## 4 Simulation and Discussion
### Multimodal Switching Simulation Analysis
Whether from ascent mode to cruise mode (winglet from stretch out to draw back) or cruise mode to ascent mode (winglet from draw back to stretch out), the designed control strategy could achieve stable and smooth switching control for NMV. Furthermore, the ranges of oscillation amplitude generated by the switching method proposed in [28] were \(\Delta V\approx[10,20]\) and \(\Delta h\approx[5,15]\), and the switching transition time intervals were \(t_{V}\approx[8,15]\) and \(t_{h}\approx[4,8]\). Compared with the method proposed in [28], the ranges of oscillation amplitude generated by the switching method proposed in this paper were \(\Delta V\approx[1,5]\) and \(\Delta h\approx[1,3]\), and the switching transition time intervals were \(t_{V}\approx[1,3]\) and \(t_{h}\approx[1,3]\). Obviously, the switching method based on the type-2 fuzzy logic system had smaller oscillation amplitude, shorter transition time, and stronger disturbance rejection ability. Figures 11 and 12 present the actuator response and the change rules of the output weight of the type-2 fuzzy controller, respectively. It can be seen from Figure 11 that the switching method proposed in [28] generated a large number of high frequency oscillations. Compared to the method proposed in [28], the switching method proposed in this paper had smaller oscillation amplitude and smoother response curve. It can be seen from Figure 12 that NLADRC and LADRC were used in the ascent phase and cruise phase,  
Figure 12: (**a**) The output weight of the type-2 fuzzy controller of the velocity subsystem. (**b**) The output weight of the type-2 fuzzy controller of the altitude subsystem. Figure 13: (**a**) The angle of attack. (**b**) The flight path angle. respectively. Because there are always state errors and disturbance estimation errors in the whole switching process, the weight value cannot be taken as 0 or 1, but it still reflects the switching process of the controller. Figure 13 presents the responses of the angle of attack and the flight path angle. It can be seen that the switching method proposed in [28] caused a wide range of sudden changes for the attitude angle, which could easily lead to instability in the switching process. Compared to the method proposed in [28], the switching method proposed in this paper had smaller oscillation amplitude and smoother response curve, which can ensure stability in the switching process. The above simulation analysis shows that the LADRC/NLADRC control method can realize stable tracking control for NMVs with a wide range of uncertain parameters and has strong disturbance rejection capability. Furthermore, the LADRC/NLADRC switching control method based on the type-2 fuzzy logic system can realize stable and smooth switching control for NMV multimodal switching. The proposed method has the advantages of small oscillation amplitude, shorter transition time, and stronger disturbance rejection capability. Case 3: Validate the effectiveness of LADRC/NLADRC switching control during the transition from supersonic flight states to hypersonic flight states for NMVs. In this case, the reference trajectories of velocity and altitude were set as the following subsection function:  
\[\left\{ \begin{array}{l}V=10t+590,t<120\\ V=1790,t\geq 120\\ h=50t+3528,t<120\\ h=9528,t\geq 120\\ \end{array} \right. \tag{41}\]  
When \(t\in[0,120)\), the winglet set as the stretch out states, the reference area \(s=389(\text{m}^{2})\) and the mean aerodynamic chord \(\overline{c}=30(\text{m})\), the aerodynamic parameters were given as \(\text{C}_{i,sc}\). When \(t\in[120,180]\), the winglet set as the draw back states, the reference area \(s=369(\text{m}^{2})\) and the mean aerodynamic chord \(\overline{c}=28(\text{m})\), the aerodynamic parameters were given as \(\text{C}_{i,sh}\). When \(t\in[120,130)\), the aerodynamic parameters were given as \(x(t)=x_{1}(t)e^{(-\lambda(t-120))}+x_{2}(t)(1-e^{(-\lambda(t-120))})\). The simulation results are given in Figures 14-18. In these images, \"SMC switching\" represents the algorithm proposed in [28].