# A Lateral-Directional Control Method for High Aspect Ratio Full-Wing UAV and Flight Tests
## 4 Simulations and Flight Tests
### Simulations  
#### 4.1.1 Attitude Control  
Verify the effectiveness, robustness, and anti-disturbance ability of the proposed yaw angle control law based on the nonlinear dynamic inversion and active disturbance rejection control (NDI-ADRC) theory with simulations. Figure 9 is the response curves of the NDI-ADRC yaw angle controller when tracking commands at 8, 11, and 17 m/s. In order to verify the robustness of the controller, the aerodynamic parameters is 30% bigger than the original ones, while the control efficiency of the differential propeller thrust is 20% smaller during the simulations. At the same time, in order to test  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Parameters** & \(K_{\psi}\) & \(r_{cmax}\) & \(\beta_{1}\) & \(\beta_{2}\) & \(\sigma\) & \(\delta\) & \(K_{r}\) & \(\Delta\delta_{pmax}\)  
the wind resistance ability of the controller, when \(t=100\) s, add a cross discrete gust wind in the simulations. The gust amplitude and length are 3 m/s and 50 m. Figure 10 is the response curves of the NDI-ADRC controller when tracking the command under the condition of an 11-m/s speed and disturbed by yaw moment \(n=1.2\) sign \(\left(\sin\left(\frac{\pi}{4}t\right)\right)N\cdot m\). Comparing the control effects, the PID controller has the same gain parameters as the NDI-ADRC controller.  
Figure 9a shows that even if the aerodynamic parameters and the control efficiency of the differential propeller thrust are changed, the NDI-ADRC yaw angler controller can still track command signals effectively at different flying speeds. The tracking process is smooth and without overshoot. The rise time is about 5 s when tracking a 90\({}^{\circ}\) step signal in the time range of 45-50 s. Figure 9b shows the sideslip angle \(\beta<\pm 8^{\circ}\) during the simulation. As shown in Figure 9c, the output time of the differential propeller thrust is very shot, and there is no output in most cases. From Figure 9a,b, we can learn that the gust will influence the sideslip angle \(\beta\). According to Table 1, we can see \(\left|C_{l\beta}\right|\gg\left|C_{n\beta}\right|\), so the cross gust wind mainly affects the roll angle, not the yaw angle.  
As shown in Figure 10a, the average tracking error and error amplitude of the NDI-ADRC controller are 0.37\({}^{\circ}\) and 1.00\({}^{\circ}\) during 10-40 s, while those of PID controller are 2.30\({}^{\circ}\) and 2.92\({}^{\circ}\). Obviously, the NDI-ADRC controller has a much better anti-disturbance ability than the PID controller, which is mainly because ESO has a very effective observation of the disturbance in Figure 10d. Although the disturbance moment of 1.2 N is very large for such a small aircraft, the differential propeller thrust is still not saturated, which shows that the control efficiency of the differential propeller thrust is very high in flight.  
Figure 9: The yaw angle (**a**), side-slip angle (**b**), differential propeller thrust (**c**) and observer (**d**) curves of the nonlinear dynamic inversion and active disturbance rejection control (NDI-ADRC) yaw angle controller when tracking the command at different speeds.