Sensor Location for Diagnosis in Linear Systems: A Structural Analysis

• Published in: IEEE transactions on automatic control Vol. 52; no. 2; pp. 155 - 169
• Main Authors: Commault, C., Dion, J.-M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Cost engineering; Costs; Disturbances; Exact sciences and technology; Fault detection; Fault detection and isolation (FDI); Graphs; Linear systems; Marketing; Mathematical analysis; Modelling and identification; Particle separators; Position (location); Sensor systems; Sensors; structured systems; Studies; structured systems; Measurement sensor; Fault detection and isolation (FDI); Location problem; System decomposition; graphs; Transducer position; Diagonal matrix; Observer; Mechanical system; System identification; Solvability; Fault diagnostic; Defect detection
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2006.889865

We consider here the fault detection and isolation (FDI) problem for linear systems. We are interested in designing a set of observer-based residuals, in such a way that the transfer from the faults to the residuals is diagonal and the transfer from the disturbances to the residuals is zero. We deal with this problem when the system under consideration is structured, that is, the entries of the system matrices are either fixed zeros or free parameters. This problem can be solved in terms of the graph that can be associated in a natural way with a structured system. When the FDI solvability conditions are not satisfied, we assume that internal variables can be measured at a cost and look into the question of wether the problem is solvable with these new measurements. We give solvability conditions for a solution with a minimal number of additional sensors and among such solutions provide a minimal cost solution for the sensor location problem under consideration. We pay particular attention to the internal analysis of the system, and we propose a structural decomposition of the system associated graph based on some particular separators. This analysis leads to the definition of a reduced system. We prove that some potential additional sensors are inefficient for solving our FDI problem and that the FDI problem can be solved using only measurements on the reduced system