Observer based active fault tolerant control of descriptor systems

The active fault tolerant control (AFTC) uses the information provided by fault detection and fault diagnosis (FDD) or fault estimation (FE) systems offering an opportunity to improve the safety, reliability and survivability for complex modern systems. However, in the majority of the literature the roles of FDD/FE and reconfigurable control are described as separate design issues often using a standard state space (i.e. non-descriptor) system model approach. These separate FDD/FE and reconfigurable control designs may not achieve desired stability and robustness performance when combined within a closed-loop system.This work describes a new approach to the integration of FE and fault compensation as a form of AFTC within the context of a descriptor system rather than standard state space system. The proposed descriptor system approach has an integrated controller and observer design strategy offering better design flexibility compared with the equivalent approach using a standard state space system. An extended state observer (ESO) is developed to achieve state and fault estimation based on a joint linear matrix inequality (LMI) approach to pole-placement and H∞ optimization to minimize the effects of bounded exogenous disturbance and modelling uncertainty. A novel proportional derivative (PD)-ESO is introduced to achieve enhanced estimation performance, making use of the additional derivative gain. The proposed approaches are evaluated using a common numerical example adapted from the recent literature and the simulation results demonstrate clearly the feasibility and power of the integrated estimation and control AFTC strategy. The proposed AFTC design strategy is extended to an LPV descriptor system framework as a way of dealing with the robustness and stability of the system with bounded parameter variations arising from the non-linear system, where a numerical example demonstrates the feasibility of the use of the PD-ESO for FE and compensation integrated within the AFTC system.A non-linear offshore wind turbine benchmark system is studied as an application of the proposed design strategy. The proposed AFTC scheme uses the existing industry standard wind turbine generator angular speed reference control system as a “baseline” control within the AFTC scheme. The simulation results demonstrate the added value of the new AFTC system in terms of good fault tolerance properties, compared with the existing baseline system

Analyse et commande des systèmes paramétrés, par la fonction signe matricielle

This thesis focuses on some new methods for analysis and control problems of parameter-dependent systems. These problems are reformulated as a parameter-dependent Riccati, Lyapunov and/or Sylvester equation.As an alternative to the LMI framework, we show initially that these problems can be solved thanks to the matrix sign function, or direct inversion methods of parameter-dependent matrices.Several approaches are proposed along the manuscript. First the use of non-iterative methods, based either on a direct inversion method, or on the integral definition of the matrix sign function is proposed.A second way mixes the matrix sign function together with the spectral decomposition of a matrix in an original method for the solution of non-standard Sylvester equations.Then, several methods, called iterative methods, are also proposed based on different mathematic tools such as the Laurent polynomial expansion, the inverse via Discrete Fourier Transform, etc.All along the manuscript, examples are shown, simultaneously in the constant and parameter-dependent cases, in order to show to the reader the applicability and the limits of the proposed methods.La thèse présentée ici a pour objet de proposer des méthodes de résolution de problèmes d’analyse et de commande de systèmes paramétrés. Ces problèmes sont ramenés à la résolution d’équations de Riccati, de Lyapunov et/ou de Sylvester paramétrées.S’inscrivant comme une alternative au formalisme LMI nous montrons dans un premier temps que ces équations peuvent être résolues à l’aide de la fonction signe matricielle ou des méthodes d’inversion directe de matrices paramétrées.Différentes approches sont proposées tout au long du manuscrit. On notera dans un premier temps l’utilisation de méthodes non itératives, se basant soit sur une méthode d’inversion directe, soit sur la définition dite intégrale de la fonction signe matricielle. Une seconde voie explorée combine la fonction signe matricielle avec la séparation de spectre d’une matrice pour la résolution d’équations de Sylvester non standards. Ensuite, différentes méthodes, dites itératives, sont proposées également se basant sur des outils mathématiques tels que l’expansion en polynômes de Laurent, les inversions de Fourier, etc. Tout au long du manuscrit, des exemples sont proposés, tant sur le plan constant que paramétré afin d’estimer l’applicabilité, l’efficacité ainsi que les limites des différentes méthodes proposées

Extended H2 Controller Synthesis for Continuous Descriptor Systems

International audienceThis paper presents a complete solution to the nonstandard H2 output feedback control problem for continuous descriptor systems where unstable and nonproper weighting functions are used. In such a problem, the desired controller has to satisfy two conditions simultaneously: (i) the closed-loop is admissible and has a minimum H2 norm, (ii) only the internal stability of a part of the closed-loop is sought. The condition of the existence of such a controller is deduced. An explicit characterization of the optimal solution is also formulated, based on two generalized algebraic Riccati equations (GAREs) and two generalized Sylvester equations. A numerical example is included to illustrate the validity of the proposed results