## 5 Stability Analysis and Augmentation Adjustment of UAV
### Influence Analysis of Dynamic Stability
#### 5.3.2 Lateral/Directional Stability Augmentation Design  
The aileron actuator, sweep angle actuator, and rudder actuator are all regarded as simple hysteresis elements, and the transition frequency is 30. The bending modal filter is ignored. Because the positive control surface deflection produces a negative torque, an inverter is added to the output matrix of the control surface actuator. At the same time, considering that the asymmetric change in sweep angle can be used as an additional input for the lateral/directional maneuvering control, the rudder, aileron, and sweep angle are combined into a three-input and two-output system, which is connected in series with the controlled system. \[\mathbf{a}_{a}=\left[ \begin{array}{ccc}-30&0&0\\ 0&-30&0\\ 0&0&-30\end{array} \right],\ \mathbf{b}_{a}=\left[ \begin{array}{ccc}30&0&0\\ 0&30&0\\ 0&0&30\end{array} \right],\ \mathbf{c}_{a}=\left[ \begin{array}{ccc}-1&0&0\\ 0&-1&0\\ 0&0&-1\end{array} \right],\ \mathbf{d}_{a}=\left[ \begin{array}{ccc}0&0&0\\ 0&0&0\\ 0&0&0\end{array} \right] \tag{15}\]  
The washout filter is combined into the three-input and four-output models, which are directly connected to the first pair of inputs and outputs, which are as follows:  
\[\mathbf{a}_{w}=[-1/\tau_{w}],\ \mathbf{b}_{w}=\left[ \begin{array}{cc}0&1/\tau_{w} \end{array} \right],\ \mathbf{c}_{w}=\left[ \begin{array}{cc}0\\ -1\end{array} \right],\ \mathbf{d}_{w}=\left[ \begin{array}{cc}1&0\\ 0&1\end{array} \right] \tag{16}\]  
where the time constant of the external washing filter is a compromised value. If the time constant is too large, the yaw damper impedes turn entry [38]. In this research, the time  
Figure 14: The short-period damping ratio \(\xi\) and oscillation frequency \(\omega_{n}\) of the UAV system after stability augmentation adjustment when Ma = 0.5. (**a**) Damping ratio \(\xi\), (**b**) oscillation frequency \(\omega_{n}\). Figure 13: The short-period damping ratio \(\xi\) and oscillation frequency \(\omega_{n}\) of the UAV system after stability augmentation adjustment when Ma = 0.3. (**a**) Damping ratio \(\xi\), (**b**) oscillation frequency \(\omega_{n}\). constant \(\tau_{w}=1.05\) s, and the closed-loop feedback gains of the roll rate and yaw rate loop are \(K_{p}=0.2\) and \(K_{r}=1.6\), respectively. Figures 15 and 16 show the damping ratio \(\xi\) and the oscillation frequency \(\omega_{n}\) of the Dutch roll modal of the pre-selected model, after the stability augmentation adjustment, with \(\Lambda_{\text{out}}\) corresponding to the configurations at different Mach numbers. In general, the value of \(\xi\) increases first and then decreases with an increase in \(\Lambda_{\text{out}}\). When the flight speed is low and \(\Lambda_{\text{out}}\), corresponding to the configurations, is small, the Dutch roll damping ratio \(\xi\) increases, and the oscillation frequency \(\omega_{n}\) increases first and then decreases monotonically with the wingspan proportion of the inner section. When \(\Lambda_{\text{out}}\), corresponding to the configurations, is large, the wingspan proportion of the inner section is greater, and the Dutch roll \(\xi\) and \(\omega_{n}\) are smaller. At higher flight speeds, the Dutch roll \(\xi\) decreases with an increase in the wingspan proportion of the inner section. When the wingspan proportion of the inner section is relatively large, and the \(\Lambda_{\text{out}}\) corresponding to the configurations is relatively small, the configuration change has little effect on \(\xi\) of the Dutch roll modal. When the \(\Lambda_{\text{out}}\) corresponding to the configurations is small, \(\omega_{n}\) shows a monotonically changing rule of first increasing and then decreasing with the wingspan proportion of the inner section. When \(\Lambda_{\text{out}}\), corresponding to the configurations, is large, \(\omega_{n}\) gradually increases with the wingspan proportion of the inner section.