# Model-Free-Based Single-Dimension Fuzzy SMC Design for Underactuated Quadrotor UAV
## 4 Control Design
### MFSDF-SMC Control Design Using Model-Free Approach
Figure 12 shows the helical trajectory followed by quadrotor using conventional F-SMC control design, whereas Figure 13 shows the translational responses along with the angular velocities roll, pitch and yaw responses in Figure 3.1 This chattering effect is reduced once one amalgamates the fuzzy logic control design with sliding mode control. Figure 3.2 Roll, pitch and yaw responses using SMC Control technique. Figure 3.3 Quadrotor following helical trajectory using F-SMC control design. The number of high oscillations is now reduced by using the conventional fuzzy-based sliding mode control (F-SMC). The graphs demonstrated in Figures 13 and 14 show that this technique can tackle the Zeno effect intelligently but cannot handle the unmodelled dynamic factors and external disturbances. The only limitation of the SDF-SMC simulations as shown in Figures 15 and 16, is computation time that depends on fuzzification, inference of rules and defuzzification steps. This limits the underactuated quadrotor craft from doing aggressive maneuvers. The single-dimension-based fuzzy sliding mode control improves this response and enables the  
Figure 3.4 Roll, pitch and yaw response using F-SMC control technique. Figure 3.5 Position response derived using F-SMC control technique. drone to perform aggressive maneuvers without chattering noise. Through the induction of unmodelled dynamic factors and external disturbance, same problem appears that our drone deviates from its track on 47.01 s and again comes on track at exactly 69.01 s, as demonstrated in Figure 3.6  
Figure 3.7 Roll, pitch and yaw responses using SDF-SMC control technique. Figure 3.8 Position response derived using SDF-SMC control technique. To tackle the unmodelled dynamic factors and external disturbances due to which underactuated quadrotor craft cannot follow the helical trajectory properly, paper proposes the model-free single-dimension fuzzy-based sliding mode control (MFSDF-SMC). The results of trajectory tracking are shown in Figure 18, whereas the translational and angular responses are shown in Figures 19 and 20, respectively. Here, the underactuated quadrotor successfully improves its tracking performance and does not deviate from helical trajectory at any instant, but very low chattering effect is observed. The Table 4 compares and summarizes the entire performance of these techniques such as SMC, F-SMC, SDF-SMC and MFSDF-SMC control techniques. The comparison is done in terms of computational time, Zeno effect (chattering), control input energy and the duration for which it deviates from the track since SDF-SMC is 50% faster than the conventional F-SMC but deviates due to unmodelled dynamic factors and disturbances, whereas MFSDF-SMC algorithm improves the convergence time and tracking performance with no deviation from helical trajectory. Figure 3.9 Quadrotor following helical trajectory using SDF-SMC (without model-free approach). Figure 5.0 Quadrotor following helical trajectory using MFSDF-SMC control design. Figure 5.1 Position response derived using SDF-SMC control technique. Figure 5.2 Roll, pitch and yaw responses using SDF-SMC control technique. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Control** & **Execution Time** & **Chattering** & **Control Input** & **Deviation Time** \\
**Designs** & **(s)** & **Effect** & **Energy (CIE)** & **(s)** \\ \hline
**SMC** & 100 & 4.25\% & 5.54\% & 4.0 \\ \hline
**F-SMC** & 100 & 3.25\% & 5.54\% & 4.0 \\ \hline
**SDF-SMC** & 50 & 2.35\% & 3.75\% & 22 \\ \hline
**MFSDF-SMC** & 50 & 2.03\% & 3.07\% & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison between SMC, F-SMC, SDF-SMC and MFSDF-SMC algorithms. Figure 21: Position error rates while maneuvering using MFSDF-SMC. Figure 22: Yaw error rates while maneuvering using MFSDF-SMC. The total control input energy (CIE) as mentioned in Table 4 is the total power consumption by the four rotors of quadrotor. It is calculated using ordinary integral square method. The same method is used for the computation of chattering phenomena.