# Model-Free-Based Single-Dimension Fuzzy SMC Design for Underactuated Quadrotor UAV
## 2 Literature Review
The precise mathematical model for underactuated quadrotor unmanned aerial vehicle is difficult because of several types of time-varying parameters that instantaneously change, such as wind disturbance, the payload mass variation (smooth and non-smooth), the chattering effect and other external disturbances. To address this issue, researchers have proposed model-free control techniques to control and stabilize the system. Researchers have proposed different versions such as piecewise recursive approach [34; 35; 36], time delay estimation control design [37], algebraic method-oriented hybrid PID control designs [38; 39; 40] and many more. This manuscript proposes a model-free single-dimension fuzzy-based sliding mode control (SDF-SMC) design. The technique of single-dimension fuzzy-based sliding mode control has been proposed previously without model-free approach for several applications such as deep submergence rescue vehicle (DSRV) [41], double pendulum-type overhead crane [42] and NPS AUV II [43] for Pantograph-Cateary system [44] and for underactuated quadrotor craft [45]. This algorithm produced many methods, such as fast convergence rate, prompt execution time response, less chattering effect and less control input energy (CIE). The output response of SDF-SMC in all research contributions produces sound results until the induction of external disturbances and unmodelled dynamic factors. In contrast with fuzzy-based control design [46], artificial neural network and genetic algorithm [47; 48], SMC is the better control technique for such underactuated systems. The only limitation is its high sensitivity to unmodelled dynamic factors and disturbances, which results in it generating high number of oscillations due to sliding surface [49]. This section shows that sliding mode control has many more perks than other control designs. It has one issue of chattering phenomenon, which is high number of oscillations that appear on four rotors of underactuated quadrotor [50]. Researchers have hybridized SMC with fuzzy logic control (FLC) [51] to improve the performance and reduce the chattering or Zeno phenomenon. The only issue with this control strategy is consumption of huge computational time, bandwidth and power source. This is all because of its several sub-stages such as fuzzification, inference of rules and lastly the defuzzification stage, whereas the intelligent algorithms as mentioned in [52] are not recommended because they do not facilitate the quadrotor in real-time self-tuning of the gains or the improvement of impulsive behavior [53; 54]. Similarly, if one discusses the fuzzy Hoo output feedback control then its output is also quantized and therefore either introduces the chattering noise or provides some delay [55; 56]. This manuscript proposes sliding mode control design with an adaptive flavor. This combines the SMC with an improved version of Fuzzy logic control to acquire the maximum computational speed with maximum efficiency and of course enough capability to tackle the unmodelled dynamic factors and external disturbances. This technique is named the model-free single-dimension fuzzy-based sliding mode control (MFSDF-SMC). By doing this, the chattering phenomenon will be reduced comparatively from the responses and the quadrotor will be able to perform the aggressive maneuvers. Novelty of this approach is that it ensures the stability and tracking under any uncertainty that is created due to unmodelled dynamic factors and unknown external disturbances. This model-free approach will ensure the bounded tracking errors, whereas the single-dimension fuzzy-based sliding mode control will try to stabilize the underactuated system by eliminating the bounded error in a finite time. In addition to this, MFSDF-SMC will also reduce the computational time and control input energy so that the quadrotor can play aggressive operations.