Detection and isolation of incipient sensor faults for a class of uncertain non-linear systems

The present study proposes a new scheme for detection and isolation of incipient sensor faults for a class of uncertain non-linear systems by combining sliding mode observers (SMOs) with a Luenberger observer. Initially, a state and output transformation is introduced to transform the original system into two subsystems such that the first subsystem (subsystem-1) has system uncertainties but is free from sensor faults and the second subsystem (subsystem-2) has sensor faults but without any uncertainties. The sensor faults in subsystem-2 are then transformed to actuator faults using integral observer-based approach. The states of subsystem-1 are estimated using an SMO to eliminate the effects of uncertainties. However, since subsystem-2 does not have any uncertainties, the incipient faults present in this subsystem are detected by designing a Luenberger observer. These faults are then isolated by applying a bank of SMOs to subsystem-2. The sufficient condition of stability of the proposed scheme has been derived and expressed as linear matrix inequalities (LMIs). The design parameters of the observers are determined by using LMI techniques. The effectiveness of the proposed scheme in detecting and isolating sensor faults is illustrated considering an example of a single-link robotic arm with revolute elastic joint. The results of the simulation demonstrate that the proposed scheme can successfully detect and isolate sensor faults even in the presence of system uncertainties.