## 5 Numerical Simulation  
In this section, to illustrate the effectiveness of the proposed control scheme, a comparison simulation was carried out. The geometric characteristics, aerodynamic coefficients and other model parameters of the saucer-shaped UAV are given in Table 2. The aerodynamic configuration design philosophy is derived from Ref. [42], especially, since it investigated a sweepback fin-shaped winglet to efficiently reduce the induced drag caused by the low-aspect-ratio configuration. This design is also adopted in the current version of saucer-shaped UAV to improve the aircraft aerodynamic efficiency. In order to give a more intuitive presentation on the aerodynamic characteristics of the saucer-shaped UAV, we made a comparison of the saucer-shaped UAV with a somewhat similar BWB aircraft illustrated in [43]. The typical aerodynamic coefficients of the vehicle in [43] are outlined as \(C_{La}=5.486\), \(C_{ma}=-0.1036\) and \(C_{mq}=-0.7001\). The saucer-shaped UAV has a smaller lift curve slope \(C_{La}\) as it has larger sweepback and the S-shaped airfoil with a low-aspect-ratio configuration. The pitching moment coefficient \(C_{ma}\) of the two aircrafts are negative as both of them have longitudinal static stability, while the aerodynamic centre of the saucer-shaped UAV is located further forward. The absolute value of pitch-damping coefficient of the saucer-shaped UAV, \(\big{|}C_{mq}\big{|}\), is less than that of the BWB aircraft in [43], which leads to a smaller damping ratio in the short-period mode. The main task is to steer the vehicle to track the prescribed altitude reference. To be specific, the initial flight condition was assumed as \(h_{0}=350m\), \(\mu_{0}=0 deg\), \(\alpha_{0}=3.41 deg\) and \(q_{0}=0 deg/s\), and the command reference starts at the initial altitude and ends at the altitude of \(450m\). Besides, the command \(h_{d}\) was smoothened through a filter described as \(0.02/\big{(}s^{2}+0.3s+0.02\big{)}\). To confirm the superiority and effectiveness of the proposed ESO, \(15\%\) of uncertainties of aerodynamic coefficients were introduced to the actual vehicle model. The disturbances imposed on the flight path angle \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Mass \(m\)(kg) & \(13\) & \(C_{L0}\) & \(0.0752\) \\ Reference area \(S\)(m\({}^{2}\)) & \(2.097\) & \(C_{La}\) & \(0.03865\) \\ Chord \(c_{A}\)(m) & \(0.97991\) & \(C_{m0}\) & \(-0.0181\) \\ Air density \(\rho_{h}\)(kg/m\({}^{3}\)) & \(1.225064\) & \(C_{ma}\) & \(-0.0261\) \\ Inertial moment \(I_{y}\)(kgm\({}^{2}\)) & \(1.79715\) & \(C_{mq}\) & \(-0.04\) \\ Gravitational acceleration \(g\)(m/s\({}^{2}\)) & \(9.8\) & \(C_{mke}\) & \(-0.18\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the saucer-shaped unmanned aerial vehicle. rate loop are taken as \(0.5\sin(0.3t)+2.5e^{-0.2t}\sin(1.2t)\) and \(2\sin(0.4t)+12e^{-0.09t}\sin(0.8t)\), respectively, which includes the un-modelled coupling effects and external disturbances. Moreover, to further illustrate the robustness of the proposed scheme, an abrupt disturbance of additional constant moment is introduced at the instant \(t=60\)s, with the value \(10N\cdot m\) and duration \(\Delta t=0.5\)s.  
The design parameters for the finite-time-convergent second-order differentiator were chosen as \(\varepsilon_{b}=1\), \(\beta=1/3\) and \(\varepsilon=0.006\). According to the design principle of the ESO in Section 3.2 and the analysis in Remark 4, the corresponding parameters were set as \(w_{1\mu}=4\), \(w_{2\mu}=8\), \(w_{3\mu}=2\), \(\varepsilon_{1\mu}=0.5\) and \(\varepsilon_{2\mu}=0.05\) for the ESO in the \(\mu\) loop and \(w_{1q}=1.5\), \(w_{2q}=10\), \(w_{3q}=0.5\), \(\varepsilon_{1q}=0.1\) and \(\varepsilon_{2q}=0.02\) for the ESO in the \(q\) loop.