## 5 Results and Discussion
### Robustness Analysis with NLDI and MNLDI
Uncertainties or unmodeled dynamics are the main challenges for the UAV flight control system, therefore a sinusoidal signal is added to \(c_{l},c_{m},c_{n}\) aerodynamic roll, pitch, and yaw moment coefficients, respectively, given in [21] as uncertainty in aerodynamic model. In Figure 10, the perturbation signal amplitude is very high in comparison to the accurate model parameters. The most important shortcoming associated with NLDI approach is the vulnerability to any uncertainties as it is a model-dependent control method, while MNLDI is robust against any model uncertainties as it is a model-independent flight control concept. Figure 11 shows the effect of the uncertain aerodynamic model given in Figure 10 in the performance of NLDI and MNLDI flight controller. NLDI is sensitive to the uncertainties; therefore, it is unable to track the desired references which confirms that the NLDI flight controller must be augmented with any other robust flight controller. In contrast, MNLDI is robust against model uncertainties; moreover, it still has absolute decoupling between roll and yaw angles. As a result, practically using MNLDI as a stand-alone flight control system is preferable. In Figure 12, the high amplitude angular rates performed by NLDI confirms the internal instability of using NLDI under model uncertainties. Meanwhile, MNLDI is still internally stable, as the angular rates required for achieving a sharp pitch maneuvers are within the allowable limits of angular rates. In Figure 13, the difference between the desired attitude angle and the actual response of both flight controller confirms that MNLDI is more robust against than NLDI. Figure 7: Inner loop rate response for outer pitch angle excitation. Figure 8: Attitudes response with NLDI and MNLDI with pitch angle excitation with wind disturbances. Figure 9: Inner loop rate response for outer pitch angle excitation with wind. Figure 11: Attitudes response with NLDI and MNLDI with pitch angle excitation with wind disturbances and uncertainties. Figure 10: Moments coefficient perturbation. Secondly, the tracking performance and flight control robustness against the wind disturbances and unmodeled dynamics of the roll and yaw channels were analyzed. Due to the traditional shape of the Tiger UAV, there is a coupling between the lateral states, which decreases the accuracy of tracking the desired command with accepted performance which leads to instability. However, the robust flight controller must be able to handle all variations to keep tracking the desired command. Similar to the pitch channel, both NLDI and MNLDI are tracking the desired commands in accepted performances without any uncertainties or wind disturbances. Moreover, the designed law of control given in Equations (7)-(9) for inner loop and Equations (20)-(22) ensure of asymptotic error decaying regardless of the external wind disturbances. However, NLDI flight controller is unable to overcome the uncertainties introduced to the model as it is completely model dependent. Conversely, MNLDI is a robust flight control technique against wind disturbances and uncertainties. Figure 12: Inner loop rate response for outer pitch angle excitation with wind and uncertainties. Figure 13: Attitude angle error for outer pitch angle excitation with wind and uncertainties. The roll channel response is shown in Figure 14, which confirms the ability of MNLDI to overcome the model uncertainties and wind disturbances; meanwhile, NLDI is sensitive to the model uncertainties. Figure 15 shows the need for the modification of NLDI to be able to overcome the model uncertainties; the high angular rates associated with the pure NLDI are beyond the allowable physical limitation of the Tiger-Trainer UAV, while MNLDI angular rates are within the limits. Figure 16 shows the effect of the wind disturbances on the desired command tracking for both NLDI and MNLDI.