## 3 Experimental Flight and System Identification
### Dynamic Model Analysis and Verification  
Single or a combination of multiple sets of experimental flight data were tested to obtain the best identified dynamic model. This was completed to evaluate the consistency of the identification results and sensitivity of the identification methods. It was found that identified parameters related to velocities along the x- and z-axes had relatively larger deviations because they were not available using onboard sensors. In addition, high-frequency noises and nonlinear body dynamics not included in the model also affected identification results. By following all the selection criteria, six identified dynamic models were considered. Table 3 shows parameters of the identified dynamic model with the indirect method. Each of the selected dynamic models was named based on the identification method used to refine it and numbers represent datasets used for the identification. Fit percentages of \begin{table}
\begin{tabular}{c c} \hline \hline
**Identification Method** & **Characteristics** \\ \hline GNA & The adaptive subspace Gauss–Newton search method. \\  & This minimizes the objective function, which is the sum of squared errors that is \\  & approximately quadratic in the parameters near the optimal solution. \\  & Convergence is not guaranteed, and it might converge only to a local optimum, depending on \\ \hline LM & The Levenberg–Marquardt least square search method. \\  & This updates the parameters by adaptively combining the Gauss–Newton and gradient \\  & descent approaches, depending on the parameter errors. \\  & This is a refinement to the Gauss–Newton search method that improves the chance of local \\  & convergence and prevents divergence. \\  & This method is more robust than the Gauss–Newton and gradient descent search methods. \\ \hline GRAD & The Steepest descent or Gradient descent search method. \\  & This updates the parameters towards the largest directional derivative or negative gradient \\  & direction of the objective function to reduce the sum of squared errors. \\  & When close to minimum, the iteration process becomes relatively slow. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: General characteristics of each identification method. identified models obtained using irregular and high-frequency reference signals were much lower than those obtained using regular and low-frequency reference signals. Thus, they were discarded. The fit percentage of the dynamic model from CFD was only about 22%. This low fit percentage was mainly because only wing parts were considered to obtain the stability derivative-related parameters, instead of using the whole body of the KUBeetle. The whole body of the KUBeetle, including the wings, was considered to obtain mass and moments of inertia. The average fit percentage of the identified dynamic models was approximately 49%, which was more than double that of the CFD dynamic model. Most parameter values obtained from the three different identification methods and CFD were quite similar to each other. The CG of the new KUBeetle design, being lower than the CG of the previous KUBeetle design, increased the magnitude of \(M_{u}\). This was in accordance with the shift of the CG position due to the relocation of the control board and RF module from the top of the flapping mechanism to under the motor. The increase in \(M_{q}\) showed that the system had higher damping than that initially given from CFD. This indicated that the body of the KUBeetle greatly affected system stability. According to system identification results, aerodynamic forces along the x- and z-axes, \(X_{\gamma p}\) and \(Z_{\gamma p}\), had larger magnitudes than that previously measured. When measuring the control derivative, only the wings and frames near the wing were included. Because of a mounting problem, the lower body of the KUBeetle could not be included, which could be one of the possible reasons for the difference. Other parameters maintained similar values to CFD values.