## 4 Numerical Demonstrations
And \(T_{s}\) is given as 8 s. The aerodynamic uncertainty is set as \(\pm 20\%\), and the strong disturbances of AOA channel and pitch rate channel are given as  
\[d_{\alpha}=\sin(t)  
**Scenario 3.** To demonstrate the advantage of fixed-time convergence of the proposed controller independent of initial conditions, four cases with different initial conditions are considered as shown in Table 3. \(T_{s}\) is set as 8 s, the aerodynamic uncertainty is set as \(\pm 40\%\), and the strong disturbances of the AOA channel and pitch rate channel are given as Equations (64) and (65).  
Figure 8: Elevator deflection in Scenario 2.  
Figure 10: \(d_{\omega_{z}}\) and its estimation in Scenario 2.  
Figure 9: \(d_{\alpha_{x}}\) and its estimation in Scenario 2.  
As shown in Figures 11 and 12, the AOA tracking errors will converge to a neighborhood of origin in a short time under different initial conditions in the presence of disturbances and uncertainty, and this verifies the fixed-time convergence of the proposed controller. Figure 13 shows the elevator deflection under different cases; the elevator deflections are smooth and change slowly due to the AOA command apart from the initial short chattering. As shown in Figures 14 and 15, the disturbance estimation errors of the proposed disturbance observer can converge to the neighborhood of the origin instantaneously.  
**Scenario 4.** For the HMW, the symmetrical wing morphing has a significant impact on the flight state of the aircraft. Therefore, it is necessary to verify the controller's ability to guarantee flight stability at different morphing speeds. Therefore, four cases with different morphing speeds are chosen as shown in Table 4. The aerodynamic uncertainty is set as \(\pm 40\%\), and the strong disturbances are the same as those in Scenario 3.  
Figure 14: Estimation errors of \(d_{a}\) in Scenario 3.  
Figure 13: Elevator deflection in Scenario 3.  
Figure 15: Estimation errors of \(d_{a_{x}}\) in Scenario 3.  
The additional forces and moments caused by wing morphing are shown in Figure 16; it is obvious that the morphing will result in significant additional forces and moments, which will change with the aircraft's attitude.  
As shown in Figures 17 and 18, the AOA can track the command accurately, and the AOA tracking errors will converge to a neighborhood of origin under different morphing speeds in the presence of disturbances and uncertainties; this indicates that the proposed controller has good adaptability in response to different morphing speeds. The elevator deflection is smooth and changes slowly, as shown in Figure 19. As shown in Figures 20 and 21, the disturbance estimation errors of the proposed disturbance observer can converge to the neighborhood of the origin in a short time. In summary, for the proposed controller, symmetrical morphing speed has little influence on the attitude control of the HMW.  
Figure 19: Elevator deflection in Scenario 4.  
Figure 20: Estimation errors of \(d_{a}\) in Scenario 4.  
Figure 18: Angle of attack tracking errors in Scenario 4.  
**Scenario 5.** In the HMW flight process accompanied by high dynamics, the actuators often face harsh environments, which in turn lead to the dangerous situation of different wing extension lengths on both sides, jeopardizing the HMW flight stability. This scenario focuses on the dangerous situation of asymmetric morphing of wings. In this scenario, in order to check the adaptive capability of the proposed controller in response to dangerous situations of asymmetric wing morphing, the reference angle of attack command is tracked based on the proposed controller in the presence of strong external disturbances and uncertainties. Therefore, four cases with different asymmetry morphing are chosen, as shown in Table 5. The aerodynamic uncertainty is set as \(\pm\)40%, and the strong disturbances of the AOA channel and pitch rate channel are given as Equations (64) and (65). The asymmetry morphing rate is defined as  
\[\chi_{1}=L_{w2}/L_{w1} \tag{66}\]  
where \(L_{w1}\) and \(L_{w2}\) denote the wing span of the left wing and the right wing, respectively.