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

We propose a framework for inversion-based estimation of certain categories of faults in discrete-time linear systems. First, we develop a novel methodology for direct estimation of unknown inputs by using only measurements of either minimum or non-minimum phase systems as well as systems with transmission zeros on the unit circle. The 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 dynamics as well as provide an unbiased estimation of the unknown input. Next, we have applied our proposed methodology to the problem of fault estimation and 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 to demonstrate the capabilities and advantages of the developed strategies.