Fault estimation and active fault tolerant control for linear parameter varying descriptor systems

Starting with the baseline controller design, this paper proposes an integrated approach of active fault tolerant control based on proportional derivative extended state observer (PDESO) for linear parameter varying descriptor systems. The PDESO can simultaneously provide the estimates of the system states, sensor faults, and actuator faults. The L₂ robust performance of the closed-loop system to bounded exogenous disturbance and bounded uncertainty is achieved by a two-step design procedure adapted from the traditional observer-based controller design. Furthermore, an LMI pole-placement region and the L₂ robustness performance are combined into a multiobjective formulation by suitably combing the appropriate LMI descriptions. A parameter-varying system example is given to illustrate the design procedure and the validity of the proposed integrated design approach

Stabilisation of descriptor Markovian jump systems with partially unknown transition probabilities

This paper is concerned with the stability and stabilisation problems for continuous-time descriptor Markovian jump systems with partially unknown transition probabilities. In terms of a set of coupled linear matrix inequalities (LMIs), a necessary and sufficient condition is firstly proposed, which ensures the systems to be regular, impulse-free and stochastically stable. Moreover, the corresponding necessary and sufficient condition on the existence of a mode-dependent state-feedback controller, which guarantees the closed-loop systems stochastically admissible by employing the LMI technique, is derived; the stabilizing state-feedback gain can also be expressed via solutions of the LMIs. Finally, numerical examples are given to demonstrate the validity of the proposed methods

Bounded real lemmas for positive descriptor systems

A well known result in the theory of linear positive systems is the existence of positive definite diagonal matrix (PDDM) solutions to some well known linear matrix inequalities (LMIs). In this paper, based on the positivity characterization, a novel bounded real lemma for continuous positive descriptor systems in terms of strict LMI is first established by the separating hyperplane theorem. The result developed here provides a necessary and sufficient condition for systems to possess H?H? norm less than ? and shows the existence of PDDM solution. Moreover, under certain condition, a simple model reduction method is introduced, which can preserve positivity, stability and H?H? norm of the original systems. An advantage of such method is that systems? matrices of the reduced order systems do not involve solving of LMIs conditions. Then, the obtained results are extended to discrete case. Finally, a numerical example is given to illustrate the effectiveness of the obtained results

Fault-Tolerant Control Based on Virtual Actuator and Sensor for Discrete-Time Descriptor Systems

This article proposes a fault-tolerant control (FTC) strategy based on virtual actuator and sensor for discrete-time descriptor systems subject to actuator and sensor faults. The fault-tolerant closed-loop system, which includes the nominal controller and observer, as well as the virtual actuator and the virtual sensor, hides the effects of faults. When an observer-based state-feedback law is considered, the existence of algebraic loop may prevent the practical implementation due to the current algebraic states depending on the current control input, that affects also the implementation of the virtual actuator/sensor. To deal with this issue, an observer-based delayed feedback controller and a delayed virtual actuator are proposed for discrete-time descriptor systems. Furthermore, the satisfaction of the separation principle is shown, and an improved admissibility condition is developed for the design of the controller and virtual actuator/sensor. Finally, some simulation results including an electrical circuit are used to demonstrate the applicability of the proposed methods.acceptedVersio

Reduced-order dissipative filtering for discrete-time singular systems

This paper is concerned with the reduced-order dissipative filtering problem of discrete-time singular systems. By considering an equivalent representation of the solution set, a necessary and sufficient dissipativity condition of singular systems is proposed in terms of strict LMI. By using the system augmentation approach, a reduced-order filter is designed such that the filtering error system is admissible and strictly (Q, S, R)-dissipative. A numerical example is presented to demonstrate the usefulness of the derived theoretical results. © 2013 IEEE.published_or_final_versio

Positivity of Continuous-Time Descriptor Systems With Time Delays

This technical note is concerned with positivity characteristic of continuous-time descriptor systems with time delays. First, a set of necessary and sufficient conditions is presented to check the property. Then, considering a descriptor time-delay system with two assumptions, a new time-delay system is established whose positivity is equivalent to that of the original system. Furthermore, a set of necessary and sufficient conditions is provided to check the positivity of the new system. Finally, a numerical example is given to illustrate the validity of the results obtained

Advances in state estimation, diagnosis and control of complex systems

This dissertation intends to provide theoretical and practical contributions on estimation, diagnosis and control of complex systems, especially in the mathematical form of descriptor systems. The research is motivated by real applications, such as water networks and power systems, which require a control system to provide a proper management able to take into account their specific features and operating limits in presence of uncertainties related to their operation and failures from component malfunctions. Such a control system is expected to provide an optimal operation to obtain efficient and reliable performance. State estimation is an essential tool, which can be used not only for fault diagnosis but also for the controller design. To achieve a satisfactory robust performance, set theory is chosen to build a general framework for descriptor systems subject to uncertainties. Under certain assumptions, these uncertainties are propagated and bounded by deterministic sets that can be explicitly characterized at each iteration step. Moreover, set-invariance characterizations for descriptor systems are also of interest to describe the steady performance, which can also be used for active mode detection. For the controller design for complex systems, new developments of economic model predictive control (EMPC) are studied taking into account the case of underlying periodic behaviors. The EMPC controller is designed to be recursively feasible even with sudden changes in the economic cost function and the closed-loop convergence is guaranteed. Besides, a robust technique is plugged into the EMPC controller design to maintain these closed-loop properties in presence of uncertainties. Engineering applications modeled as descriptor systems are presented to illustrate these control strategies. From the real applications, some additional difficulties are solved, such as using a two-layer control strategy to avoid binary variables in real-time optimizations and using nonlinear constraint relaxation to deal with nonlinear algebraic equations in the descriptor model. Furthermore, the fault-tolerant capability is also included in the controller design for descriptor systems by means of the designed virtual actuator and virtual sensor together with an observer-based delayed controller.Esta tesis propone contribuciones de carácter teórico y aplicado para la estimación del estado, el diagnóstico y el control óptimo de sistemas dinámicos complejos en particular, para los sistemas descriptores, incluyendo la capacidad de tolerancia a fallos. La motivación de la tesis proviene de aplicaciones reales, como redes de agua y sistemas de energía, cuya naturaleza crítica requiere necesariamente un sistema de control para una gestión capaz de tener en cuenta sus características específicas y límites operativos en presencia de incertidumbres relacionadas con su funcionamiento, así como fallos de funcionamiento de los componentes. El objetivo es conseguir controladores que mejoren tanto la eficiencia como la fiabilidad de dichos sistemas. La estimación del estado es una herramienta esencial que puede usarse no solo para el diagnóstico de fallos sino también para el diseño del control. Con este fin, se ha decidido utilizar metodologías intervalares, o basadas en conjuntos, para construir un marco general para los sistemas de descriptores sujetos a incertidumbres desconocidas pero acotadas. Estas incertidumbres se propagan y delimitan mediante conjuntos que se pueden caracterizar explícitamente en cada instante. Por otra parte, también se proponen caracterizaciones basadas en conjuntos invariantes para sistemas de descriptores que permiten describir comportamientos estacionarios y resultan útiles para la detección de modos activos. Se estudian también nuevos desarrollos del control predictivo económico basado en modelos (EMPC) para tener en cuenta posibles comportamientos periódicos en la variación de parámetros o en las perturbaciones que afectan a estos sistemas. Además, se demuestra que el control EMPC propuesto garantiza la factibilidad recursiva, incluso frente a cambios repentinos en la función de coste económico y se garantiza la convergencia en lazo cerrado. Por otra parte, se utilizan técnicas de control robusto pata garantizar que las estrategias de control predictivo económico mantengan las prestaciones en lazo cerrado, incluso en presencia de incertidumbre. Los desarrollos de la tesis se ilustran con casos de estudio realistas. Para algunas de aplicaciones reales, se resuelven dificultades adicionales, como el uso de una estrategia de control de dos niveles para evitar incluir variables binarias en la optimización y el uso de la relajación de restricciones no lineales para tratar las ecuaciones algebraicas no lineales en el modelo descriptor en las redes de agua. Finalmente, se incluye también una contribución al diseño de estrategias de control con tolerancia a fallos para sistemas descriptores