## 3 Experimental Flight and System Identification
### Dynamic Model Analysis and Verification
Using the current flight data and dynamic model structure, it was not easy to obtain dynamic model parameters with high fit percentage, even using the black box model approach where there were no parameter restrictions. Moreover, it was found that the parameters obtained were a little sensitive to the datasets used for system identification. The possible reasons for this were: (1) velocities along x- and z-axes were not measured, which degraded the accuracy of the related parameters, \(X_{u}\), \(X_{u}\), \(X_{q}\), \(Z_{u}\), \(Z_{w}\), and \(Z_{q}\); (2) high-frequency noise also contributed to accuracy degradation; and (3) there were nonlinear coupling dynamic terms not included in the model. It has been reported that accuracy can be improved if velocities along the x- and z-axes are available and nonlinear coupling terms are included [77]. Although all dynamic model candidates showed similar fit percentages, GRAD1 was chosen for analysis and evaluation since it had the highest fit percentage. Identified  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multirow{2}{*}{**CFD (Initial)**} & \multicolumn{6}{c}{**Identified Dynamic Model**} \\ \cline{2-9}  & & **GRA 1** & **LM 1** & **GRAD 1** & **GRA 2** & **LM 2** & **GRAD 2** & **Average** \\ \hline \(X_{u}/m\) & \(-1.351\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) \\ \hline \(Z_{u}/m\) & \(0.060\) & \(0.001\) & \(0.  
parameters were evaluated in the basic form of the dynamic model [34], where filters and servo dynamics were not included. The basic dynamic model is described as follows:  
\[\dot{x}_{basic}=A_{basic}\;x_{basic}+B_{basic}\;u_{basic}, \tag{12}\]  
\[y_{basic}=C_{basic}\;x_{basic}, \tag{13}\]  
\[x_{basic}=\left[ \begin{array}{c}u\\ w\\ q\\ \end{array} \right], \tag{14}\]  
\[A_{basic}=\left[ \begin{array}{ccc}\frac{X_{x}}{m}&\frac{X_{x}}{m}&\frac{X_ {q}}{m}&g\\ \frac{Z_{y}}{m}&\frac{Z_{y}}{m}&\frac{Z_{q}}{m}&0\\ \frac{M_{x}}{l_{yy}}&\frac{M_{y}}{l_{yy}}&\frac{M_{q}}{l_{yy}}&0\\ 0&0&1&0\\ \end{array} \right], \tag{15}\]  
\[B_{basic}=\left[ \begin{array}{c}\frac{X_{xp}}{m}\\ \frac{Z_{xp}}{m}\\ \frac{M_{xp}^{2}}{l_{yy}}\\ 0\\ \end{array} \right], \tag{16}\]  
and \(C_{basic}\) was set as \(\left[ \begin{array}{ccc}0&0&0&1\\ \end{array} \right]\) to describe the pitch angle measurement. Figure 7 shows the open-loop frequency responses and a Nyquist diagram of the GRAD1 and CFD dynamic models. When the frequency was under 0.01 rad/s, the low-frequency gain of the identified GRAD1 dynamic model was similar to that of the CFD dynamic model. As the frequency increased to higher than 0.3 rad/s, the gain of the GRAD1 dynamic model was smaller than that of the CFD dynamic model. Moreover, at mid-frequency, the GRAD1 dynamic model had a local minimum point. As the frequency further increased to higher than 5 rad/s, both dynamic models had similar characteristics. Poles of the GRAD1 were (2.86 \(\pm\) 8.46i, \(-\)9.35, \(-\)1.64), while those of the CFD model were (3.69 \(\pm\) 7.58i, \(-\)9.22, \(-\)0.76). The unstable pole locations did not move much. However, the magnitude of the stable dominant pole of the GRAD1 dynamic model was larger than that of the CFD dynamic model. Thus, it is expected that response of the GRAD1 dynamic model is faster than that of the CFD dynamic model. Both basic dynamic models encircle the (\(-\)1, 0) point two times in the Nyquist diagram, meaning that if the loop is closed, the two systems will be stable. However, Figure 7b shows that both models have very small phase margins, with less than 8 degrees. The simulation was used to analyze and compare extended dynamic models as shown in Figure 8. Gain and phase margins of the GRAD1 dynamic model were 17.2 dB and 39.0\({}^{\circ}\), respectively, while the gain and phase margins of the CFD dynamic model were 16.5 dB and 30.3\({}^{\circ}\), respectively. In the Nyquist diagram, both extended dynamic models encircled the (\(-\)1, 0) point two times.