Conditions on diagnosis and accommodation delays for actuator fault recoverability

In this paper, conditions on the the fault detection and the fault accommodation delays are defined and developed in order to guarantee the actuator fault´s recoverability. The study is based on the classical Pseud-Inverse Method PIM, used as an active fault tolerant control. A performance index dealing with the variation between the nominal dynamic and the faulty one is defined and computed for different post-fault time intervals. The indicated criterion, compared to a fixed admissibility limit, allows the determination of optimal detection and accommodation instants for recoverable faults either with or without accommodation. The main contribution, in this work, is the definition of conditions on the detection and accommodation times, so that the fault is recoverable with guaranteeing a tradeoff between the closeness of the faulty output to the nominal one and the requested control to accommodate the fault.