## 6 Simulation Results  
The GTM is a scaled-down, 5.5% model of a commercial twin-engine aircraft developed by NASA, serving as a vital research tool for studying aircraft dynamics under adverse flight conditions, such as structural damage. It acts as a testbed to examine how damage affects the aerodynamics, stability, and inertial properties of the aircraft, including changes in aerodynamic forces, stability derivatives, and the center of gravity. The GTM is utilized in wind tunnel tests, numerical simulations, and computational modeling to investigate how different damage scenarios, like wing separation, influence flight dynamics, such as reductions in lift and pitch moment variations, and coupling effects between longitudinal and lateral motions. These insights are crucial for developing adaptive flight control strategies that can compensate for the altered dynamics and maintain aircraft stability. By supporting the creation of resilient control systems, the GTM aligns with the objectives of NASA's Aviation Safety Program, which aims to enhance aircraft survivability and safety in emergency situations involving structural damage. The GTM aerodynamic modeling used for the simulation can be found in the reference by [PERSON] et al. [28]. The simulation of the GTM is processed by applying the proposed INDI controller that estimates model uncertainties with the NDO and without the NDO. The control allocation matrix used for the simulation is  
\[\hat{B}_{\delta}=\left[ \begin{array}{ccc}1&0&0\\ 0&-1&0\\ 0&0&1\end{array} \right], \tag{32}\]  
implying that the controller only knows the control direction or sign. Figure 3 shows the total velocity \(V_{T}\), angle of attack \(\alpha\), and side slip angle \(\beta\) responses of the baseline controller and proposed controller. The \(V_{T}\) responses of both controllers are within 47.4 and 50.5 m/s and follow a similar trend, indicating that the dynamic pressures \(q_{\infty}\) of the aircraft under both controllers are comparable. The \(\alpha\) responses of the two systems  
also exhibit similar behaviors. However, the \(\beta\) response with the INDI-NDO shows a more dramatic response. The following Figures 4-6 demonstrate the \(p\), \(q\), and \(r\) responses to the \(p_{cmd}\), \(q_{cmd}\), and \(r_{cmd}\) results of our proposed controller and ordinary INDI. Figures 2 and 4 clearly demonstrate that the INDI-NDO method reduces steady-state error compared to the proposed INDI with NDO, particularly in the \(p\) and \(r\), while Figure 5 shows a reduction in oscillation in \(q\) response. Figure 4: Roll rate responses of the proposed INDI with the NDO and without the NDO. Figure 3: \(V_{T}\), \(\alpha\), and \(\beta\) responses of the proposed INDI with the NDO and without the NDO. The \(\beta\) responses in Figure 3 of the proposed and baseline controllers can be explained by the \(p\) and \(r\) responses as all of them are related to the lateral motion of the aircraft. The ordinary controller has an inaccurate control allocation matrix as in Equation (32) and leads to wrong control input calculation prompting steady-state error and performance deterioration. The aileron and rudder input based on Equation (32) controlling lateral motion \(p\) and \(r\) was not enough, resulting in the steady-state error exhibited in Figures 4 and 6, and also resulting in subtle movement in \(\beta\). The INDI-NDO overcame this issue and exerted more aggressive control, removing the steady-state error in \(p\) and \(r\), resulting in more substantial movement in \(\beta\). The ideal state estimation and disturbance in Equation (24) leads to \(\dot{\omega}=\
u_{\omega}\). The response of error \(\dot{e}_{i\omega}=\left[ \begin{matrix}\
u_{p}-\dot{p}&\
u_{q}-\dot{q}&\
u_{r}- \dot{r}\end{matrix} \right]^{T}\) is generated as in the following Figures 7-9.