Interval observer versus set-membership approaches for fault detection in uncertain systems using zonotopes

This paper presents both analysis and comparison of the interval observer–based and set-membership approaches for the state estimation and fault detection (FD) in uncertain linear systems. The considered approaches assume that both state disturbance and measurement noise are modeled in a deterministic context following the unknown but bounded approach. The propagation of uncertainty in the state estimation is bounded through a zonotopic set representation. Both approaches have been mathematically related and compared when used for state estimation and FD. A case study based on a two-tanks system is employed for showing the relationship between both approaches while comparing their performancePeer ReviewedPostprint (author's final draft

Actuator-fault Detection and Isolation based on Interval Observers and Invariant Sets

Abstract — This paper proposes an interval observer-based actuator fault detection and isolation (FDI) approach. An interval observer matching the healthy system mode is designed to monitor the system. When the system is in different modes, state or output interval vectors predicted by the interval observer manifest different dynamical behaviors. To guarantee reliable FDI, a collection of invariant set-based FDI conditions are established. Under these conditions, actuator faults can be accurately detected and isolated during the transition between different modes. At the end, the effectiveness of this proposed approach is presented by using a numerical example. I

Actuator-fault detection and isolation based on interval observers and invariant sets

This paper proposes an interval observer-based actuator fault detection and isolation (FDI) approach. An interval observer matching the healthy system mode is designed to monitor the system. When the system is in different modes, state or output interval vectors predicted by the interval observer manifest different dynamical behaviors. To guarantee reliable FDI, a collection of invariant set-based FDI conditions are established. Under these conditions, actuator faults can be accurately detected and isolated during the transition between different modes. At the end, the effectiveness of this proposed approach is presented by using a numerical example

Diagnosis and fault-tolerant control using set-based methods

The fault-tolerant capability is an important performance specification for most of technical systems. The examples showing its importance are some catastrophes in civil aviation. According to some official investigations, some air incidents are technically avoidable if the pilots can take right measures. But, relying on the skill and experience of the pilots, it cannot be guaranteed that reliable flight decisions are always made. Instead, if fault-tolerant strategies can be included in the decision-making procedure, it will be very useful for safer flight. Fault-tolerant control is generally classified into passive and active fault-tolerant control. Passive fault-tolerant control relies on robustness of controller, which can only provide limited fault-tolerant ability, while active fault-tolerant control turns to a fault detection and isolation module to obtain fault information and then actively take actions to tolerate the effect of faults. Thus, active fault-tolerant control generally has stronger fault-tolerant ability. In this dissertation, one focuses on active fault-tolerant control, which for this case considers model predictive control and set-based fault detection and isolation. Model predictive control is a successful advanced control strategy in process industry and has been widely used for processes such as chemistry and water treatment, because of its ability to deal with multivariable constrained systems. However, the performance of model redictive control has deep dependence on system-model accuracy. Realistically, it is impossible to avoid the effect of modelling errors, disturbances, noises and faults, which always result in model mismatch. Comparatively, model mismatch induced by faults is possible to be effectively handled by suitable fault-tolerant strategies. The objective of this dissertation is to endow model predictive control with fault-tolerant ability to improve its effectiveness. In order to reach this objective, set-based fault detection and isolation methods are used in the proposed fault-tolerant schemes. The important advantage of set-based fault detection and isolation is that it can make robust fault detection and isolation decisions, which is key for taking right fault-tolerant measures. This dissertation includes four parts. The first part introduces this research, presents the state of the art and gives an introduction of used research tools. The second part proposes set-based fault detection and isolation for actuator or=and sensor faults, which are involved in interval observers, invariant sets and set-membership estimation. First, the relationship between interval observers and invariant sets is investigated. Then, actuator and sensor faults are separately coped with depending on their own features. The third part focuses on actuator or=and sensor fault-tolerant model predictive control, where the control strategy is robust model predictive control (tube-based and min-max approaches). The last part draws some conclusions, summarizes this research and gives clues for the further work.La capacidad de los sistemas para tolerar fallos es una importante especificación de desempeño para la mayoría de sistemas. Ejemplos que muestran su importancia son algunas catástrofes en aviación civil. De acuerdo a investigaciones oficiales, algunos incidentes aéreos son técnicamente evitables si los pilotos pudiesen tomar las medidas adecuadas. Aun así, basándose en las habilidades y experiencia de los pilotos, no se puede garantizar que decisiones de vuelo confiables serán siempre posible de tomar. En cambio, si estrategias de tolerancia a fallos se pudieran incluir en el proceso de toma de decisión, los vuelos serían mucho más seguros. El control tolerante a fallos es generalmente clasificado en control pasivo y activo. El control pasivo se basa en la robustez del controlador, el cual sólo provee una habilidad limitada de tolerancia a fallos, mientras que el control tolerante a fallos de tipo activo se convierte en un modulo de detección y aislamiento de fallos que permite obtener información de éstos, y luego, activamente, tomar acciones para tolerar el efecto de dichos fallos. Así pues, el control activo generalmente tiene habilidades más fuertes de tolerancia a fallos. Esta tesis se enfoca en control tolerante a fallos activo, para lo cual considera el control predictivo basado en modelos y la detección y aislamiento de fallos basados en conjuntos. El control predictivo basado en modelos es una estrategia de control exitosa en la industria de procesos y ha sido ampliamente utilizada para procesos químicos y tratamiento de aguas, debido a su habilidad de tratar con sistemas multivariables con restricciones. A pesar de esto, el desempeño del control predictivo basado en modelos tiene una profunda dependencia de la precisión del modelo del sistema. Siendo realistas, es imposible evitar el efecto de errores de modelado, perturbaciones, ruidos y fallos, que siempre llevan a diferencias entre el modelo y el sistema real. Comparativamente, el error de modelo inducido por los fallos es posible de ser manejado efectivamente por estrategias adecuadas de control tolerante a fallos. Con el fin de alcanzar este objetivo, métodos de detección y aislamiento de fallos basados en conjuntos son utilizados en los esquemas de tolerancia a fallos propuestos en esta tesis. La ventaja importante de estas técnicas de detección y aislamiento de fallos basadas en conjuntos es que puede tomar decisiones robustas de detección y aislamiento, lo cual es clave para tomar medidas acertadas de tolerancia a fallos. Esta tesis esta dividida en cuatro partes. La primera parte es introductoria, presenta el estado del arte y hace una introducción a las herramientas de investigación utilizadas. La segunda parte expone la detección y aislamiento de fallos en actuadores y/o sensores, basándose en teoría de conjuntos, a partir de observadores de intervalo, y conjuntos invariantes. La tercera parte se enfoca en el control predictivo robusto (con enfoques basados tanto en tubos robustos como en min-max) con tolerancia a fallos en actuadores y/o sensores. La cuarta parte presenta algunas conclusiones, hace un resumen de esta investigación y da algunas ideas para trabajos futuros