A variable structure observer for unknown input estimation in sampled systems

This paper considers the design of a variable structure observer for unknown input estimation and/or fault reconstruction in systems where the process measurements are sampled. It is well known that the principle of the equivalent injection signal from the sliding mode domain can be used for reconstruction of unknown inputs but much of the associated theory is predicated on output sampling of infinite frequency. Sample rate may be a physical constraint of the process and the reconstruction properties of such continuous time sliding mode observers degrade under this constraint. This paper explores how a recently developed ultimately bounded stable variable structure discrete time observer can be used for unknown input estimation. The main novelty of the approach is that the design of the observer is written as an optimization problem with linear constraints with the output sampling incorporated explicitly in the model used for observer design. The design methodology is shown to have advantages in terms of reconstruction accuracy when the performance is compared to that of a classical sliding mode observer on a case study.