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In time-critical systems such as spacecraft systems, fault detection and isolation requirements are of paramount importance and necessity. This paper uses a second order nonlinear sliding mode observer to detect actuator faults in the attitude control subsystem of a satellite with four reaction wheels in a tetrahedron configuration. Through a postprocessing of residual signals it is shown how to isolate and reconstruct the faults in all four reaction wheels. Simulation results show that the proposed strategy can successfully detect, isolate and reconstruct reaction wheel faults.