# A Lateral-Directional Control Method for High Aspect Ratio Full-Wing UAV and Flight Tests
## 3 Lateral-Directional Control Law Design  
### Lateral-Directional Attitude Control Law Based on ADRC and NDI  
The lateral-directional attitude of UAVs can be divided into the roll angle and yaw angle. The full-wing drone in this paper has no aileron or rudder, so the yaw control moment can only be generated by the differential propeller thrust. Although the yaw control moment generated by the rudder in the paper [23] achieved roll angle control, the control process was not direct enough, and the response speed was slow. Therefore, this paper draws lessons from [PERSON]'s [24] lateral-directional attitude control law, that is using the differential propeller thrust to control the yaw angle, while the roll angle is not considered in the control process.  
When the roll angle and the roll angle rate are not taken into consideration, Equation (1) can be simplified as:  
\[\begin{cases}\dot{\psi}=q\sin\phi\sec\theta+r\cos\phi\sec\theta\\ \dot{r}=\Gamma_{5}pq-\Gamma_{1}qr+\Gamma_{4}l+\Gamma_{6}n\end{cases} \tag{9}\]  
Obviously, Equation (9) can be divided into a yaw angular rate loop and a yaw angle loop. According to the time scale separation theory, the yaw angle control loop and yaw rate control loop can be designed, respectively. Therefore, ADRC control with a strong disturbance rejection ability and good robustness was adopted in the yaw angle rate loop because it is sensitive to disturbance moment and has no accurate mathematical model, while the yaw angle loop does. Thus, using NDI  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Roll Subsidence Mode**} & \multicolumn{2}{c}{**Dutch Roll Mode**} & \multicolumn{2}{c}{**Spiral Mode**} \\ \hline
**Mode Parameters** & **Characteristic** & **Characteristic** & **Damping Ratio** & **Natural Frequency** & **Characteristic** \\ \hline full-wing & \(-13.34\) & \(-0.26\pm 1.48i\) & \(-0.17\) & \(1.50\) & \(-0.050\) \\ conventional & \(-18.98\) & \(-0.55\pm 3.39i\) & \(0.16\) & \(3.44\) & \(-0.055\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The lateral-directional modes of full-wing and conventional configurations.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Roll Subsidence Mode**} & \multicolumn{2}{c}{**Dutch Roll Mode**} & \multicolumn{2}{c}{**Spiral Mode**} \\ \hline \(C_{Y\beta}\) & **Characteristic** & **Characteristic** & **Damping Ratio** & **Natural Frequency** & **Characteristic** \\ \hline \(-0.1\) & \(-13.32\) & \(0.020\pm 1.48i\) & \(-0.014\) & \(1.48\) & \(-0.050\) \\ \(-0.2\) & \(-13.33\) & \(-0.088\pm 1.49i\) & \(0.059\) & \(1.49\) & \(-0.050\) \\ \(-0.3\) & \(-13.33\) & \(-0.20\pm 1.49i\) & \(0.13\) & \(1.50\) & \(-0.051\) \\ \(-0.4\) & \(-13.34\) & \(-0.26\pm 1.48i\) & \(0.17\) & \(1.50\) & \(-0.051\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The lateral-directional modes of the full-wing drone at different \(C_{Y\beta}\).  
controller not only has a good control ability, but also solves the singularity problem that appears when \(\psi=\pm 180^{\circ}\) and the ADRC controller is used. The control structure is shown in Figure 5.