# Superior Control of Spacecraft Re-Entry Trajectory
## 3 Numerical Simulation Results and Analysis
### Simulation Results and Analysis  
Several trajectories were obtained through a simulation, and each algorithm took one trajectory to serve as an example in this article. Figure 2 shows the trajectory diagrams of two optimized lunar return spacecraft's re-entry and landing at the same target location. The blue trajectory represents the result obtained by the superior control algorithm, and the green trajectory represents the result obtained by the weighted optimal control algorithm. It can be seen that the trajectories obtained by both algorithms have achieved the goal of reaching the target destination. Relatively speaking, the green trajectory is smoother, while the blue trajectory has more small turns. This is because the blue trajectory will change the currently optimized index in real time based on whether the current performance index value reaches 80% of the maximum allowable limit. Therefore, the current speed direction in the optimized trajectory will also change accordingly. Figure 3 is a 2D diagram of the trajectories optimized by the two algorithms, including a top view and a side view. Figure 4 shows a comparison of moving the starting points of the two trajectories to the same location. It can be clearly be seen from the middle that the trajectories are very similar during the initial period of re-entry, indicating that the selection of weighted design during the initial period is easy to ensure that multiple indicators are within the ideal range. Figure 5 shows the curves of the velocity of the trajectories optimized by the two algorithms over time. It can be seen that the trends of the two curves are similar, and the landing time is relatively shorter compared to the superior control algorithm. Figure 1: Horizontal direction diagram of wind field. Figure 6 shows a comparison of the heating rates of trajectories optimized by the two algorithms. Figure 7 is a comparison of the overload of trajectories optimized by the two algorithms. Combining the two figures, it can be seen that in Figure 6--when the heating rate value of the superior control exceeds the maximum allowable limit of 80%, indicated by the red dashed line in the figure--priority is given to optimizing only the heating rate performance indicator. At this time, the overload has not reached 80% of the maximum allowable limit, so the overload is allowed to continue to rise. In Figure 7, it can be seen that the maximum overload value obtained by superior control is nearly twice as large as that of the weighted optimal control, but its value is still within the allowable range. This is because the weighted class control algorithm calculates the weights of each performance indicator as fixed values, which is an empirical calculation method that cannot adapt to the state of each performance indicator itself in practice. In practical applications, it cannot adapt to every sudden or unknown state in natural situations. Figure 3: Two algorithms’ optimized re–entry trajectory 2D diagrams. Figure 2: Two algorithms’ optimized re–entry trajectory 3D diagrams. Figure 8 shows the temperature changes over time for the trajectories optimized by the two algorithms. It can be seen that under the same external environment, the temperature trends of both algorithms are similar, with a sharp increase at first, fluctuations at high temperatures, and then a decrease. After a period of time, they rise again and reach a maximum before decreasing. The maximum value is basically the same, and the minimum and maximum values are slightly higher trajectories for superior control algorithms. Figure 9 shows the variation of path and heading angle over time for the two optimized algorithms. Figure 4: Comparison diagram of two algorithms’ optimized re–entry trajectories moving to the same starting point. Figure 5: Time–dependent graph of speed optimized by two algorithms. Figure 10 shows the variation of control variables of trajectories optimized by the two algorithms over time.