## 5 Simulation Results
### Scenario 2: Simulation of Controller for AHV  
In this subsection, the AHV is flying in the cruise phase, and the initial parameters of the AHV are set as \(V_{0}=4590\) m/s, \(h_{0}=33528\) m, \(\gamma=0^{\char 60}\), \(\alpha=2.745^{\char 60}\), and \(q=0^{\char 60}\)/s, and the model parameters of the AHV are given in Table 2.  
The simulation command signals are set as follows: \(h_{c}(t)=h_{0}+\Delta h(t)\), \(V_{c}(t)=V_{0}+\Delta V(t)\); \(\Delta h(t)\) and \(\Delta V(t)\) are generated by the filter of the input step, the setting of which is as follows:  
\[\frac{\Delta h(s)}{h_{step}(s)}=\frac{0.15^{5}}{(s+0.15)^{5}},\frac{\Delta V(s) }{V_{step}(s)}=\frac{0.3^{4}}{(s+0.3)^{4}}\]  
where the altitude step signal is set as \(h_{\text{step}}=100\) m, and the velocity step signal is set as \(V_{\text{step}}=100\) m/s. In control input \(\mathbf{u}= \begin{bmatrix}\beta_{c}&\delta_{c}\end{bmatrix} ^{T}\), the marginal value of \(\beta_{c}\) is 0\(\rightarrow\)2, and the marginal value of \(\delta_{c}\) is \(\pm\)20. To verify the performance of the method proposed in this paper, we consider two kinds of uncertainties:  
(1) Mismatched uncertainties are set as 20%, which are represented as follows:  
\[|\Delta_{i}|=0.2\sin(0.02\pi t),\text{ where }i=m,I_{yy},\rho,s,\,\bar{c},c_{e},C _{L},C_{D},C_{T},C_{M}^{\mathbf{s}},C_{M}^{\mathbf{d}},C_{M}^{\mathbf{\delta}_{c}}\]  
(2) Uncertain parameters of control input, set as follows:  
\[\beta_{c}=\beta_{c0}+0.25,\,\,\delta_{c}=\delta_{c0}+10^{\circ}\]  
In the simulation, the controller is adopted as Equation (76) and the adaptive laws are developed as Equation (77); the parameters of the controller are presented in Table 3.  
In order to verify the efficiency of the method proposed in this paper, two control schemes are provided for the following comparison: sliding mode control using traditional double power reaching law (SMC); backstepping sliding mode control using traditional double power reaching law (BSMC). The simulation results of the AHV are shown in Figures 4-11.  
respectively Therefore, it can be seen that, compared with SMC and BSMC, the altitude tracking error and velocity tracking error of the proposed method in this paper is the smallest, and the proposed method can track stably. Figures 8 and 9 show the responses of attack angle and pitch angle rate, respectively, and the responses under the proposed method are smooth and within a reasonable range. Figures 10 and 11 are the control input responses for the AHV. It can be seen that responses of the throttle setting change smoothly in Figure 10, and \(\beta_{c}\), under three controllers, fluctuates within the margin range. In Figure 11, in the initial stage of simulation, the responses of the elevator deflection under the method proposed vary slightly, and are within the acceptable range; in the process of altitude climbing, the fluctuation of the elevator deflection is suboptimal, but within the acceptable range. Figure 4: Responses of velocity tracking. Figure 5: Tracking errors of velocity. Figure 8: Responses of attack angle. Figure 6: Responses of altitude tracking. Figure 7: Tracking errors of altitude. Figure 11: Responses of elevator deflection. Figure 9: Responses of pitch angle rate. According to the simulation results above, the following conclusions can be drawn:  
1. The proposed method in this paper shows better tracking performance than SMC and BSMC. Firstly, the tracking error of altitude and velocity under the proposed method in this paper is smaller than that for SMC or BSMC. Secondly, the responses of the flight path angle, attack angle, and pitch angle rate under the proposed method in this paper change smoothly and steadily. Thirdly, the control input change under the proposed method is smooth and within the acceptable range. Therefore, the proposed method achieves better flight performance than BSMC and SMC. 2. The method proposed in this paper can effectively attenuate the influence of uncertainties surrounding AHVs.