Fractional Order Unknown Input Filter Design for Fault Detection of Discrete Linear Systems

This work deals with the problem of filter design for disturbance decoupling in discrete-time linear fractional order systems (FOS) under noisy environments. To this end, Fractional Unknown Input Filter (FUIF) is developed based on Fractional Kalman Filter (FKF) framework. Accordingly, the proposed structure can result in robustness against unknown inputs (UIs) in noisy environments. This algorithm can be used for robust fault detection since the disturbance is decoupled from state estimation error. The designed filter is applied to a fractional order (FO) model of an ultra-capacitor (UC), under noisy condition, for the state estimation and fault detection purposes. Simulation results illustrate the benefits of the proposed approach.