Esmaeil Naderi

Esmaeil Naderi, Khashayar Khorasani

In this work, we propose explicit state-space based fault detection, isolation and estimation filters that are data-driven and are directly identified and constructed from only the system input-output (I/O) measurements and through estimating the system Markov parameters. The proposed methodology does not involve a reduction step and does not require identification of the system extended observability matrix or its left null space. The performance of our proposed filters is directly connected to and linearly dependent on the errors in the Markov parameters identification process. The estimation filters operate with a subset of the system I/O data that is selected by the designer. It is shown that the proposed filters provide asymptotically unbiased estimates by invoking low order filters as long as the selected subsystem has a stable inverse. We have derived the estimation error dynamics in terms of the Markov parameters identification errors and have shown that they can be directly synthesized from the healthy system I/O data. Consequently, the estimation errors can be effectively compensated for. Finally, we have provided several illustrative case study simulations that demonstrate and confirm the merits of our proposed schemes as compared to methodologies that are available in the literature.

Esmaeil Naderi, Khashayar Khorasani

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.

Esmaeil Naderi, Khashayar Khorasani

In this paper, we propose a framework for output tracking control of both minimum phase (MP) and non-minimum phase (NMP) systems {as well as systems with transmission zeros on the unit circle}. Towards this end, we first address the problem of unknown state and input reconstruction of non-minimum phase systems. An unknown input observer (UIO) is designed that accurately reconstructs the minimum phase states of the system. The reconstructed minimum phase states serve as inputs to an FIR filter for a delayed non-minimum phase state reconstruction. It is shown that a quantified upper bound of the reconstruction error exponentially decreases as the estimation delay is increased. Therefore, an almost perfect reconstruction can be achieved by selecting the delay to be sufficiently large. Our proposed inversion scheme is then applied to solve the output-tracking control problem. {We have also proposed a methodology to handle the output tracking problem of systems that have transmission zeros on the unit circle in addition to MP and NMP zeros.} Simulation case studies are also presented that demonstrate the merits and capabilities of our proposed methodologies.