The polytopic model (PM) structure is often used in the areas of automatic control and fault detection and isolation (FDI). It is an alternative to the multiple model approach which explicitly allows for interpolation among local models. This thesis proposes a novel approach to PM estimation by modeling the set of PM weights as a random vector with Dirichlet Distribution (DD). A new approximate (adaptive) PM estimator, referred to as a Quasi-Bayesian Adaptive Kalman Filter (QBAKF) is derived and implemented. The model weights and state estimation in the QBAKF is performed adaptively by a simple QB weights' estimator and a single KF on the PM with the estimated weights. Since PM estimation problem is nonlinear and non-Gaussian, a DD marginalized particle filter (DDMPF) is also developed and implemented similar to MPF. The simulation results show that the newly proposed algorithms have better estimation accuracy, design simplicity, and computational requirements for PM estimation.

In order to reduce the detrimental effects of inter-area oscillations on system stability, it is possible to use Linear Matrix Inequalities (LMIs) to design a multi-objective state feedback. The LMI optimization finds a control law that stabilizes several contingencies simultaneously using a polytopic model of the system. However, the number of cases to be considered is limited by computational complexity which increases the chances of infeasibility. In order to circumvent this problem, this paper presents a method for solving multiple polytopic problems having a common base case. The proposed algorithm determines the necessary polytopic control for a particular contingency and classifies the data as belonging to that polytopic domain. The technique has been tested on an 8-machine, 13 bus, system and has been found to give satisfactory results. / Master of Science

The traditional approach to damp inter-area oscillations is through the installation of Power System Stabilizers (PSSs) which provide damping control action through excitation control systems of the generating units. However, study of recent blackouts has shown that the control action provided by a PSS alone is not sufficient for damping oscillations in modern power systems which operate under stressed conditions. An integrated form of control using remote measurements to coordinate the different control elements present in the system is the need of the hour. One way of implementing such a coordinated control is through the development of a Linear Matrix Inequality (LMI)-based polytopic model of the system that guarantees pole placement for a variety of operating conditions. The size of the polytopic formulation is an issue for application of LMIs to large systems. The use of Selective Modal Analysis (SMA) alleviates this problem by reducing the size of the system. The previous attempts have used a model containing all the and modes, with SMA being used to eliminate all the other states. In practical applications the resulting system was still found to be too large to use in a polytopic model. This thesis presents an algorithm to reduce the size of the system to the relevant modes of oscillations. A 16 machine, 68 bus equivalent model of the New England-New York interconnected power system is used as the test case with DC lines and SVCs acting as the control. The algorithm is then applied to a 127-bus equivalent model of the WECC System. The use of ESDs as a form of control is also demonstrated. The results indicate that the proposed control successfully damps the relevant modes of oscillations without negatively damping the other modes. The control is then transferred to a more detailed 4000+ bus model of the WECC system to realize its performance on real-world systems. / Master of Science

Ce travail propose de nouvelles structures de contrôle pour la téléopération bilatérale à travers des réseaux de communication non dédiés. L’enjeu est donc de concevoir et calculer des structures de commande garantissant la stabilisation et un bon degré de performance en termes de synchronisation (suivi des positions et vitesse) et de transparence (ressenti des forces) sous les retards variables et asymétriques.Nous faisons tout d’abord un tour d’horizon des recherches récentes dans le domaine des systèmes de téléopération et de leurs caractéristiques. Puis, nous considérons des modèles linéaires à plusieurs retards variables pour lesquels nous proposons une approche d’analyse de stabilité par fonctionnelles de Lyapunov-Krasovskii et contrôle robuste H [infinity symbol . Ensuite, trois structures de téléopération seront proposées en temps continu, la comparaison de ces architectures montre que, pour un retard de réseau maximum donné ou calculé, toutes garantissent un suivi de position et vitesse. Les deux dernières, qui utilisent les forces mesurées ou estimées de l’opérateur humain et de l’environnement, garantissent de plus un suivi en force. Au final, la troisième structure (avec proxy) présente la meilleure performance, même si elle demande un peu plus de calcul. Puis, afin d’analyser et d’améliorer les performances de la troisième structure pour des modèles encore plus réalistes, une étude est menée en temps discret, mais aussi sur un modèle non linéaire ou non stationnaire sous perturbations bornées en norme. L’implantation sur la plate-forme est décrite dans un quatrième et dernier chapitre, et puis l’analyse des résultats expérimentaux est alors menée / This PhD thesis is dedicated to the control scheme design of the bilateral teleoperation under asymmetric communication channels: the stabilization and a high-level performance under asymmetric time-varying delays and the perturbations of the human operator and environment. After a review of the recent researches and their features in the field of teleoperation system, a less conservative Lyapunov-Krasovskii functional together with H [infinity symbol] control theory has been applied to linear time delay systems, and then the LMI theorems have been obtained in order to calculate the controllers in the control schemes.Firstly, three novel teleoperation control schemes have been presented. Comparing three architectures, all of them guaranteed the stability and the position tracking thanks to the position/velocity information. Force-reflecting control scheme without or with proxy, in addition, ensured the force tracking by using the estimated/measured force of the human operator and the environment. Here, the control scheme with the proxy got a better performance. Secondly, a discrete-time approach has been developed to analyze the force-reflecting control scheme with proxy and obtain a better system performance. Besides, more general systems with time-varying uncertainties (the polytopic-type uncertainties and the norm-bounded model uncertainties) have been considered. Finally, the experimental test-bench and the real system implementation have been designed, which involved the identification and linearizing control of the subsystems (the master/slave robots). The experimental results have illustrated the effectiveness of the approaches proposed in this thesis