## 4 Simulation and Analysis
Since the FACM algorithm has no disturbance observer module, the control effects of this algorithm are the worst among the three; the CCFNSM algorithm achieves the accurate tracking of the desired attitude in three axes; in the pitch channel and the yaw channel, for the attitude tracking error, although converging to zero in about 1 s, overshooting phenomenon occurs in the process of convergence; in the roll channel, the error convergence effect is better, and the error convergence is achieved in about 1 s with no overshooting phenomenon. Under the control of the FDOACM algorithm, the accurate tracking of the attitude is also achieved; in the roll channel, the control effects of the FDOACM and the CCFNSM are the same, and the convergence time of the pitch tracking error is nearly the same; in the pitch channel, the convergence time of the FDOACM control algorithm is slightly longer than that of the CCFNISM algorithm; in the yaw channel, the FDOACM algorithm has a much lower amount of overshooting. \begin{table}
\begin{tabular}{c c c c} \hline
**Disturbance (rad/s\({}^{2}\))** & \(\mathbf{0\leq t\leq 2}\) & \(\mathbf{2<t\leq 6}\) & \(\mathbf{t>6}\) \\ \hline \(d_{p}\) & \(-3\) & \(-8\) & \(-6-2\sin(0.1\pi t)\) \\ \(d_{q}\) & \(5\) & \(6\) & \(2+10\sin(0.2\pi t)\) \\ \(d_{r}\) & \(-3\) & \(-6\) & \(-6-2.4\sin(0.25\pi t)\) \\ \hline \end{tabular}
\end{table} 
Table 1: Total disturbance to the system. Figure 6: Anti-saturation auxiliary system compensation states change results. (**a**) denotes the amount of compensation state \(\lambda_{1}\). (**b**) denotes the amount of compensation state \(\lambda_{2}\). Figure 7: Comparison of attitude tracking results in the disturbance situation with study [46] and FACM. (**a,b**) denote the attitude tracking results and tracking errors of the roll channel. (**c,d**) denote the attitude tracking results and tracking errors of the pitch channel. (**e,f**) denote the attitude tracking results and tracking errors of the yaw channel. Figure 8 shows the change in the states of the anti-saturation auxiliary system. From the figure, it can be seen that the pitch channel triggered the anti-saturation auxiliary controller, so the compensation state of the pitch channel changed. In contrast, the roll channel and the yaw channel show no change in the compensation state quantity because there is no saturation phenomenon. From the figure, it can be seen that, in the initial stage of simulation, the control effects of the FDOACM algorithm in this paper are not as good as those of the CCFNTSM algorithm for the following reasons: due to the attitude angle error being larger in the initial moments, it triggers the anti-saturation controller in the FDOACM, which leads to the torque maintaining saturation for a shorter time; however, from the subsequent overall results, with the anti-saturation auxiliary state converging to zero, the controller designed in this paper is still able to outperform and give a better control performance. From Figures 7 and 8, it can be seen that the convergence times of the compensated states and the error are almost the same, and the values of the compensated states are in the same order of magnitude as the error, so it can be judged that the slower convergence time is due to the compensated states. Figure 9 represents the results of different observers for the disturbance. In the initial stage of the simulation, the observer of the study [46] shows an extremely sharp change, especially in Figure 9, the observer result changes abruptly from the initial zero to about \(420\) rad/s\({}^{2}\), and then gradually converges; when the subsequent disturbance shows a large sudden change, the output of the observer of the study [46] also changes abruptly, and the observation results approximate the actual disturbance in a linear relationship, and a certain degree of an overshooting phenomenon occurs.