Fault detection of fractional‐order system based on finite frequency H−/H∞${{H}_{-}}/{{H}_{\infty }}$ unknown input observer

Abstract

This study is about fault detection observer design in finite frequency domain for fractional‐order systems with unknown input disturbances. In order to make the generated residuals fault‐sensitive, robust to the non‐decoupling parts of unknown input disturbances, and guarantee the stability requirements of fractional‐order error systems, the authors derive the fault detection conditions of unknown input observers. First, using the condition of observer, the unknown input is decomposed into decoupling part and non‐decoupling part, and the decoupling part is eliminated from the estimation error. Second, the residuals generator of the unknown input observer is designed by using the finite frequency performance indicator, so that the residuals are robust to the non‐decoupling part of the unknown input and sensitive to fault signals. In particular, variable linearization methods are introduced to convert design conditions into a series of LMIs. Finally, the simulation results show the effectiveness of the designed method.