## 5 Nominal Simulation and Monte Carlo Shooting Simulation
### Compilation and Comparison of the Results of Three Transition Phase Designs  
The deceleration process of fixed height, which is 12 s after switching to rotary-wing mode, is shown in Figure 20 and the three design methods of transition phase are compared. The nominal simulation results under three transition phase designs are summarized and the distribution ranges of each parameter are shown in Table 4.  
Figure 19: MC shooting simulation of 10 s switching mode. Figure 17: MC shooting simulation of 5 s switching mode. Figure 18: Nominal simulation of transition phase with 10 s switching mode. The comparison results in Table 4 show that:  
1. A soft transition design with switching mode, after switching to rotary-wing mode, reduces the maximum pitch angle from 20.5\({}^{\circ}\) to 1.1\({}^{\circ}\), by about 94%. In addition, the maximum pitch angle rate is reduced by about 72%. Therefore, it can inhibit the sudden change in pitch angle and pitch angle rate. 2. The soft transition design reduces the height fluctuation from 24 m to 1.1 m, which is a reduction of about 95%, so it has an enhanced effect on height maintenance. 3. The soft transition design reduces throttle usage by approximately 17% and therefore predictably withstands greater uncertainties, reducing the risks of \(\delta_{T}\) saturation. 4. When model uncertainty is excluded, the nominal simulation results of the soft transition design with a 5 s switching mode show little difference compared to the design with 10 s switching mode. Therefore, when UAV modeling is accurate, the soft transition design with 5 s switching mode is relatively ideal. The comparison results in Table 5 show that:  
1. The design of the transition phase with 5 s has passed 100 MC shooting simulations with 20% model uncertainty. However, the design of the 10 s switching mode and the direct switching design have failed in some cases. 2. Under the random seed condition with poor pitch angle and height control in the 5 s switching mode design, good command tracking is obtained for the 10 s switching mode design. Therefore, the design of the transition phase with switching mode can effectively reduce the impact of model uncertainty and improve the robustness of the UAV transition phase, and the longer the duration of the switching mode within a certain limit, the better the flight stability. 3. Under the design of the 10 s switching mode, the occurrence of throttle and rotor speed saturation in a few extreme cases can be avoided. Therefore, extending the switching mode duration within a certain limit can reduce the possibility of extreme cases caused by mode switching, thereby improving the safety of the UAV transition phase. Therefore, considering the uncertainty of the model, the MC shooting simulation results of the soft transition design with 10 s switching mode show greater advantages than those of the \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Direct Switching** & **5 s Switching Mode** & **10 s Switching Mode** \\ \hline \(\theta\) (deg) & \(-\)0.5–20.5 & \(-\)0.2–1.2 & \(-\)0.1–1.1 \\ \(q\) (deg/s) & \(-\)11.6–16.5 & \(-\)1.7–5.3 & \(-\)1.0–4.7 \\ \(\delta_{e}\) (deg) & \(-\)0.1–6.0 & \(-\)0.1–6.9 & \(-\)0.1–7.9 \\ \(\Omega_{pitch}\) & \(-\)0.046–0.007 & \(-\)0.004–0 & \(-\)0.039–0 \\ \(h\) (m) & 100.0–124.0 & 98.9–100.0 & 98.9–100.0 \\ \(v\) (m/s) & 11.42–18.92 & 11.97–18.92 & 11.98–18.92 \\ \(\delta_{T}\) & 0.177–0.700 & 0.294–0.580 & 0.294–0.583 \\ \(\Omega_{base}\) & 0.095–0.443 & 0.095–0.487 & 0.095–0.486 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the ranges of state variables in nominal simulation.