Reconstruction of sensor faults for a class of uncertain nonlinear systems using adaptive sliding mode observers

Abstract

The present paper proposes a new scheme for estimating sensor faults for a class of uncertain nonlinear systems using adaptive sliding mode observers (SMOs). 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. Two SMOs are designed such that the effects of system uncertainties in subsystem-1 are completely eliminated and the sensor faults presenting in subsystem-2 can be reconstructed using the equivalent output error injection term. The Lipschitz constant is assumed to be unknown in the work and this problem can be solved by integrating adaptation laws to the gain of SMOs. The sufficient condition of the stability of the proposed scheme has been derived and expressed as Linear Matrix Inequalities (LMIs). The effectiveness of the proposed scheme in reconstructing sensor faults is illustrated considering an example of a single-link robotic arm with revolute elastic joint. The simulation results demonstrate that the proposed scheme can reconstruct sensor faults even in the presence of large system uncertainties. Incipient sensor faults can also be accurately estimated using the proposed scheme.