## 3 Performance Analysis
### Transition Corridor  
In a complete mission profile, the conversion mode is the process of conversion between the vertical takeoff and landing mode and the fixed wing mode. At this stage, the gravity and drag of the aircraft need to be overcome by the reasonable distribution of the aerodynamic force and power system. However, when flying at a low speed, the required angle of attack may be too large, resulting in a stall. When flying forward at a high speed, it may cause thrust and drag imbalance. Under so many restrictions, the F-35B vehicle can only convert the vertical takeoff and landing mode and fixed wing mode within a certain speed range. This speed range consists of all feasible tilting paths, namely, the tilting transition corridor. The transition corridor is constructed by AES methods. AES is the equilibrium point set that the aircraft can achieve inside the control efficiency boundaries, which is widely used in the controllable boundary establishment of aircrafts. After setting the constraint conditions, the equilibrium boundary can be acquired by trimming the aircraft in all possible states. The calculation procedure is shown below in Figure 10:  
Figure 9: Track angle analysis diagram: (**a**) velocity stability analysis; (**b**) global flight path angle feasible region; (**c**) comparison of flight path angle feasible region.  
The constraints on the state variables are:  
\[\left\{\begin{array}{l}\dot{\alpha}=0,\dot{q}=0,q=0\\ \alpha_{\min}<\alpha<\alpha_{\max}\\ V_{x}=V_{Tas}\cos\alpha,V_{z}=V_{Tas}\sin\alpha\\ \dot{V}_{x}=0,\dot{V}_{z}=0\\ V_{Tas}=V_{0}\\ \delta_{N}=\delta_{0}\end{array}\right. \tag{15}\]  
where \(\dot{\alpha}\) and \(\dot{q}\) are the derivatives of the angle attack and pitch angular rate versus time, \(\alpha_{\min}\) and \(\alpha_{\max}\) are the boundaries of the angle of attack, \(u_{b}\) and \(w_{b}\) are the velocity components along the body x-axis and z-axis, and \(V_{Tas}\) and \(\delta_{N}\) are the true airspeed and 3 BSD deflection angles.  
Besides, the control input saturation parameters should be given according to the control efficiency, as shown in Table 3:  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Actuators** & **Max Value** \\ \hline \(\delta_{e}\) & \([-35^{\circ},35^{\circ}]\) \\ \(T_{f}\) & \([0,80\text{N}]\) \\ \(T_{N}\) & \([0,80\text{N}]\) \\ \(\delta_{N}\) & \([0,90^{\circ}]\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The limits of the F-35B actuators.  
Figure 10: Conversion corridor establishment logic.  
According to the aforementioned constraint conditions, the aircraft was trimmed in all possible states. For those single failure points, they were replaced by their neighbors. The results whose trimming flight path angles, \(\gamma\), were over 20 degrees were removed for a smooth transition trajectory. Figure 11 presents the transition corridor. It is reasonable that the left boundary is limited by the tilt angle of the 3 BSD nozzle, as the gravity is balanced mainly by the thrust vectors, and the right boundary is limited by the attainable thrust to balance the aerodynamic drag. Having obtained the transition corridor, a straight line was plotted inside the corridor and was chosen as the initial transition trajectory for optimization.