# Design of a Hand-Launched Solar-Powered Unmanned Aerial Vehicle (UAV) System for Plateau
## 4 UAV Flight Control
### Analysis of Stability and Flight Quality  
By using Taylor expansion, the nonlinear dynamics model is linearized and the lateral-directional small-disturbance equations are obtained as Formula (21).  
\[\dot{x}=Ax+Bu \tag{21}\]  
where state vector \(x=\left[\begin{array}{cccc}\beta&p&r&\varphi&\psi\end{array}\right]^{T}\), state matrix \(A\) is shown in Formula (22), and \(B\) is control matrix, control input \(u=[\delta_{r}]^{T}\).  
\[A=\left[\begin{array}{cccc}Y_{\beta}&\alpha*+Y_{P}&Y_{r}-1&g\cos\theta*/V*&0 \\ L_{\beta}&L_{p}&L_{r}&0&0\\ N_{\beta}&N_{p}&N_{r}&0&0\\ 0&1&\tan\theta*&0&0\\ 0&0&\sec\theta*&0&0\end{array}\right] \tag{22}\]where \(\alpha*\) and \(V*\) represent angle of attack and speed of UAV at trim point. The characteristic roots of lateral-directional state matrix represent the flight quality of UAV lateral-directional mode.  
The design mission environment of MP Solar UAV was for 4500-m elevation above plateau. Therefore, the aileron-free UAV still needs to have a good flight performance in high altitude. The change of the UAV's system characteristic roots with speed increase at an altitude of 500 m and 5000 m, respectively, are shown in Figure 11. The speed range was 8-12 m/s.  
Figure 11: The change of system characteristic roots with different altitude and speed in lateral-directional mode. (**a**) Spiral mode. (**b**) Roll mode. (**c**) Dutch roll mode.  
It can be seen from Figure 11a,b that, when flying at high altitude, the characteristic root of roll mode and spiral mode moved to the right of the complex plane compared with that at low altitude, and the flight quality became worse.  
The move of characteristic roots of the Dutch roll mode (Figure 11c) in real axis had no obvious directionality, but the characteristic roots dispersion was larger than that of low-altitude flight, which means that the stability of the Dutch roll mode was more sensitive to the flight speed at high altitude. At the same altitude, with the increase of flight speed, the characteristic roots of lateral-directional mode all moved to the left of the complex plane, and the flight quality became better.  
The Cooper-Harper rating is a systematic method of quantifying the results of an experiment, which is divided into three grades to describe the flight quality of an aircraft [18]. Among them, the level-one flight quality represents the flight quality to ensure the successful completion of all flight missions. At an altitude of 500 m, both the roll mode and the Dutch roll mode were of level-one flight quality in the full speed range. However, when the speed was lower than 9 m/s, the characteristic root of spiral mode was positive and the doubling time was 23 s. In other words, although the spiral mode diverged at a low speed, it still met the level-one flight quality requirements.  
At an altitude of 5000 m, the maximum rolling constant of convergence time was 0.13. With the change of flight speed, the frequency of Dutch rolling mode almost remained unchanged, about 2.32, and the minimum damping was about 0.149. That is, both the rolling mode and Dutch rolling mode (Figure 11b,c) met the level-one quality within the full speed range of 5000 m. At the cruise speed of 10 m/s, the half-value period was 25.7 s, and the spiral mode met the level-one flight quality requirements. However, when the flight speed was lower than 9 m/s, the spiral mode no longer met the level-one flight quality, and continued to deteriorate with the flight speed decrease. Therefore, high-altitude flight needs to avoid flying at too low a speed to prevent deterioration of flight quality.