## 6 Simulation Experiments and Analysis  
Numerical simulations were conducted for the designed controller to verify the effectiveness of the control methods described above. Due to the need for the three-axis stable control of satellites, a large torque output is required in the rolling axis direction. Therefore, a scissor-configuration CMG is installed in the rolling axis direction, and flywheels are installed on the other two axes, as shown in Figure 4. The performance parameters of CMG and the flywheel are shown in Tables 1 and 2. The satellite is allowed a maximum rotational speed of \(8^{\circ}/\mathrm{s}\) and a maximum angular acceleration of \(10^{\circ}/\mathrm{s}^{2}\). Controller parameters are selected as \(k=0.005\), \(k_{1}=5\), \(k_{2}=0.1\), \(k_{3}=3\), \(k_{4}=2.1\), \(\frac{p}{q}=\frac{5}{3}\), and \(\frac{m}{n}=\frac{5}{7}\). The microsatellite undergoes three sequential large-angle maneuvers. Specifically, it starts with an initial attitude of (0, 0, 0) rad and an angular velocity of (0, 0, 0) rad/s. In the first maneuver, it moves to a desired attitude of (0, 0, \(\frac{\pi}{4}\)) rad and holds this position for 5 s. Following this, in the second maneuver, it shifts to another desired attitude (0, \(\frac{\pi}{6}\), \(-\frac{\pi}{6}\)) rad, holding again for 5 s. In the third and final maneuver, it transitions to the desired attitude (\(\frac{\pi}{6}\), \(\frac{\pi}{6}\), \(\frac{\pi}{3}\)) rad with a desired angular velocity of (0, 0, 0) rad/s. Without external disturbances, the spacecraft's desired and actual attitudes are illustrated in Figures 5-8. Figure 8: Actual angular velocity. Figures 5-8 highlight that the spacecraft's attitude almost aligns with its desired attitude. A minor fluctuation occurs when the angular velocity changes cease, resulting from a sudden change in the satellite's state. The controller cannot immediately track this change and requires a brief period to converge. However, as inferred from Figure 8, this convergence time is quite short. Such transient behaviors do not significantly impact the satellite's control performance and fall within acceptable limits. This suggests that the designed controller can effectively manage the spacecraft during large-angle maneuvering observation tasks. Simulations were conducted to compare the performance of the proposed controller with the conventional power reaching law, which is defined as follows:  
\[\dot{S}=-5|S|^{\frac{5}{3}}\text{sgn}(S)-0.1|S|^{\frac{1}{3}}\text{sgn}(S) \tag{41}\]  
Figures 9-12 depict the Euler angle control precision and angular velocity control precision during large-angle attitude maneuvers using two distinct reaching laws. Figures 13 and 14 present the control torque comparisons for these reaching laws. Figure 9: Error in Euler angles of the piecewise power reaching law. Figure 11: Error in angular velocity of the piecewise power reaching law. Figure 12: Error in angular velocity of the conventional power reaching law. Figure 10: Error in Euler angles of the conventional power reaching law. Figures 9 and 10 reveal that throughout the spacecraft's observation task, there is an amplification in Euler angle and angular velocity errors during the satellite's acceleration or deceleration phases, primarily due to controller delays. The attitude control algorithm based on the conventional power reaching law converges around 5 s, with the Euler angle error reaching up to 0.1\({}^{\circ}\). In contrast, based on the segmented power reaching law, the developed attitude control algorithm can converge within 2 s, with a maximum error of 0.03\({}^{\circ}\). Compared to the conventional power reaching law, there is a reduction in convergence time by approximately 3 s and a 70% improvement in control accuracy. This underscores the rapid convergence and high-precision advantages of the controller designed in this paper. Figures 11 and 12 highlight that the angular velocity control precision of both reaching law-based attitude control algorithms is comparable and around 0.15\({}^{\circ}\)/s.