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

What is it about?

Fault detection and isolation is a crucial part of modern control systems. Knowing when a specific system component is malfunctioning allows corrective actions to be effectively taken before the fault causes catastrophic damages. However, there are faults that, without an external intervention, cannot be detected and/or isolated. In this work we adress this problem in linear time-invariant systems by proposing a state feedback input law that, under certain conditions, forces fault diagnosability in the closed-loop system.

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Photo by Egor Myznik on Unsplash

Photo by Egor Myznik on Unsplash

Why is it important?

The active fault detection and isolation problem has been extensively investigated over the last few decades. Most approaches consists of periodically injecting an external auxiliary signal into the system, which forces fault diagnosability. However, the computation of this signal requires solving complex optimization problems and the faults can only be diagnosed in finite time intervals. In our work, the auxiliary signal is designed as a state feedback law that forces the diagnosability of a desired fault all along the time, avoiding the hazardous diagnosis delay introduced by other approaches. Also, novel properties of unobservability subspaces and (A,B)-invariant subspaces are derived to compute the proposed state feedback law in polynomial time.