Unbiased Inversion-Based Fault Estimation of Systems with Non-Minimum Phase Fault-to-Output Dynamics

Abstract: We propose a framework for inversion-based estimation of certain categories of faults in discrete-time linear systems. The fault signal, as an unknown input, is reconstructed from its projections onto two subspaces. One projection is achieved through an algebraic operation, whereas the other is given by a dynamic filter whose poles coincide with the transmission zeros of the system. A feedback is then introduced to stabilize the above filter as well as to provide an unbiased estimate of the unknown input. Our solution has two distinctive and practical advantages. First, it represents a unified approach to the problem of inversion of both minimum and non-minimum phase systems as well as systems having transmission zeros on the unit circle. Second, the feedback structure makes the proposed scheme robust to noise. We have shown that the proposed inversion filter is unbiased for certain categories of faults. Finally, we have illustrated the performance of our proposed methodologies through numerous simulation studies.