## 6 Experimental Results
### Time Results  
The overshoot, rise time and settling time values obtained by the ZN method, GAs, PSO and CSA during controlling the parameter inputs of the PID controller, namely, roll (\(\phi\)), pitch (\(\theta\)), yaw (\(\psi\)) and thrust (\(z\)), while controlling the movement of the quadcopter are presented in Table 2.  
The overshoot, rise and settling times in Table 2 obtained by the ZN method and optimization process conducted by GAs, PSO and CSA for the PID controller parameters for a quadcopter illustrate the efficiency of these methods in controlling the movement of the quadcopter. It is clearly noted from Table 2 that the overshoot, rise time and settling time reported by the ZN method for the roll, pitch, yaw and thrust inputs of the quadcopter are relatively large. The overshoot for input yaw of the ZN method is analogous to the overshoot for the thrust input. The rise and settling times reported for the input yaw by the ZN method are very small, compared to the rise and settling times reported for the input thrust. Moreover, the settling time reported for the input roll by the ZN method is comparable to that of the input roll reported for the input pitch. The overshoot, rise time and settling time obtained by the GA-based approach are relatively small. Further, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameter** & **Value** \\ \hline GA & Number of genes & 100 \\  & Mutation fraction & 0.1 \\  & Crossover fraction & 0.8 \\  & Lower bound & 0 \\  & Upper bound & 50 \\  & Number of iterations & 100 \\ \hline PSO & Number of particles & 100 \\  & Inertia weight (\(\omega\)) & 1 \\  & Cognitive parameter (\(\alpha\)) & 1.5 \\  & Social parameter (\(\gamma\)) & 2.0 \\  & Lower bound & 0 \\  & Upper bound & 50 \\  & Number of iterations & 100 \\ \hline CSA & Number of crows & 100 \\  & Awareness probability (\(AP\)) & 0.1 \\  & Flight length (\(f\)) & 2 \\  & Lower bound & 0 \\  & Upper bound & 50 \\  & Number of iterations & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter setting of GA, PSO and CSA used in this study. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Method** & \multicolumn{2}{c}{**ZN**} & \multicolumn{4}{c}{**GAs**} \\ \hline
**Evaluation** & **Overshoot** & **Rise time** & **Settling time** & **Overshoot** & **Rise time** & **Settling time** \\ \hline Roll & 6.334 & 0.26 & 0.781 & 1.9857 & 0.117 & 0.164 \\ Pitch & 4.791 & 0.168 & 0.79 & 0.0451 & 0.224 & 0.364 \\ Yaw & 10.266 & 0.0023 & 0.019 & 1.351 & 0.160 & 0.263 \\ Thrust & 10.2668 & 0.189 & 1.582 & 1.999 & 0.038 & 0.517 \\ \hline
**Method** & \multicolumn{2}{c}{**PSO**} & \multicolumn{4}{c}{**CSA**} \\ \hline
**Evaluation** & **Overshoot** & **Rise time** & **Settling time** & **Overshoot** & **Rise time** & **Settling time** \\ \hline Roll & 0 & 0.119 & 0.181 & 0.390 & 0.141 & 0.2182 \\ Pitch & 0.0386 & 0.192 & 0.28 & 0.0193 & 0.2236 & 0.362 \\ Yaw & 0.0425 & 0.166 & 0.296 & 5.84 & 0.141 & 1.507 \\ Thrust & 0.0159 & 0.044 & 0.564 & 0 & 0.099 & 0.9603 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Overshoot, rise time and settling time obtained by ZN, GAs, PSO and CSA. the overshoot values obtained with the GA-based approach are small, compared to the corresponding overshoot values obtained by the ZN method. However, the rise and settling times obtained by the ZN method for inputs yaw and thrust are smaller than those inputs obtained with the GA-based approach. The overshoot values for inputs roll, pitch and thrust obtained by CSA are smaller than those obtained by GA. However, the overshoot value for the input yaw-obtained CSA-based approach is smaller than that obtained by GA. By comparing the control responses from GA- and CSA-based methods for the position and orientation of the PID controller, the CSA-based method has smaller overshoots for inputs roll and yaw of the quadcopter. However, the CSA-based method has longer settling times for these inputs.