Performance Guarantee of a Class of Continuous LPV System with Restricted-Model-Based Control

This paper considers the problem of the robust stabilisation of a class of continuous Linear Parameter Varying (LPV) systems under specifications. In order to guarantee the stabilisation of the plant with very large parameter uncertainties or variations, an output derivative estimation controller is considered. The design of such controller that guarantee desired  induced gain performance is examined. Furthermore, a simple procedure for achieving the  norm performance is proved for any all-poles single-input/single-output second order plant. The proof of stability is based on the polytopic representation of the closed loop under Lyapunov conditions and system transformations. Finally, the effectiveness of the proposed method is verified via a numerical example

Derivative based control for LPV system with unknown parameters: An application on a Permanent Magnet Synchronous Motors

International audienceThis paper deals with the robust stabilization of a class of Linear Parameter Varying (LPV) systems in the continuous time case. Instead of using a state observer or searching for a dynamic output feedback, the controller is based on output derivative estimation. This allows the stabilization of the plant with very large parameter variation and uncertainties. The proof of stability is based on the polytopic representation of the closed loop, Lyapunov conditions and system transformations. The result is a control structure with only few parameters which are tuned via very simple conditions. This paper illustrates the usefulness on real application: Permanent Magnet Synchronous Motors (PMSM) position control

Echantillonnage dépendant de l'état : une approche discrète

International audienceCe travail concerne l'adaptation des instants d'échantillonnage pour des systèmes différentiels linéaires stationnaires contrôlés par retour d'état. De façon complémentaire à de nombreux travaux qui garantissent la stabilisation indépendamment des variations de la cadence d'échantillonnage, il s'agit ici de concevoir des séquences d'instants d'échantillonnage stabilisantes. Ici, on adapte dynamiquement les ressources nécessaires au calcul des lois de commande en agissant sur leurs instants d'échantillonnage qui ne sont plus périodiques. La solution proposée détermine une séquence d'échantillonnage en fonction de la valeur mesurée de l'état. On développe un algorithme d'ordonnancement dynamique optimisant, sur un horizon d'échantillonnage donné, une séquence parmi un ensemble discret de solutions. Nos preuves sont inspirées des techniques de systèmes hybrides à commutations, alliant fonctions de Lyapunov et optimisation LMI. L'étude théorique est ensuite illustrée par une implémentation algorithmique sous Matlab/TRUETIME simulant l'interaction commande/ordonnancement

State-Dependent Sampling for Linear Time Invariant Systems: A Discrete Time Analysis

International audienceThis work concerns the adaptation of sampling times for Linear Time Invariant (LTI) systems controlled by state feedback. Complementary to various works that guarantee stabilization independently of changes in the sampling rate, here we provide conditions to design stabilizing sequences of sampling instants. In order to reduce the number of these sampling instants, a dynamic scheduling algorithmoptimizes, over a given sampling horizon, a sampling sequence depending on the system state value. Our proofs are inspired on switched system techniques combining Lyapunov functions and LMI optimization. To show the applicability of the technique, theoretical study is illustrated by an implementation in Matlab/ TRUE TIME

201: Are QT intervals correlated to apnea-hypopnea index in obstructive sleep apnea?

IntroductionSeveral studies proved that obstructive sleep apnea (OSA) is associated with cardio-vascular diseases such as cardiac arrhythmia. QT duration and dispersion reflect the heterogeinity of ventricular repolarization and are considered as precursors of ventricular arrhythmiaAimThe aim of this study is to assess the relation between the severity of OSA parameters as apnea hypopnea index and QT intervals.MethodsForty patients (18 men and 22 women) who were diagnosed with OSA by overnight polysomnography were included in this prospective study. The mean age was 56±10 years old. They were all in sinus rhythm. Before initiating continuous positive airway pressure therapy, we calculated on a 12 lead ECG : QT duration (QTend) corrected to Bazett formula and QT dispersion (QT end max -QT end min).ResultsTwenty four patients had severe OSA (AHI >30), 4 had moderate OSA (AHI between 15 and 30) and 12 had a mild OSA (AHI between 5 and 15). There was a significant positive correlation between QT dispersion and AHI (r=0.48, p=0.001)ConclusionThe severity of OSA seems to be correlated with ventricular repolarization heterogeinity These results suggest that the higher is the AHI the higher is the risk of ventricular arrhythmia occurence. Further studies are needed to validate these results

Robust control for time varying parameters systems

Les travaux de cette thèse portent sur l'analyse de stabilité et la synthèse de commandes robustes pour les systèmes non linéaires. La conception des contrôleurs/observateurs nécessite souvent la connaissance totale ou partielle du modèle du procédé à contrôler. Néanmoins, l'obtention d'un modèle à la fois exploitable et suffisamment fidèle est difficile et chronophage, ce qui provoque l'augmentation du coût total de développement d'un système d'asservissement. Afin de réduire la quantité ainsi que la qualité des informations nécessaires sur le système, de nouvelles méthodes de synthèse d'observateurs et de contrôleurs ont été développées dans cette thèse. En effet, si le modèle est connu, une loi de commande par retour de sortie à base d'observateur de type Luenberger a été proposée. Pour cette loi de commande, le système bouclé est vu comme l’interconnexion de deux sous systèmes : la boucle fermée idéale et l'erreur d'observation. Dans le cas où peu d'informations sont disponibles, une loi de commande à modèle restreint (''sans modèle'') a été développée. Afin d’estimer l’état du système, des dérivateurs/estimateurs non-asymptotiques tel que les dérivateurs numériques basés sur l’algèbre différentielle ou encore les dérivateurs asymptotiques tels que les observateurs et les filtres ont été considérés. Les deux lois de commande proposées ont permis de conserver l'aspect non linéaire du système ainsi que d'obtenir des résultats les plus généraux que possible en reformulant les problèmes sous la forme de systèmes polytopiques convexes. Les travaux de cette thèse font appel principalement à la méthode directe de Lyapunov avec fonction quadratique.This work focuses on the stability analysis and the robust control synthesis for nonlinear systems. The design of controllers/observers ofen require a complite or partiel knowledge of the process model to control. Nevertheless, obtaining a model both reable and sufficiently accurate is not only difficult and time-consuming but also it increases the total cdevelopment cost of a control system. In order to reduce the quantity and quality of informations required on the system, new methods of observers and controllers synthesis have been proposed. With known models, an output feedback controller based Luenberger observer was proposed. For this control law, the system closed loop is viewed as the interconnection composed with the ideal closed loop and the observation error. In case where few informations are available, a restricted-model (''model-free'') controller is proposed. In order to estimate the system state, non-asymtotic derivators /estimators based on differentiel algebra or asymptotic ones such as observers or filters have been considered. Both of these control laws have allow to maintain the nonlinear aspects of the system and to obtain general results by reformulating the problem into convex polytopic systems forms. The works of this thesis mainly relies on direct Lyapunov method with quadratic function

Model-free control of LTI systems: An algebraic state estimation approach

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Robust Control for Continuous LPV System with Restricted-Model-Based Control

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Derivative Based Control For LTV System With Unknown Parameters

International audienceThis paper deals with the robust stabilization of a class of linear time varying systems. Instead of using a state observer or having dynamic structure, the controller is based on output derivative estimation. This allows the stabilization of linear time varying systems with very large parameter variation and a small number of controller parameters. The proof of stability is based on the polytopic representation of the closed loop and Lyapunov conditions. The result is proposed in a Linear Matrix Inequality (LMI) form. The validity of this approach is illustrated by a second order system case of study

Derivative-Based Sampled Data Control for Continuous Linear Parameter Varying System With Unknown Parameters

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