Fault diagnosis (FD) is one of the main roles of fault-tolerant control (FTC) systems. An FD should not only identify the presence of a fault, but also quantify its magnitude and location. In this work, we present a robust fault diagnosis method for quadcopter unmanned aerial vehicle (UAV) actuator faults. The state equation of the quadcopter UAV is examined as a nonlinear system. An adaptive sliding mode Thau observer (ASMTO) method is proposed to estimate the fault magnitude through an adaptive algorithm. We then obtain the design matrices and parameters using the linear matrix inequalities (LMI) technique. Finally, experimental results are presented to show the advantages of the proposed algorithm. Unlike previous research on quadcopter UAV FD systems, our study is based on ASMTO and can, therefore, determine the time variability of a fault in the presence of external disturbances.