Fault reconstruction from sensor and actuator failures

Many fault detection filters have been developed to detect and identify sensor and actuator faults by using analytical redundancy. In this paper, an approach for reconstructing sensor and actuator faults from the residual generated by the fault detection filter is proposed. The transfer matrix from the faults to the residual is derived in terms of the eigenvalues of the fault detection filter and the invariant zeros of the faults. For each fault, the fault reconstruction process is derived by applying a projector to the transfer matrix and taking inverse. In order to have a well-conditioned fault reconstruction process, the invariant zeros of the faults have to be in the left-half plane. Furthermore, for reconstructing a sensor fault, the system has to be detectable with respect to the other sensors.