An Easy to Apply Methodology for Fault Detection and Isolation in Linear Systems

Miguel Hernandez
National Polytechnic Institute, Electrical and Mechanical Engineering School, Campus Culhuacan
Av. Santa Ana No. 1000, 04430, Mexico City, MEXICO

Basilio Del Muro
National Polytechnic Institute, Electrical and Mechanical Engineering School, Campus Culhuacan
Av. Santa Ana No. 1000, 04430, Mexico City, MEXICO

Domingo Cortes
National Polytechnic Institute, Electrical and Mechanical Engineering School, Campus Culhuacan
Av. Santa Ana No. 1000, 04430, Mexico City, MEXICO

Juan Carlos Sanchez
National Polytechnic Institute, Electrical and Mechanical Engineering School, Campus Culhuacan
Av. Santa Ana No. 1000, 04430, Mexico City, MEXICO

Abstract:

Although the fault detection and isolation problem has been there for over three decades and many solutions using various approaches has been proposed, simpler and feasible methods to quickly and efficiently solve this problem are still valuable. In this paper, a very easy to implement method to solve the fault detection and isolation problem for linear systems is proposed. Experimental result using the three-tank system, commonly used as a benchmark, shows the feasibility of the proposed method. The technique is based on an unusual application of a long standing result of the geometric control theory for linear systems, initially proposed for the disturbance decoupling problem. Nevertheless it avoids the involved calculations that are usual in geometric-based algorithms.

Keywords:

Fault Detection and Isolation, Linear Systems, Three-tank System.

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CITE THIS PAPER AS: Miguel HERNANDEZ, Basilio DEL MURO, Domingo CORTES, Juan Carlos SANCHEZ, An Easy to Apply Methodology for Fault Detection and Isolation in Linear Systems, Studies in Informatics and Control, ISSN 1220-1766, vol. 21 (3), pp. 275-282, 2012. https://doi.org/10.24846/v21i3y201206

1. Introduction

In general, a fault can be defined as a not allowed deviation in the system which leads to the inability to fulfill its intended purpose. This deviation could be in properties, characteristics or parameters which alter the system with respect to its nominal or acceptable condition [7]. To ensure the security and stability of the control system, it is important to design a feasible fault-tolerant control strategy. For any fault-tolerant strategy to work, it is necessary to detect and isolate faults quickly and effectively.

Consequently methods for detection and isolation of faults that do not affect system safety and efficiency of production are required. This represents a major challenge and is the cause why the development of techniques for Fault Detection and Isolation (FDI) has been drawn so much attention over the last three decades. The importance of the subject has led to several surveys to be published [7, 4, 5, 6, 8, 3, 19].

A great variety of approaches has been used to solve the Fault detection problem. Several overlapping taxonomies are used in the field usually depending on authors orientation: control engineering, mathematical, statistical or artificial intelligence. A classification that has become more or less standard is a) Data methods: Limit checking and trend checking, data analysis, spectrum analysis, pattern recognition [16] ; b) Knowledge-based methods: expert systems, fuzzy logic, neural networks [15]; c) Process model: residual generators based on state observers or parameter estimation [14]. The reader can see the surveys previously cited, particularly [19] and the references therein for a thoroughly revision of the subject.

Although the fault detection and its related problems have been researcher for a long time the subject is far from being studied completely. On the contrary is still a very active field of research. Some examples of very recent works in the area [12, 9, 1]. On [12] an online-learning strategy is used to detect faults in a class of uncertain nonlinear system. The principal components analysis method is used to detect and localize water leakage in a water distribution network. An approach based on fuzzy models is proposed in [1] for fault detection and isolation of a compression system with some uncertain parameters.

Since the field of fault detection has become so vast, recently the research in fault detections has move from trying to solve the general problem to focus in particular applications. In [13] a solution to the FDI problem for electrical networks is proposed. The invertibility of switched system are analyzed using a set of differential equations. A solution to cope with the main source of disturbances in satellite system is proposed in [11] and an entire survey in the area is done in [18]. In [10] the parity equation method together with neural networks are used to implement a FDI system in a diesel engine. These are just some representative examples.

Unlike most model-based FDI techniques which requires complex algorithms with involved calculations, in this paper a very easy to apply methodology for multivariable linear systems is proposed. The idea of residual generator is used, however instead of a bank of observers a single one, with a different output for each fault, is required. Furthermore, conditions under which faults can be detected are easy to check. The technique developed is based on a reinterpretation of a result proposed within the context of disturbance decoupling problem in geometric control theory (see [17]).

The problem addressed in this work is precisely described in Section 2. In Section 3 some well know results within the context of geometric control theory are presented. These results are the basis for the proposed method. In Section 4 the proposed technique is developed. It can be summarized as follows. First a fault is selected from the set of possible faults. Then, an observer to non available inputs (which happens to be the others faults) is constructed to “performs well” when faults we are not interesting in, are present. The same observer “performs bad” when the selected fault is present. Hence the residue is zero regardless other faults but becomes nonzero when the selected fault arises. These steps are repeated for each fault. Curiously the same observer can be employed for all faults just the observer output has to be changed.

Experimental application of this methodology is illustrated in Section 5 where a system consisting of three tanks interconnected by a pipe is used as a benchmark. This system has the typical characteristics of tanks, pipelines and pumps used in many industries. It has been declared as a benchmark of the COSY project of the European Science foundation. The example developed in Section 5 shows that the proposed methodology could be used as an alternative to that proposed in [9]. Finally the conclusions are given in the last Section.

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