# Short Landing for Flying-Wing Unmanned Aircraft with Thrust Vector
## 6 Simulation Verification and Discussion
### Flight Boundary Protection with the Additional Angle-of-Attack Command  
The findings from the short-landing performance study in Section 3 indicate that setting the angle-of-attack command at 6 degrees can achieve good results. However, when certain parameters are perturbed, such as lift coefficient, mass properties, and lift fan force, the sink rate may become uncontrollable. In the first scenario, if the lift coefficient is less than the estimated value or the UAV's weight exceeds the pre-calculated value, the nominal reference angle of attack may not generate enough lift force to maintain the sink-rate command. This is demonstrated in Case 2 in Figure 23a, where the UAV cannot sustain its sink rate and falls to the ground before reaching the target point. In the second scenario, if the lift coefficient is greater than the CFD calculation results, the UAV moves up and down in response to the velocity command, as observed in Case 1. Both of these scenarios should be avoided to ensure short-landing precision and safety.  
Figure 23: Simulation and analysis for the angle-of-attack control: (**a**) fixed angle-of-attack command simulation results, with Case 1 as \(-20\%\) perturbation of the nominal lift coefficient and Case 2 as \(+20\%\) perturbation of the nominal lift coefficient; and (**b**) trim results for different angles of attack and sink rates (at 80 percent of lift fan’s maximum rotation speed).  
Figure 22: Nominal simulation results of short landing: (**a**) AGL (Above Ground Level)response, (**b**) angle-of-attack response, (**c**) velocity response, (**d**) roll-angle response, (**e**) sink-rate response, (**f**) roll-angular-rate response, (**g**) pitch-angle response, (**h**) side-slip-angle response, (**i**) pitch-angle-rate response, (**j**) Yaw-angle-rate response, (**k**) actuator response, (**l**) nozzle-pitch-angle response, (**m**) lift-fan-rotation-speed response, and (**n**) throttle response.  
During short landing, the throttle is used to compensate for the aerodynamic lift force, while a portion of the lift fan's control power is used to balance the pitch moment produced by the vectored thrust. In order to ensure that there is enough pitch controllable margin to meet the extra pitch control moment requirement, 20% of the lift fan's control power is allocated to pitch angular rate control. The trim results, using 80% of the lift fan's control power, are presented in Figure 23b.  
To prevent the throttle command value from exceeding the lift fan's trim boundary, an additional angle-of-attack command is calculated and added to the baseline value. This additional command can be expressed as follows:  
\[\Delta\alpha_{c}(t)=\min\biggl{(}\max\biggl{(}\frac{(\delta_{vTc}-\delta_{vTs })T_{vmax}\sin\delta_{vq}}{Z_{a}mV},-\Delta\alpha_{c}(t-\Delta T)\biggr{)}, \alpha_{cmax}-\alpha_{c}(t)\biggr{)} \tag{57}\]  
where \(\Delta\alpha_{c}(t)\) and \(\Delta\alpha_{c}(t-\Delta T)\) are the current and previous additional angle-of-attack command values, respectively; \(\alpha_{c\text{ max}}\) is the maximum angle of attack command value, which is set at 10 degrees; and \(\delta_{vTs}\) is the threshold of the throttle, which is set to 0.6 based on the trim results in Figure 23b. In Stage III, the current angle-of-attack value is used to determine the angle-of-attack command value, and the additional angle-of-attack command value is added to compensate for the perturbations in lift coefficient, mass properties, and lift fan force, ensuring precise and safe short landings:  
\[\alpha_{c}(t)=\alpha(t)+\Delta\alpha_{c}(t) \tag{58}\]