Active fault detection and isolation in linear time‐invariant systems: A geometric approach

• Published in: Asian journal of control 2023-03, Vol.25 (2), p.710-721
• Main Authors: Flores‐León, Héctor, Begovich, Ofelia, Ruiz‐León, Javier, Ramírez‐Treviño, Antonio
• Format: Article
• Language: English
• Subjects: active fault diagnosis; Fault detection; fault isolation; Faults; geometric analysis; Invariants; Optimization; Polynomials; residual generation; State feedback; state feedback law; Subspaces; unobservability subspaces
• ISSN: 1561-8625; 1934-6093
• DOI: 10.1002/asjc.2854

In this work, a novel approach on active fault detection and isolation for linear time‐invariant systems, named forced diagnosability, is proposed. This approach computes a continuous state feedback law to render a fault diagnosable, even when it cannot be diagnosed by using passive diagnosis methods. To do that, this work derives novel geometric relationships between unobservability and (A,B)$$ \left(A,B\right) $$‐invariant subspaces that, under certain conditions, guarantee the existence of such state feedback law. The objective of the state feedback law is to force all the faults, except the one required to be diagnosed, named Ld$$ {L}_d $$, to reside in an unobservability subspace. This effectively decouples the effect of Ld$$ {L}_d $$ on the system output, from the effect of the other faults, allowing the design of a residual generator to detect and isolate the desired fault. The proposed state feedback law continuously forces diagnosability, and it can be computed in polynomial time. This avoids testing faults only at fixed time intervals and solving complex optimization problems required in other active diagnosis approaches. A numerical example is presented to illustrate the efficiency of the proposed approach.