Continuous-discrete time observers for a class of MIMO nonlinear systems

International audienceThe observer design problem for nonlineardynamical systems has received a remarkable attention over thelast four decades. A considerable effort has been devoted to theobserver design for systems that are observable for any inputusing the high gain concept for exponential convergence purposes.It is however worth mentioning that the available results aremainly devoted to the continuous-time measurements case in spiteof some nice contributions concerning the sampled measurementscase. The motivation of this talk consists in addressing theproblem of redesigning a high gain continuous-time observer for aclass of MIMO nonlinear systems that are observable for any inputin the case of non uniformly sampled measurements. This provides ahigh gain continuous-discrete time observer witch is more suitablefrom an engineering practice point of view. Two design features ofthe proposed continuous-discrete time observer are worth to bepointed out. Firstly, the observer is particularly described by aset of differential equations with instantaneous state impulsescorresponding to the measured samples and their estimates and ishence an impulsive system in nature. Secondly, the involvedobserver gain is time-varying and its calibration is achievedthroughout the tuning of two design parameters. A particularemphasis in put on the exponential convergence of the observerprovided that the sampling process is not too fast in a welldefined sense. Moreover, a suitable interpretation of the proposedcontinuous-discrete time observer is given, namely it is shownthat the underlying impulsive system can be put under the form ofa hybrid system witch is synthesized using a continuous-timedesign with an inter sample output predictor. The effectiveness ofthe proposed continuous-discrete time observer is emphasizedthroughout simulation results involving useful observer designproblems

Observability for any input: a canonical form for MIMO systems

International audienceA canonical form characterizing systems that are observable for any input is firstly proposed. Then, the synthesis of a high gain observer for these systems is detailed. The proposed class of systems is particularly composed by cascade subsystems where each subsystem is associated to a subset of the output variables and assumes a triangular dependence on its own state variables and may depend on the state variables of all other subsystems. The main contribution consists in extending the available results to allow more interconnections between the subsystems. Of fundamental interest, it is shown that he underlying observation error exponentially converges to zero in the absence of uncertainties. Moreover, the observation error can be made as small as desired by properly specifying the observer design parameter in the case where uncertainties are considered

Synthèse d observateurs pour les systèmes non linéaires

Les observateurs sont des capteurs logiciels ayant pour but la reconstruction d'état pour la supervision, la commande ou le diagnostic des systèmes. Dans cette thèse, on s'intéresse à la résolution du compromis entre la rapidité de la convergence et la sensibilité aux bruits de mesure duquel souffre l'observateur à grand gain. Dans un premier temps, on a proposé la synthèse d'un observateur à grand gain dynamique pour certaines classes de systèmes non linéaires multi-sorties uniformément observables. La caractéristique principale de ce type des observateurs réside dans le fait que le gain de l'observateur est pris variable au cours de temps et obéit à une dynamique de type Ricatti. La convergence exponentielle de l'observateur à grand gain dynamique a été détaillée. Ensuite, on a adopté une stratégie floue pour la résolution du dit compromis et on a validé cette approche sur un réacteur chimique. Dans la dernière partie de la thèse, on traite la synthèse d'une commande avec retour d'état pour une classe des systèmes non linéaires afin de résoudre un problème de poursuite de trajectoire. Les performances des observateurs proposés sont illustrées en simulation à travers des exemples académiques et des exemples réels d'application relatifs à un réacteur chimique.The observers are considered as soft sensors. They are designed for the supervision, for the control or for diagnosis of systems. In this thesis, we deal with the resolution of the tradeoff between the convergence rapidity and the sensibility to the noise measurements from which suffers the high gain observer. Firstly, we propose the synthesis of a dynamic high gain observer for some classes of nonlinear uniformly observable systems. The main characteristic of this observer lies in the fact that the observer's gain is taken variable throughout the time and obeys to a Ricatti dynamic. The exponential convergence of the proposed observer is detailed. Then, we adopt a fuzzy strategy to resolve the latter compromise and we confirm this approach throughout a chemical reactor. In the last part of the thesis and in order to resolve a tracking trajectory problem, we treat the synthesis of a state feedback control law for a class of nonlinear systems. The performances of the proposed observers are illustrated in simulation through academic examples and real ones dealing with a chemical reactor.CAEN-BU Sciences et STAPS (141182103) / SudocSudocFranceF

Identification of continuous-time linear systems with time-delay

International audienceThis paper addresses the identification problem of time-delay linear continuous-time systems. More specifically, the involved parameters and time-delay are jointly estimated using a suitable adaptive observer. The latter heavily borrows from the high gain observer design that has been widely investigated throughout the last decade. Global exponential convergence of the parameters and time delay estimates to their trues values is established under an appropriate persistent excitation property. The performance of the proposed identification approach is demonstrated by a simulation study involving an academic example

Output feedback control of a class of nonlinear systems

International audienceThe problems of observation and control of nonlinear systems have received a particular attention throughout the last four decades. Considerable efforts were dedicated to the analysis of the structural properties to understand better the concepts of controllability and of observability of nonlinear systems. Several control and observer design methods were developed thanks to the available techniques, namely feedback linearisation, flatness, high gain, variable structure, sliding modes and backstepping. The main difference between these contributions consist in the design model, and and henceforth the considered class of systems, and the nature of stability and performance results. A particular attention has been devoted to the design of state feedback control laws incorporating an observer satisfying the the separation principle requirements as in the case of linear systems. The motivation of this talk consists in providing an output feedback controller for a class of nonlinear controllable and uniformly observable systems. The output feedback controller is obtained by simply combining an appropriate high gain state feedback control with a standard high gain observer. The high gain concept is particulary appropriate to take off the separation principle challenge inherent for nonlinear systems. The state feedback control design was particularly suggested from the the high gain observer design bearing in mind the control and observation duality. Of particular interest, the controller gain involves a well defined design function which provides a unified framework for the high gain control design, namely several versions of sliding mode controllers are obtained by considering particular expressions of the design function. Furthermore, it is shown that a filtered integral action can be simply incorporated into the control design to carry out a robust compensation of step like disturbances while reducing appropriately the noise control system sensitivity. The effectivene- s of the proposed output feedback control method is emphasized throughout simulation results involving useful process control problems, namely chemical rector temperature tracking and induction motor sensorless control