Diagnosis of time-delay fractional systems using observer-based methods

In this paper, two model-based methods are considered for the diagnosis of time-delay fractional systems. Time-delay fractional Luenberger observer without unknown input and time-delay fractional unknown input observer are developed and used for fault detection and isolation. A single observer scheme is needed for fault detection and a bank of generalized (respectively dedicated) observers is required for fault isolation. A theoretical study investigating the convergence condition for each observer-based method in terms of matrix inequalities is presented. Residual sensitivities to faults and to disturbances are studied. Time-delay fractional unknown input observer parameters are computed to obtain structured residuals. This observer ensures unknown input decoupling from the state which results residual insensitive to unknown inputs. Two numerical examples to validate the efficiency of the proposed approaches are given.