L'objectif principal de ce travail de recherche est de contrôler l'évolution de la distribution des tailles de cristaux (DTC) dans un procédé de cristallisation en batch. Nous avons été amenés à chercher une résolution numérique du bilan de population et à proposer un algorithme rapide et précis. La méthode numérique a été étendue au cas de la taille des cristaux multidimensionnels en utilisant un maillage mouvant. Nous avons étudié le problème de la commandabilité du système à partir de son modèle discrétisé et puis à partir du modèle continu. Nous avons conçu une loi de commande en boucle fermée pour atteindre la DTC désirée à partir de la condition initiale. Pour compenser l'incertitude des paramètres du modèle, nous avons ajouté un second contrôle par retour d'état afin d'assurer la poursuite de la DTC désirée en présence de l'incertitude des paramètres. Nous avons construit un observateur qui nous permet d'avoir en ligne l'estimation des variables d'états. Ces variables d'état estimées sont utilisées dans la synthèse de la loi du contrôle / The main objective of this research is to control the evolution of the Crystal Size Distribution (CSD) in a batch crystallization process. We are led to study a numerical resolution of the population balance and propose an algorithm for fast and accurate simulation. This method was extended to the case of the two-dimensional crystal by using a moving mesh. We studied the problem of controllability of the system from its discretized model and then from the continuous model. To compensate the uncertainty of the model parameters, we added the second state feedback control to ensure the tracking of the desired CSD in presence of parameter uncertainty. We constructed an observer who provides us with on-line estimation of state variables. These state variables estimated are used in the control law synthesis

Understanding crystallisation in magma chambers is a key challenge for igneous petrology. It is particularly important to understand the origins of layering in peralkaline rocks, e.g. the kakortokite (nepheline syenite), Ilímaussaq Complex, S. Greenland, as these are commonly associated with high value multi-element economic deposits. The kakortokite is a spectacular example of macrorhythmic (>5 m) layering. Each unit consists of three layers comprising arfvedsonite-rich (sodic-amphibole) black kakortokite at the base, grading into eudialyte-rich (sodic-zirconosilicate) red kakortokite, then alkali feldspar- and nepheline-rich white kakortokite. Each unit is numbered -19 to +17 relative to a characteristic well-developed horizon (Unit 0), however there is little consensus on their development. This project applies a multidisciplinary approach through field observations combined with petrography, crystal size distributions (CSDs), mineral and whole rock chemistries on Units 0, -8 to -11 and a phonolite/micro-nephelinolite (“hybrid”) sequence that crosscuts the layered kakortokite. Textures and compositions are laterally consistent across outcrop and indicators of current activity are rare. CSDs indicate in situ crystallisation with gravitational settling as a minor process. Chemical discontinuities occur across unit boundaries. The layering developed through large-scale processes under exceptionally quiescent conditions. The discontinuities reflect open-system behaviour; units were formed by an influx of volatile-rich magma that initiated crystallisation in a bottom layer. Nucleation was initially suppressed by high volatile element concentrations, which decreased to allow for crystallisation of arfvedsonite, followed by eudialyte, then alkali feldspar and nepheline to form each tripartite unit. The chemistry of the hybrid indicates mixing between a primitive (sub-alkaline) magma and kakortokite. Thus injections of magmas of varying compositions occurred, indicating a complex plumbing system below current exposure. The lessons learned at Ilímaussaq, which is extremely well exposed and preserved, are relevant to understanding magma chamber dynamics in the more common instances of pervasively altered peralkaline rocks.