## 8 Discussion of the Results  
It is clearly observed from Table 2 that PSO reports overshoot values for the quadcopter inputs that are significantly lesser than the overshoot values reported by the ZN method, shown in Table 2, for the same corresponding quadcopter inputs. Further, GA and CSA reported overshoot values as shown in Table 2, which are lower than those reported by the ZN method for the corresponding inputs. These findings are attributed to the powerful features of GA, CSA and PSO as meta-heuristic optimization methods and the robustness of the presented multi-objective fitness function given in Equation (31). However, the overshoot values reported by PSO for the inputs of the quadcopter in Table 2 are lower than those reported by GA and CSA as shown in Table 2.  
The rise and settling times reported by GA, CSA and PSO for all quadcopter inputs are remarkably lower than those reported by the ZN method for the same corresponding inputs. This clarifies and may prove that GA, CSA and PSO are reliable and more effective than the classical ZN method in controlling the movements of the quadcopter, using PID control parameters. Additionally, the differences in the rise and settling times between the control process developed based on PSO, GA and CSA for the four inputs of the quadcopter are respectively less than 0.0045, 0.0209, 0.00925, and 0.431625, on average, which are small and not statistically significant. Overshoot of the motor signal of the quadcopter is a critical factor that should be slashed. If the temperature of the insulation of the motor of a quadcopter is elevated further away than its rated limits, then the motor will be ruined rapidly [49]. Table 2 states that the overshoot values of all movements of the quadcopter reported by PSO are close to zero in all cases considered; the overshoot values for all movements of the quadcopter reported by GA and CSA are very small in all cases considered. Outstandingly, this outcome is highly desirable for reaching an extremely low temperature for the motors of the quadcopter to protect them from destruction. The control approaches developed based on GA, CSA and PSO report very low fitness values for all quadcopter inputs, which simply means that the controlling processes developed using these meta-heuristic algorithms for the PDI controller of the quadcopter reached an optimal control for the movements of the quadcopter. Moreover, there is no significant difference between the cost values of these algorithms, whereas the differences in fitness cost values between the optimization developed based on PSO, GA and CSA for the four inputs of the quadcopter are, respectively, less than 0.0015475 and, 0.0209, 0.00925, and 0.009815, on average, which are not statistically significant. Simply put, the step signals representations of the quadcopter inputs plotted using GA, CSA and PSO demonstrate that these meta-heuristic algorithms are robust tuning algorithms for the quadcopter's PID controller and are better than the conventional tuning \begin{table}
\begin{tabular}{l l l l l l} \hline \(i\) & **Method** & \(z\) & \(p\)**-Value** & \(\alpha\div i\) & **Hypothesis** \\ \hline
1 & CSA & 0.27386 & 0.78419 & 0.0500 & Not rejected \\
2 & GA & 1.36930 & 0.17090 & 0.0250 & Not rejected \\
3 & ZN & 2.73861 & 0.00616 & 0.0166 & Rejected \\ \hline \end{tabular}
\end{table} 
Table 5: Results of [PERSON]’s method based on the overshoot measure. methods, such as the evaluated ZN method. In short, this expected upshot asserts the reliability level of GA, CSA and PSO in optimizing the PID parameters for the quadcopter. All in all, the following observations can be made from the experimental results of GA, CSA and PSO when used to optimize the PID parameters to control the movements of the quadcopter.