## 4 Experimental Evaluation  
In the controller design step of this study, the population size and maximum iteration number of the MH algorithms are selected as 30 and 50, respectively. In the literature, to determine the success of the controllers, several performance indexes are used such as integral of absolute error (IAE), integral of squared error (ISE), integral time absolute error (ITAE), and integral time square error (ITSE). In this study, IAE was used as the performance index and objective function of the optimization process. Maximum speeds of \(X\), \(Y\), and \(Z\) axis and phi, theta, and psi angles are (10 m/s, \(-\)10 m/s), (10 m/s, \(-\)10 m/s), (10 m/s, \(-\)10 m/s), (2 radians, \(-\)2 radians), (2 radians, \(-\)2 radians), and (2 radians, \(-\)2 radians), respectively. Reference/set value of \(X\), \(Y\), and \(Z\) axis and phi, theta, and psi angles are 10, 10, 10, 1, 1, and 1, respectively. The search interval for the P, I, and D parameters of the FOPID controllers developed for \(X\), \(Y\), and \(Z\) axis is [0, 100] and for the \(\lambda\) and \(\mu\) parameters is [0.5, 1.5]. The search interval for the P, I, and D parameters of the FOPID controllers developed for phi, theta, and psi angles is [0, 10] and for \(\lambda\) and \(\mu\) is [0.5, 1.5]. The search intervals for the FOPID controller parameters were selected considering the previous studies and preliminary experiments of this study [37; 49]. The parameters of the FOPID controllers were obtained for the control of the quadcopter using FHO, FFO, and PO algorithms. Table 2 shows the objective function values calculated by the algorithms. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** & \(X\) **Axis** & \(Y\) **Axis** & \(Z\) **Axis** & **Roll** & **Pitch** & **Yaw** \\ \hline FHO & 6.339 & 6.471 & 5.277 & 0.271 & 0.259 & 0.259 \\ FFO & 6.325 & 6.467 & 5.270 & 0.265 & 0.258 & 0.258 \\ PO & 6.281 & 6.413 & 5.261 & 0.259 & 0.256 & 0.254 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Objective function value obtained using different algorithms. Figure 8: Strategy computation [29]. In this study, five performance criteria were used to determine the success of the controllers developed by using FHO, FFO, and PO algorithms. Rising time (Tr) represents the time in which the controlled system output reaches 100% of the reference input. Peak time (Tp) is the time in which the system output reaches its highest value. Maximum overshoot (Mp) is the percentage of overshoot that is calculated by using system output and reference input. Settling time (Ts) is the time in which the system output reaches 99% of its steady state. Error of steady state (Ess) represents the percentage of the deviation of the system output from the refence input during steady state. Tr indicates how fast the quadcopter reaches a target and low Tr is important for the rapid execution of the given task. However, low Tr values may cause Tp, Ts, and Mp values to increase. Increasing Mp increases the instability in the transient response of the quadcopter and reduces the accuracy of reaching the target. If Tp and Ts values increase, the time to reach the target increases and delays the identification of a new target. Ess is the steady-state error and means that the quadcopter has a permanent error value after reaching the target. Failure to meet these criteria prevents the real-world performance of the quadcopter from being at the desired level. For example, in aerial imaging missions, it causes the image transmitted from the camera on the quadcopter to be unclear and causes the package to be delivered to the wrong location in package delivery missions. Table 3 shows the numerical details of the performance of the controllers developed with PO-based FOPID and SDCS methods on the \(X\) axis. Figure 9 includes the graphs of the performances of the developed controllers on the \(X\) axis.