# Model-Free-Based Single-Dimension Fuzzy SMC Design for Underactuated Quadrotor UAV
## 2 Literature Review  
There are number of research contributions where nonlinear dynamic model of an underactuated quadrotor craft is considered. Researchers proposed several control designs such as sliding mode control (SMC) and backstepping control (BSC) [11; 12] for stabilizing the attitude and positions during the flight mode. These techniques only focused on bounded values for unmodeled dynamic factors and external disturbances [13]. Researchers have also provided comparative study for evaluating the performance of PD control for linear and nonlinear dynamic model of quadrotor in hovering position [14]. Researchers have designed some of the algorithms that provide robust results, i.e., comparatively better convergence rate within finite time [15]. To improve tracking performances, one may find number of nonlinear model-based control designs [16; 17; 18; 19], whereas for robust control designs, they really need complete information about the system, and therefore the system requires lots of sensors and mainly one inertial measurement unit (IMU). Most of the schemes are based on Newton Euler dynamic models. A robust backstepping integral sliding mode control is proposed for the trajectory control of an underactuated and nonlinear quadrotor craft. In the proposed technique [20], one may see the approach is applied on a dynamic model that is derived using Newton Euler method leading to gimbal lock issue again. In addition to this, position errors are also observed. A gain-scheduled proportional integral derivative (G-PID) is proposed in [21] for robust tracking performance, but some overshoots along with steady-state error occurred. The controllers such as linear quadratic regulator (LQR) and PID are mostly applied to achieve better performance, but for the case of underactuated quadrotor in the presence of unmodelled dynamics, these schemes have several performance issues such as slow convergence rate, gimbal lock and transient and steady-state issues [22]. These unmodelled dynamic factors were previously considered one by one, where aerodynamic effects were addressed using integral backstepping control law and then using fractional order backstepping sliding mode controller. These schemes were not only sensitive to disturbances but also to producing high-frequency oscillations known as chattering effect (number of high oscillations on rotors) [23; 24]. It is quite clear that for proposing an intelligent control design or observer-based control, one should derive the accurate dynamic model considering all other unmodelled dynamic factors. This is one of the complex tasks, and thus it demands either more precise model derivation or more precise experiments [25]. These problems are addressed later using higher-order sliding mode control laws such as demonstrated in [26; 27]. It is an admitted fact that the Euler angles are strongly coupled to each other; hence, to invert the control inputs in object-oriented design to get the loose coupling is known as inversion control algorithm as seen in [28]. Researchers have proposed various combinations of inversion control to stabilize the quadrotor. In [29], a nonlinear dynamic inversion control law has been observed where it is developed to address the coupling issue [30; 31; 32]. For the model, the inertial and unmodelled dynamics are very difficult and can affect the UAV at same time. Therefore, researchers have used Lyapunov theorem in many papers for the stability proof. Such types of control laws and schemes can be visualized in [33]. Simply, it is not an issue of intelligent control designs, but a serious concern related to dynamic model of the unmanned aerial vehicles (UAVs). Since the paper is focused on an underactuated quadrotor craft, it considers these factors within the Newton Euler dynamic model along with hyperbolic function to address the singularity issue (Gimbal Lock).