The need to design a controller that self-schedules itself during the flight of an aircraft has been an active area of research. New methods have been developed beyond the traditional gain-scheduling approach. One such design method leads to a linear parameter varying (LPV) controller that changes based on the real-time variation of system dynamics. Before such a controller can be designed, the system has to also be represented as an LPV system. The current effort proposes a LPV modeling technique that is inspired by an affine LPV modeling techniques found in recent research. The properties of the proposed modeling method are investigated and compared to the affine modeling technique. It is shown that the proposed modeling technique represents the actual system behavior more closely than the existing affine modeling technique. To study the effect of the two LPV modeling techniques on controller design, a linear quadratic regulator (LQR) controller using linear matrix inequality (LMI) formulation is designed. This control design method provides a measure of conservatism that is used to compare the controllers based on the different modeling techniques. An F-16 short-period model is used to implement the modeling techniques and design the controllers. It was found that the controller based on the proposed LPV modeling method is less conservative than the controller based on the existing LPV method. Interesting features of LMI formulation for multiple plant models were also discovered during the exercise. A stability robustness analysis was also conducted as an additional comparison of the performance of the controllers designed using the two modeling methods. A scalar measure, called the probability of instability, is used as a measure of robustness. It was found that the controller based on the proposed modeling technique has the necessary robustness properties even though it is less conservative than the controller designed based on the existing modeling approach. / Master of Science

Le travail de recherche présenté dans ce mémoire est une contribution à l'estimation des modèles Linéaires à Paramètres Variants (LPV) à temps continu. Dans un premier temps, il traite de façon originale la modélisation quasi-LPV des échangeurs de chaleur pour la détection d'encrassement durant les régimes transitoires. La méthodologie définie dans cette thèse est introduite pas à pas pour caractériser un échangeur à courants croisés puis pour celle d'un échangeur à contre-courants montrant ainsi la généricité de l'approche pour la modélisation des échangeurs thermiques. Une méthode locale basée sur une estimation initiale de modèles LTI en différents points du domaine de fonctionnement est utilisée pour construire le modèle LPV en agrégeant les paramètres des différents modèles locaux grâce à une méthode d'interpolation polynomiale liée aux débits massiques. Le modèle quasi-LPV de l'échangeur élaboré en fonctionnement sain permet ainsi d'envisager la détection de l'encrassement dans les échangeurs de chaleur en comparant ses sorties à ceux provenant du procédé. Dans un second temps, ce travail porte sur l'identification des systèmes LPV à représentation entrée-sortie à temps continu par une approche globale. Une solution pratique pour l'identification directe de tels systèmes est proposée. Elle est basée sur l'utilisation d'un algorithme à erreur de sortie initialisé par une approche à erreur d'équation, la méthode des Moments Partiels Réinitialisés. Des simulations illustrent les performances de l'approche proposée. / The research work presented in this thesis is a contribution to the estimation of Linear Parameter Varying (LPV) models in continuous-time. First, a quasi-LPV modeling of heat exchangers is tackled in an original way. This quasi-LPV model is meant to be used for fouling detection (during transient phases). A step-by-step description of the methodology is given on how to model a cross flow heat exchanger. Applying the same approach on a counter flow shows its genericity in the heat exchanger field. A local method, based on an estimation of LTI models for different operating points, is used to build the LPV model by interpolation of the various LTI model parameters. The resulting quasi-LPV model for a clean heat exchanger can thus be used for fouling detection by comparison of real and model outputs for the same input signals. Secondly, this work concerns the identification of continuous-time input-output LPV systems through a global approach. A practical solution for the direct identification of such systems is proposed. It is based on the use of an output-error algorithm initialized by an equation error based approach, the reinitialized partial moment's method. Simulations illustrate the performance of the proposed approach.

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