## 4 Simulation Verification and Discussion
### Influence of Model Mismatches and Sensor Noises
Therefore, it would be preferable to consider the direct force produced by the rudder if the model's accuracy permits. However, to verify the proposed controller's performance under a simplified onboard calculation model, this research does not compensate for the direct force component. To compare the performance of the ESO-based and CF-based INDI controllers and investigate the effect of noise on control performance, the same noise as in Section 3.2 is added to the roll and yaw angular rate channels. Additionally, to consider coordinated roll maneuvers, the lateral acceleration command is set to zero, and the bank angle command is set to 30 degrees. The roll angle command is generated using doublet signals with a 4 s interval to simulate a rapid continuous roll maneuver. To evaluate the disturbance rejection ability, the roll and yaw angular rate channels are disturbed by Gaussian white noise with a standard deviation of 0.01 rad/s. The dashed line in Figure 11 shows the tracking performance of the INDI controller with the CF method under noise disturbance. Compared with the ESO-based INDI controller, the CF-based INDI controller has a larger overshoot in both the roll angle and angular rate response. Meanwhile, the maximum lateral acceleration also increases to 4 m/s\({}^{2}\), which exceeds the design requirement. However, the overshoot of the roll angle and angular rate responses of the ESO-based INDI controller is small. In addition, the lateral acceleration and bank angle tracking performance is consistent with the nominal simulation. Therefore, the ESO-based INDI controller exhibits better disturbance rejection ability than the CF-based INDI controller under the same noise level. However, the actuator command output shows significant differences, as seen in Figure 11e,f. When the ESO-based INDI controller is activated, the command oscillations of the aileron and rudder are immediately and significantly reduced. This is attributed to the better noise suppression property of the ESO-based angular acceleration estimator, which reduces the working load of the servo, leading to an improvement in the working life of the servo and a reduction in the working energy consumption. To further evaluate the control performance of the ESO-based INDI controller under model mismatches, several additional simulations are conducted. The parameters in Table 5 are intentionally varied to simulate different levels of model mismatches. Figure 10: Angular acceleration estimation: (**a**) Roll angular acceleration estimation and (**b**) Yaw angular acceleration estimation. To evaluate the control performance of the ESO-based INDI controller under model mismatches, the parameters of the actuator are perturbed, and the estimated actuator model is shown in Fig. 11. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Explanation** & **Uncertainty (\%)** \\ \hline \(I_{zz},I_{xx},I_{zz},m\) & Inertial parameters & \(\pm 20\) \\ \(C_{ls},C_{nl},\) & Control coefficients & \(\pm 30\) \\ \(C_{YB},C_{YX},C_{lp},C_{rpB}\) & Static aero coefficients & \(\pm 20\) \\ \(C_{ls},C_{nl},\) & Control coupling coefficients & \(\pm 20\) \\ \(C_{yp},C_{yr}\) & Aero coefficients of damping force & \(\pm 50\) \\ \(C_{lr},C_{rpp},C_{rr},C_{lp}\) & Aero coefficients of damping moment & \(\pm 80\) \\ \(q\) & Dynamic pressure & \(\pm 20\) \\ \(\omega_{a}\) & Actuator damping ratio & \(\pm 20\) \\ \(\zeta_{a}\) & Actuator natural frequency & \(\pm 20\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Model parameters mismatches. Figure 11: One thousand simulations with model mismatches and sensor noises: (**a**) Bank angle response; (**b**) Lateral acceleration response; (**c**) Roll angular rate response; (**d**) Yaw angular rate response; (**e**) Aileron deflection angle; and (**f**) Rudder deflection angle. is used in the control law design. The model parameters are sampled using a uniform distribution, and 1000 Monte Carlo simulations are conducted.