## 4 Results and Discussion
### Settling Time Analysis  
Settling time (\(t_{s}\)) and time elapsed in the tolerance band can be used to make useful conclusions about systems performance and stability. Less values of '\(t_{s}\)' imply that the system took less time to achieve a close to steady state condition. Here, the width of tolerance band is calculated as a percentage of the total change in altitude at specific time intervals. We took the band width of 20% and 5% of \(\Delta\) altitude for the change of 200 ft and 800 ft respectively.  
At the time interval from 0 to 30 s, the settling time can not be used as a performance parameter because there is no change in the altitude and the operator has to hold an existing altitude for 30 s. In time intervals between 35 to 100 s, we can see that with the realistic and exaggerated force feedback conditions, '\(t_{s}\)' is significantly reduced in each interval which proves that in the altitude hold task, we can enter a steady state condition in less time when compared with no the force feedback condition. The settling times for different time intervals are presented in Table 8.  
As we can see in Tables 8 and 9, we do not have a settling time and time elapsed in the tolerance band for realistic and exaggerated force feedback conditions from 100 to 130 s, this is due to the fact that when operators were asked to drop the altitude to 1200 ft from 2000 ft (i.e., significant altitude difference) they were not able to control the UAV to keep it in the steady state region.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time (s)** & **No Force Feedback** & **Realistic Force Feedback** & **Exaggerated Force Feedback** \\ \hline
100 to 130 & 13 & 10 & 10 \\
130 to 160 & 12 & 6 & 12 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Fall time, s (\(t_{f}\)) at different time intervals.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time (s)** & **No Force Feedback** & **Realistic Force Feedback** & **Exaggerated Force Feedback** \\ \hline
100 to 130 & 4.9 & 10.1 & 11.1 \\
130 to 160 & 1.4 & 3.1 & 5.5 \\ \hline \hline \end{tabular}
\end{table}
Table 7: % Maximum undershoot at different time intervals.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time (s)** & **No Force Feedback** & **Realistic Force Feedback** & **Exaggerated Force Feedback** \\ \hline
35 to 70 & 26 & 16 & 10 \\
70 to 100 & 26 & 23 & 18 \\
100 to 130 & 20 & - & - \\
130 to 160 & 8 & 11 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Settling time, s (\(t_{s}\)) at different time intervals.  
To support our conclusion, we also calculated the time elapsed in the tolerance band, which illustrates the total time period an operator spent in the close to steady state. The numerical values of the time elapsed in the tolerance band are presented in Table 9. We can see from Figure 13 that from 130 to 160 s of time, the response is not in the tolerance band, so we increased the width of the tolerance band to 50% \(\Delta\) altitude. Then, the time elapsed in the band was calculated for realistic and exaggerated force feedback conditions, which are significantly higher, as seen in Table 9. Accuracy is compromised by increasing the width of the tolerance band. The numerical values prove that with realistic and exaggerated force feedback conditions, the time elapsed in the tolerance band is significantly increased, thus, the operators spent more time in the steady state condition, which is good performance sign.