## 4 Simulation and Analysis
In the 0-2.5 s interval, when there is no anti-saturation auxiliary system, both the roll channel and the pitch channel can keep up with the desired attitude faster, while the FACM algorithm designed in this paper lags slightly; in the yaw channel, when there is no anti-saturation auxiliary system, it has a larger overshooting amount although it has a shorter rise time; and the FACM algorithm achieves an asymptotic convergence of the yaw angle, and the regulation of the yaw angle is slightly slower, but it is also in the range of 2.5 s. The FACM algorithm achieves an asymptotic convergence of the yaw angle, and the adjustment time is a little slower, but it also makes the tracking error converge to zero in about 2.5 s. The reason for this phenomenon is that, at the beginning, due to the existence of a large error, the control moment reaches the saturation state, as can be seen from Figure 4, and for the algorithm without the anti-saturation auxiliary controller, the control volume is in the saturation state for a longer time, and the time of the maximum torque effect is also longer, so that it can track the desired attitude faster, but at this point, there is also a consequent overshooting, and the overshooting volume of the roll channel and yaw channel is especially obvious; on the contrary, in the FACM algorithm, due to the introduction of the anti-saturation auxiliary system based on the control algorithm, when the saturation phenomenon occurs, the auxiliary states of the anti-saturation system are changed, which reduce the angular tracking error, and thus shorten the time of the control moment in the saturated state, and the time of the maximum torque action is even shorter, so the FACM algorithm cannot track the desired attitude very quickly in the initial stage. Figure 4: Control moment comparison result. Subplot (**a**–**c**) are the torques of the roll, pitch, and yaw channels, respectively, under different control algorithms. Figure 6 shows the variation in the states of the anti-saturation auxiliary system. It can be seen from the figure that the states a and b change abruptly from zero at the very beginning due to the saturation phenomenon at the initial stage. After that, with the progressive reduction in the angular tracking error, the control moments also decrease, and the system is no longer saturated, so the input of the anti-saturation auxiliary system becomes zero, and the states of the anti-saturation auxiliary system also converge to zero in a finite time. Figure 5: Attitude tracking results in comparison. (**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. Scenario 2: In order to be closely related to the real environment, in Scenario 2, it is assumed that the external disturbance is unknown, and it is controlled by using the proposed finite-time disturbance observer and anti-saturation control method (FDOACM); at the same time, to verify the effectiveness of the proposed algorithm, the FACM algorithm and the composite continuous fast nonsingular terminal sliding mode (CCFNTSM) algorithm [46] are also applied to the attitude system model of the quadrotor UAV. The total disturbance settings to which the system is subjected are shown in Table 1.  
The desired attitude is consistent with Scenario 1. The initial angle is \(\mathbf{\Theta}_{0}=[0;0;0.3]^{T}\) rad. The moment saturation intervals for the roll, pitch, and yaw channels are all \([-0.5,0.5]\) N\(\cdot\)m. The observer parameters are as follows:  
\[A_{1}= \begin{bmatrix}100&0&0\\ 0&100&0\\ 0&0&100\end{bmatrix} ,\ A_{2}= \begin{bmatrix}300&0&0\\ 0&300&0\\ 0&0&300\end{bmatrix} ,\ k= \begin{bmatrix}100&0&0\\ 0&100&0\\ 0&0&100\end{bmatrix} \]  
The simulation results are shown in Figures 7-9. Figure 7 shows the UAV attitude tracking results under different control algorithms and unknown disturbance.