## 5 Results and Discussion
### Robustness Analysis with NLDI and MNLDI  
NLDI flight control technique is known to be a standard reference model for tracking commands because it amounts to canceling the nonlinearities in a nonlinear system so that the closed-loop dynamics is in a linear form. Consequently, it is prone to disturbances either internal such as model uncertainties or external such as wind disturbance. However, the asymptotic stability of the designed control laws given in Equations (7)-(9) for inner loop and Equations (20)-(22) for outer loop guarantee the robustness of NLDI against external wind disturbances. In contrast, the model-dependence flight controller failed to compensate for any small perturbation in the model parameter or unmodeled dynamics. On the other hand, MNLDI is capable of tracking the desired command despite the external wind disturbances, model uncertainties or unmodeled dynamic as it is a model independent flight controller. The conventional configuration of the fixed-wing Tiger-Trainer UAV is suffering from the coupling between the roll and yaw planes. Consequently, the lateral plane states are coupled while the longitudinal plane states are uncoupled. The simulation results focus on the ability of the designed flight control system to decrease the coupling between roll and yaw channels in addition to highlight the robustness of the designed flight controller against wind disturbances in addition to model uncertainties. Starting with pitch channel analysis of tracking performance and robustness analysis, the desired pitch angle command was compared with the actual UAV pitch angle in an ideal environment with neither wind disturbance nor model uncertainties. Moreover, the pitch angle response in severe wind disturbance conditions and high variation of the aerodynamic model was tested. Since the lateral plane coupling degrades the efficiency of the tracking performance and also increases the tendency to be sensible for disturbances, the decoupling capability of NLDI and MNLDI flight controllers was studied. In Figure 6, a comparison between the performance of both flight controllers in response to pitch angle command with zero wind speed and accurate UAV model is illustrated. Pure feedback linearization was used successfully to address pitch angle tracking as NLDI cancels the unwanted nonlinear terms which force the control law to track the desired attitude with accepted performance. Not only NLDI meets the accepted tracking performance but also MNLDI is a good tracker, especially when it is optimally tuned. Generally, the coupling in the longitudinal plane is negligible in comparison with the lateral plane. However, MNLDI seems to eliminate the coupling between roll and yaw angles. Figure 6: Attitudes response with NLDI and MNLDI with pitch angle excitation without disturbances. One of the important issues of tracking problem is the internal stability of the system under control. The most inner loop of the flight control system responds accurately to the outer attitude loop commands. Both NLDI and MNLDI are following the standard limitations of small fixed-wing UAV allowable rates [18]. In Figure 7, a comparison between the performance of angular rates inner loop tracking in response to pitch angle command without wind and accurate UAV model is illustrated. Wind disturbance is a great challenge for the UAV flight control system, especially for small UAVs. Figure 8 confirms the robustness of the designed flight controller in both NLDI and MNLDI flight controller. Although the wind speed is very high compared with the Tiger-Trainer UAV, as it is 55% of the UAV airspeed, the designed control law is able to withstand high constant high wind disturbance. The asymptotic stability of the designed control law guarantees best tracking performance with severs flight conditions. In Figure 9, a comparison between the performance of angular rates loop tracking in response to pitch angle command with high-speed wind is illustrated.