Design of unknown input fractional order proportional–integral observer for fractional order singular systems with application to actuator fault diagnosis

摘要

This study proposes the design of an unknown input fractional order proportional-integral observer for fault diagnosis of linear fractional order singular (FOS) systems. The considered system is rectangular in general form. The necessary and sufficient conditions for the existence of the proposed observer are derived, and a systematic design approach is presented. The proposed observer is non-singular, and uses only the original coefficient matrices to estimate the norm-bounded actuator faults. Also, the unknown input appearing in measurement is considered and the effects of unknown inputs are decoupled from observer dynamics. By introducing a continuous frequency distributed model and using indirect Lyapunov approach, the convergence conditions of the proposed observer are derived in terms of linear matrix inequalities. Furthermore, for a class of non-linear FOS systems with both output disturbances and input uncertainties, a non-linear observer is developed based on the proposed design approach. The existence and convergence of this observer are proved. Finally, the effectiveness of the proposed method is illustrated via two examples.