Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
Malfunction Diagnosis of the Feedback System Based on the Gap Metric
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2005 Volume 18 Issue 10 Pages 361-367


In this paper, we propose a new approach to the malfunction diagnosis problem for feedback systems based on the controller information. We define a fault as any loss of stability of the closed loop system, and a malfunction as a variation from the nominal situation that will develop into the fault, respectively. We supervise and evaluate the variation periodically, and avoid the occurrence of those faults in which gradual changes of plant dynamics result. First, in the supervision, the plant variation is obtained by using a plant model estimated by the closed loop identification scheme proposed by Dasgupta et. al. [14]. Second, the evaluation is achieved by comparing the stability margin of the initial feedback system with the plant variation after the occurrence of any malfunction from the view point of stability of the closed loop system. The gap metric, which is closely related to the stability, is used in order to compare the above two values, and the model variation is captured in terms of the gap metric. However, the exact plant model is unknown, so its upper bound is estimated by using the set membership identification [3, 12, 19, 20] in the Dasgupta's framework. This comparison makes it possible to quantify the reliability of the feedback system.

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