Detecci on de Fallas en Sistemas Lineales y su Aplicaci on para un Sistema de Nivel de L quidos

Abstract

A fault must be understood as an undesirable change in the system, which tends to degrade its performance. Therefore, in this thesis is proposed a method for the Detection and Fault Isolation in Linear Time-Invariant Systems (LTI). Although this method can be applied to any LTI System, in this work is exposed its application into a liquid level system. Usually this kind of process are represented by a linear model, consequently we focus our analysis on the design of a waste generator observer, inspired by the geometric theory, using a reinterpretation of the problem of Disturbance Rejection by Output Injection. Altough the proposed methodology is based on geometric control theory, worth noting that the aim and one of the main contributions of this work is to avoid the di cult calculations related with the geometry (in general calculation of invariant subspaces), creating a new methodology of easy calculation and simple implementation. In general to ensure that each residue is dependent on their respective failure and decoupled from the rest of them, are imposed severe restrictions on the model. Thus, in this work we present the necessary and su cient conditions for the existence of the observer scheme (waste generator) proposed for fault detection. Finally, the results were applied into a physical process: a liquid level system, where the failures are possible leaks in tanks and/or pipes. After the experiments carried out in the physical system, the proposed scheme yields an important property, showing certain robustness to parametric variations, which is of great interest, because it continues detecting and isolating faults correctly, despite some variations in system parameters either by the wear of components or by the e ects of temperature, which leads to the conclusion that the proposed method is a good alternative to solve the problem exposed in this paper.