## 4 Simulation and Discussion
### Multimodal Switching Simulation Analysis  
Numerical simulations were executed to validate the efficiency of the linear/nonlinear active disturbance rejection switching control method. Table 4 lists the initial flight condition at the initial simulation. Here, 20% parameter uncertainties were considered, that is, \(\Delta_{i}=i_{0}\cdot 20\%\cdot\sin(\omega t)\), \(i=m,s,\overline{c}\), \(c_{e}\), \(I_{yy}\), \(C_{L}^{a}\), \(C_{L}^{0}\), \(C_{D}^{a,2}\), \(C_{D}^{a}\), \(C_{D}^{0}\), \(C_{T}^{0}\), \(C_{M}^{\dagger}\), \(C_{M}^{\dagger,\alpha^{2}}\), \(C_{M}^{\alpha,\alpha}\), \(C_{M}^{\dagger,\alpha}\), \(C_{M}^{\dagger,\beta}\). The external disturbance was set as \(d_{V}(t)=d_{h}(t)=0.5\cdot\sin(0.4t)\). Case 1: Validate the effectiveness and disturbance rejection capability of the independent LADRC and NLADRC. In this case, considering aircraft cruise status, the reference trajectories of velocity and altitude were set as step signals of \(V_{ref}=50(\mathrm{m/s})\) and \(h_{ref}=50(\mathrm{m})\). When the simulation time was \(t=50(\mathrm{s})\), both parameter uncertainties and external disturbances were added. The simulation results are given in Figures 7-9. Figure 7 presents the tracking performance of velocity and altitude. It can be seen that the whole closed-loop system was stable by the action of LADRC or NLADRC. Compared with NLADRC, LADRC had the following advantages: a faster response speed, a shorter adjustment time, and a smoother transient response without overshoot. Figure 8 presents the virtual control laws and the actual control laws of the velocity and altitude subsystems. It can be seen that every step virtual control values could quickly converge to zero, the actual control values changed with the change in the parameter uncertainty and external disturbance, and dynamic compensation was realized for system uncertainty and external disturbance. Figure 9 presents the estimation errors of the total disturbance. It can be seen that the estimation error of NLADRC was less than that of LADRC, but NLADRC generated high-frequency oscillation, which was within the rational bounds of the estimation performance. From the above analysis, it can be seen that both LADRC and NLADRC could quickly make the system stable. When an additional 20% parameter uncertainty and external disturbance were added, the system state was almost unaffected, which indicates that both LADRC and NLADRC can achieve stable flight control of NMVs and have strong disturbance rejection capability. Figure 8: (**a**) Virtual control law and actual control law of the velocity subsystem. (**b**) Virtual control law and actual control law of the altitude subsystem. Figure 9: (**a**) Disturbance estimation errors of the velocity subsystem. (**b**) Disturbance estimation errors of the altitude subsystem. Case 2: Validate the effectiveness of LADRC/NLADRC switching control based on the type-2 fuzzy logic system. In this case, the reference trajectories of velocity and altitude were set as subsection function. When \(t_{1}=t\in[0,25)\) and \(t_{3}=t\in[50,75)\), the reference trajectories were set as ascent status. When \(t_{2}=t\in[25,50)\) and \(t_{4}=t\in[75,100]\), the reference trajectories were set as cruise status. From \(t_{1}\) to \(t_{2}\) then to \(t_{3}\), the NMV mode changed from ascent to cruise then to ascent, and the winglet states changed from stretch out states to draw back states then to stretch out states. From \(t_{2}\) to \(t_{3}\) then to \(t_{4}\), the NMV mode changed from cruise to ascent then to cruise, and the winglet states changed from draw back states to stretch out states then to draw back states. The parameters are given in Table 5. The simulation results are given in Figures 10-13. In these images, \"SMC switching\" represents the algorithm proposed in [28]. Figure 10 presents the tracking performance of velocity and altitude for NMVs based on the multimodal switching control. It can be seen that the proposed control method could realize stable flight control for NMVs during modal switching.