## 1 Introduction  
The quadcopter unmanned aerial vehicles (UAVs) have drawn attention for their potential use in a wide range of technologies and applications due to their reliability, agility, mechanical simplicity, and ability to operate in narrow and dangerous spaces both in outdoor and indoor environments. This adaptability and reliability promote its universality over other UAV systems. Therefore, quadcopter UAVs have been investigated and applied in different technologies, including precision landing [1; 2], formation flight [3; 4], fault-tolerant control [5; 6] and trajectory tracking [7; 8]. Currently, the vertical and horizontal movements of a quadcopter are controlled by a pilot with a remote-control system, whereas angular movement is automatically controlled by an onboard flight controller. The attitude controller is more crucial for maintaining the quadcopter at an appropriate coordinate, because it not only allows the quadcopter to achieve the desired attitude, but also avoids crashing when the pilot operates the desired vertical and horizontal movements [9]. During operation, one critical issue with the attitude controller is the uncertainties of the model and the disturbances that the quadcopter encounters. Previous studies have proposed various control schemes, such as backstepping control [10; 11], fuzzy control [12; 13], sliding mode control [14; 15], and neural network technique [16; 17], to handle this problem. When faults occur, solving the control problem to guarantee the stability of the quadcopter becomes a greater challenge [18], because this control problem could lead to a flight failure. Therefore, fault-tolerant control (FTC) is an important factor that should be examined intensively while designing the attitude controller. Recently, the study of FTC has enabled researchers to reinforce the safety and reliability of systems. Generally, the types of faults examined in FTC systems are process, actuator, and sensor faults. The actuator is a crucial element in obtaining a specific rotation for translation, because it can connect to the control signals. Therefore, the actuator faults were investigated in this work. There are two methods to handle this kind of faults: Passive FTC (PFTC) and active FTC (AFTC). Previous studies have focused on PFTC approaches to accommodate the actuator faults using a robust controller that does not depend on robust fault detection and the fault estimation scheme. Different methods have been proposed based on adaptive control, feedback linearization, and \(H_{\infty}\) adaptive control [19; 20; 21]. These methods are good for fault compensation, but they are not sufficiently robust for disturbances and uncertainties if the system matrices are not accurate. To overcome this problem, several nonlinear techniques have been proposed based on sliding mode control, adaptive sliding mode control, neural network control, fuzzy control, and backstepping control [22; 23; 24; 25; 26; 27; 28; 29; 30; 31]. These studies present robust controllers for fault accommodation. The above-mentioned PFTC methods can address faults in fault-free and faulty operations. However, in PFTC schemes, the magnitude of faults is designed in a given boundary. To handle the large magnitude of faults, AFTC using a fault detection and identification unit, has been proposed [32]. Various approaches based on sliding mode control for the quadcopter have been investigated. For instance, several authors have proposed a sliding mode control based on active and passive FTC [33]. In this work, the PFTC mode in fault-free operation was switched over to AFTC when a fault was detected. The experimental results on Qball-X4 showed that the AFTC method can compensate better than PFTC during tracking. When faults occur in an actuator, both methods can successfully drive the quadrotor. This work also compared the merits and demerits of each approach. An on-line FTC method is also proposed based on the control allocation technique and sliding mode control [34].