## 5 Nominal Simulation and Monte Carlo Shooting Simulation  
### Simulation of Direct Switching  
100 m height, 19 m/s cruise speed, and 16 m/s switching speed are selected as simulation environment to realize the process of switching from fixed-wing mode to switching mode, and from switching mode to rotary-wing mode. The process maintains a fixed height, and the pitch angle command is zero to ensure the smallest possible pitch angle. After switching to the rotary-wing mode, it decelerates and prepares for the subsequent hovering landing. The nominal simulation of direct transition was conducted first. Direct transition refers to the process of switching from fixed-wing mode to rotary-wing mode without going through the switching mode (that is, reducing the switching mode duration to 0 s) and keeping the fixed height and airspeed command unchanged. Figure 13 displays the simulation results after entering the rotary-wing mode by direct transition. \begin{table}
\begin{tabular}{c c c} \hline  & **Average Value** & **Trim Results** \\ \hline \(\theta\) (deg) & 1.44 & 0.78 \\ \(q\) (deg/s) & 0.16 & 0 \\ \(\delta_{c}\) (deg) & 4.77 & 4.72 \\ \(h\) (m) & 74.76 & 100.00 \\ \(v\) (m/s) & 19.21 & 19.00 \\ \(\delta_{T}\) & 0.611 & 0.582 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of flight test results and trim results. Figure 12: UAV VtoLA7 flight test records in fixed-wing mode. Here, the commands \(\Omega_{pitch}\), \(\Omega_{heave}\), and \(\delta_{T}\) are dimensionless: 0 means none and 1 means the full speed of the corresponding rotor/front-mounted propeller, which are 0 RPM and 8000 RPM, respectively. Although the direct transition from fixed-wing mode to rotary-wing mode can be achieved under the current control framework, there are large fluctuations in pitch angle and altitude in the subsequent rotary-wing mode. It is preliminarily speculated that adverse situations may occur under the influence of model uncertainty, so Monte Carlo (MC) shooting simulation with model uncertainty is needed. Simple and practical MC shooting simulation is often used to verify the robustness of controllers with model uncertainties. By setting the disturbance range of all model parameters, randomly forming them, and assigning them to the simulation system, it is a direct nonlinear robustness verification method that is suitable for almost all control systems. In order to compare different switching mode designs and prevent a small amount of data from affecting the accuracy of the conclusion in parameter random perturbations, a random number sequence of 100 random numbers is generated, and the subsequent biased simulations use this group of random seeds, which can facilitate the inspection and reproduction of the simulation results, and also compare different transition phase designs under the condition of variable control. The perturbation ranges of all model parameters of the longitudinal channel designed in this manuscript are shown in Table 3.  
The results of 100 times of MC shooting simulations are drawn into images, as shown in Figure 14. For the transition phase without switching mode design, although mode switching is basically realized in the nominal simulation, problems such as pitch angle oscillation and drastic change, loss of altitude maintenance, throttle saturation and rotor speed saturation occurred in all 100 MC target shooting simulations with 20% model uncertainty. Therefore, the transition phase without switching mode may pose a serious threat to flight safety and it is more vulnerable to model uncertainty and shows relatively poor robustness.