*Article* **Generalized Sliding Mode Observers for Simultaneous Fault Reconstruction in the Presence of Uncertainty and Disturbance**

**Ashkan Taherkhani 1, Farhad Bayat 1,\*, Kaveh Hooshmandi <sup>2</sup> and Andrzej Bartoszewicz <sup>3</sup>**


**Abstract:** In this paper, a generalized sliding mode observer design method is proposed for the robust reconstruction of sensors and actuators faults in the presence of both unknown disturbances and uncertainties. For this purpose, the effect of uncertainty and disturbance on the system has been considered in generalized state-space form, and the LMI tool is combined with the concept of an equivalent output error injection method to reduce the effects of them on the reconstruction process. The upper bound of the disturbance and uncertainty are minimized in the design of the sliding motion so that the reconstruction of the faults will be minimized. The design method is applied for actuator faults in the generalized state-space form, and then with some suitable filtering, the method extends as sensors and actuators coincidentally faults. Since in the proposed approach, the state trajectories do not leave the sliding manifold even in simultaneous sensors and actuators faults, then the faults are reconstructed based upon information retrieved from the equivalent output error injection signal. Due to the importance of the robust fault reconstruction in the wind energy conversion system (WECS), the proposed approach is successfully applied to a 5 MW wind turbine system. The simulation results verify the robust performances of the proposed approach in the presence of unknown perturbations and uncertainties.

**Keywords:** sliding mode observer; fault detection; robust fault reconstruction; linear matrix inequalities (LMIs)
