# Analytic Time Reentry Cooperative Guidance for Multi-Hypersonic Glide Vehicles
## 5 Simulation and Result Analysis
### Multi-Time Constraint Reentry Guidance Simulation  
In order to verify the effectiveness of the reentry guidance algorithm of the time-resolved hypersonic glide vehicle, this section sets a different expected time and examines the limits of each design parameter in this paper as shown in Table 1; \(\Delta r\), \(\Delta V\), and \(\Delta S\) are set to 1000 m, 100 m, and 30 km, respectively. The initial terminal conditions of the experimental state quantity in this section are set as scene 1 in Table 2, and the expected times are 780 s, 790 s, and 800 s, respectively.  
Figures 2-7 show the simulation results of the proposed algorithm under three expected time constraints. As shown in Figure 2, the terminal height error under the three simulation experiments is within the set threshold, and the average altitude error is 2.47 m, which meets the terminal constraint requirements. Figure 3 shows the change in latitude and longitude. It can be seen that the three simulation trajectories can reach the target point accurately. The average terminal range error is 7.09 km, which is less than the terminal range error threshold, indicating that the proposed algorithm can meet the guidance accuracy requirements. Figure 4 shows the change in velocity with time. At the expected terminal time constraint moment, the speed of the three simulation experiment terminal moments can meet the error threshold, and the average terminal velocity error is 40.95 m/s.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Designed Parameter** & **Maximum Value** & **Minimum Value** \\ \hline \(V_{1}\) & \(6500\) m/s & \(4000\) m/s \\ \(V_{2}\) & \(4000\) m/s & \(1800\) m/s \\ \(|\varphi_{0}|\) & \(80^{\circ}\) & \(0^{\circ}\) \\ \(\Delta V_{e}\) & \(100\) m/s & \(-100\) m/s \\ \hline \hline \end{tabular}
\end{table}
Table 1: The limitation of designed parameters.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **Longitude** & **Latitude** & **Altitude** & **Velocity** & **FPA** & **Head Angle** \\ \hline Case 1 & \(5^{\circ}\) & \(0^{\circ}\) & \(70\) km & \(6500\) m/s & \(1^{\circ}\) & \(30^{\circ}\) \\ Case 2 & \(2^{\circ}\) & \(-5^{\circ}\) & \(80\) km & \(7000\) m/s & \(0.5^{\circ}\) & \(40^{\circ}\) \\ Case 3 & \(0^{\circ}\) & \(0^{\circ}\) & \(100\) km & \(7000\) m/s & \(-1^{\circ}\) & \(40^{\circ}\) \\ Terminal constraints & \(32^{\circ}\) & \(20^{\circ}\) & \(20\)Figure 4: Time histories of the velocity.  
Figure 3: Latitude and longitude changes.  
Figure 2: Time histories of the altitude.  
Figure 5 shows that under the three specified expected time conditions, the trajectory obtained by the algorithm can enter the reentry corridor, that is, it can better meet the path constraints and ensure the safety of the reentry flight. Figures 6 and 7 show the changes in the AOA profile and bank angle profile respectively, while the change in AOA profile is more pronounced.  
Figure 5: Resistance acceleration reentry corridor.  
Figure 6: Velocity histories of the AOA.  
Figure 7: Velocity histories of the bank angle.  
velocity profile conforms to the piecewise function form of parametric design. The number of tilting angle reversals is fewer, which can reduce the pressure of the actuator. The error between the stop time of the three experimental simulations and the corresponding specified expected time is 0.1 s, 0.05 s, and 0.05 s, respectively, indicating that the proposed algorithm can better meet the time constraints.  
In summary, the reentry guidance method of HGV based on the time analysis proposed in this paper can effectively complete the task of specifying the expected terminal time.