A deconvolution view of observer-based fault estimation

The objective of this discussion is to highlight the underlying problems which cause accurate time domain fault estimation from model-based observers to be difficult. Fault estimation may be regarded as an extension to fault detection since accurate non-zero fault estimates automatically imply fault detection. The estimation problem is however generally difficult in the presence of noise, due primarily to the inverse frequency response of the given system and a tendency for system transfer functions to be unstable from output to input. The discussion is based on state space observers for system dynamics in which process faults, sensor faults, and/or disturbances may be present. Knowledge gained from the study of deconvolution is applied to the system model by treating the faults and disturbances in the system as unknown inputs to that system. Hence fault estimation may be treated as a deconvolution problem, either in the context of the given state space model or in the context of robust observer-based residual generation in cases where disturbance decoupling is possible. It is shown that fault estimation is reliant on either explicit or implicit inversion of the system dynamics, and that consequently the performance of possible algorithms for fault estimation are inherently inhibited by problems of both noise sensitivity and algorithmic instability due to the transfer function characteristics of inverse systems