thesis, the integration of PDE model reduction methods with grey-box modelling tools available for finite dimensional models is considered. First, it is shown that the standard approach based on performing model reduction using some ad hoc discretization method and model order, prior to calibrating and validating the reduced model, has a number of potential pitfalls and can easily lead to falsely validated PDE models. To overcome these problems, a systematic approach based on separating model reduction errors from discrepancies between postulated model structures and measurement data is proposed. The proposed approach is successfully demonstrated on a challenging chromatography process, used for separation in biochemical production, for which it is shown that data collected at the boundaries of the process can be used to clearly distinguish between two model structures commonly used for this process.</p>

This thesis considers the problem of making dynamic models for industrial processes by combining physical modelling with experimental data. The focus is on distributed parameter systems, that is, systems for which the model structure involves partial differential equations (PDE). Distributed parameter systems are important in many applications, e.g., in chemical process systems and in intracellular biochemical processes, and involve for instance all forms of transport and transfer phenomena. For such systems, the postulated model structure usually requires a finite dimensional approximation to enable identification and validation using experimental data. The finite dimensional approximation involves translating the PDE model into a set of ordinary differential equations, and is termed model reduction. The objective of the thesis is two-fold. First, general PDE model reduction methods which are efficient in terms of model order for a given level of accuracy are studied. The focus here is on a class of methods called moving mesh methods, in which the discretization mesh is considered a dynamic degree of freedom that can be used for reducing the model reduction error. These methods are potentially highly efficient for model reduction of PDEs, but often suffer from stability and robustness problems. In this thesis it is shown that moving mesh methods can be cast as standard feedback control problems. Existing moving mesh methods are analyzed based on tools and results available from control theory, and plausible explanations to the robustness problems and parametric sensitivity experienced with these methods are provided. Possible remedies to these problems are also proposed. A novel moving finite element method, Orthogonal Collocation on Moving Finite Elements (OCMFE), is proposed based on a simple estimate of the model reduction error combined with a low order linear feedback controller. The method is demonstrated to be robust, and hence puts only small demands on the user. In the second part of the thesis, the integration of PDE model reduction methods with grey-box modelling tools available for finite dimensional models is considered. First, it is shown that the standard approach based on performing model reduction using some ad hoc discretization method and model order, prior to calibrating and validating the reduced model, has a number of potential pitfalls and can easily lead to falsely validated PDE models. To overcome these problems, a systematic approach based on separating model reduction errors from discrepancies between postulated model structures and measurement data is proposed. The proposed approach is successfully demonstrated on a challenging chromatography process, used for separation in biochemical production, for which it is shown that data collected at the boundaries of the process can be used to clearly distinguish between two model structures commonly used for this process. / QC 20101020

Cette recherche vise à résoudre un problème particulier du contrôle de vibration des structures intelligentes. Notre objectif est de réduire les vibrations dans une zone spécifique de la structure intelligente avec une perturbation qui couvre une large gamme de fréquences. De plus, dans cette zone spécifique, ni l'actionnement ni la détection ne sont possibles.Ici, nous faisons face à plusieurs défis principaux. Premièrement, nous devons contrôler les vibrations d’une zone spécifique de la structure, alors que nous n’avons accès aux mesures que dans d’autres zones. Deuxièmement, la large bande passante de la perturbation implique que nombreux modes doivent être contrôlés au même temps, ce qui nécessite l'utilisation de plusieurs actionneurs et capteurs. Cela conduit à un contrôleur MIMO difficile à obtenir avec les méthodes classiques de conception de contrôleur. Troisièmement, il faut éviter le problème de propagation, qui consiste à garantir la stabilité en boucle fermée lorsque le contrôleur basé sur un modèle est appliqué à la configuration réelle. Pour relever ces défis, nous étudions deux stratégies de contrôle: le contrôle centralisé et le contrôle distribué.Pour le contrôle centralisé, nous proposons une méthodologie qui nous permet d’obtenir un contrôleur MIMO simple permettant de relever ces défis. Tout d'abord, plusieurs techniques de modélisation et d’identification sont appliquées pour obtenir un modèle précis d'ordre faible de la structure intelligente. Ensuite, une méthode de synthèse basée sur le contrôle H_∞ avec un critère H_∞ particulièrement proposé est appliquée. Ce critère H_∞ intègre plusieurs objectifs de contrôle, y compris les défis principaux. En particulier, le problème de débordement se transforme en un problème de stabilité robuste et sera garanti en utilisant ce critère. Le contrôleur H_∞ obtenu est une solution standard du problème H_∞. Le contrôleur final est obtenu en simplifiant ce contrôleur H_∞ sans perdre la stabilité en boucle fermée ni dégrader les performances. Cette méthodologie est validée sur une structure de poutre avec des transducteurs piézoélectriques et la zone centrale est celle où les vibrations devraient être réduites. L'efficacité du contrôleur obtenu est validée par des simulations et des expériences.Pour le contrôle distribué, on considère la même structure de poutre et les mêmes objectifs de contrôle. Il existe des méthodes visant à concevoir des contrôleurs distribués pour les systèmes spatialement interconnectés. Cette recherche propose une méthode basée sur la FEM, associée à plusieurs techniques de réduction de modèle, permettant de discrétiser spatialement la structure de poutre et d'en déduire les modèles d’espace d'état des sous-systèmes interconnectés. La conception des contrôleurs distribués ne sera pas abordée dans cette recherche. / This research aims at solving a particular vibration control problem of smart structures. We aim at reducing the vibration in a specific zone of the smart structure under the disturbance that covers a wide frequency band. Moreover, at this specific zone, neither actuation nor sensing is possible.Here we face several main challenges. First, we need to control the vibration of a specific zone of the structure while we only have access to measurements at other zones. Second, the wide bandwidth of the disturbance implies that numerous modes should be controlled at the same time which requires the use of multiple actuators and sensors. This leads to a MIMO controller which is difficult to obtain using classical controller design methods. Third, the so-called spillover problem must be avoided which is to guarantee the closed-loop stability when the model-based controller is applied on the actual setup. To tackle these challenges, we investigate two control strategies: the centralized control and the distributed control.For centralized control, we propose a methodology that allows us to obtain a simple MIMO controller that accomplishes these challenges. First, several modeling and identification techniques are applied to obtain an accurate low-order model of the smart structure. Then, an H_∞ control based synthesis method with a particularly proposed H_∞ criterion is applied. This H_∞ criterion integrates multiple control objectives, including the main challenges. In particular, the spillover problem is transformed into a robust stability problem and will be guaranteed using this criterion. The obtained H_∞ controller is a standard solution of the H_∞ problem. The final controller is obtained by further simplifying this H_∞ controller without losing the closed-loop stability and degrading the performance. This methodology is validated on a beam structure with piezoelectric transducers and the central zone is where the vibration should be reduced. The effectiveness of the obtained controller is validated by simulations and experiments.For distributed control, we consider the same beam structure and the same control objectives. There exist methods aiming at designing distributed controllers of spatially interconnected system. This research proposes a FEM based method, combined with several model reduction techniques, that allows to spatially discretize the beam structure and deduce the state-space models of interconnected subsystems. The design of distributed controllers will not be tackled in this research.