Sliding mode observer for robust fault reconstruction of time delay systems

Abstract

A sliding mode observer in the presence of known output delay and its application to robust fault reconstruction is studied. The observer is designed using a singular perturbation method for which sufficient conditions are given in the form of linear matrix inequalities (LMIs) to guarantee ultimate boundedness of the error dynamics. Though an ideal sliding motion cannot be achieved in the observer when the outputs are delayed, ultimately bounded solutions can be obtained, provided the delay is sufficiently small. The bound on the solution is proportional to the delay and the magnitude of the switching gain. The proposed observer design is applied to the problem of fault reconstruction under delayed outputs and system uncertainties. It is shown that actuator or sensor faults can be reconstructed reliably from the output error dynamics. An example of observer design for an inverted pendulum system is used to demonstrate the merit of the proposed methodology, compared with existing sliding mode observer design approaches.