## 3 Results
### Simulation Results
#### 3.2.2 Graphic Results  
Figures 7 and 8 depict the close-loop and open-loop trajectory generation, respectively. There exists minor differences between both sets of simulations, due to the small error between real and desired trajectories, and thus similar results are obtained, and similar comments can be issued; henceforth, we provide common comments on them; however, notice that different resources are required to instrument either open- or closed-loop motion planner. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**ISE**} & \multicolumn{2}{c}{**ITSE**} & \multicolumn{2}{c}{**IAE**} & \multicolumn{2}{c}{**ITAE**} \\ \hline LMT & A-PI & PID & A-PI & PID & A-PI & PID & A-PI & PID \\ \hline \(\alpha\) & 0.17 & 0.60 & 35.39 & 155.15 & 6.68 & 12.72 & 1549.88 & 3347.34 \\ \(\beta\) & 0.07 & 0.29 & 21.89 & 86.67 & 3.81 & 7.90 & 1036.49 & 2098.94 \\ \hline ALMA & & & & & & & & \\ \(\alpha\) & 0.64 & 1.41 & 133.66 & 467.23 & 13.69 & 22.33 & 3684.98 & 7195.58 \\ \(\beta\) & 0.37 & 1.20 & 136.08 & 511.55 & 8.84 & 16.50 & 2891.74 & 5655.61 \\ \hline IRO & & & & & & & & \\ \(\alpha\) & 0.004 & 0.01 & 0.74 & 2.51 & 0.98 & 1.46 & 162.17 & 238.85 \\ \(\beta\) & 0.06 & 0.08 & 5.60 & 7.07 & 2.52 & 2.78 & 328.38 & 388.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance rating A-PI and PID controllers for open–loop trajectory generation. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**ISE**} & \multicolumn{2}{c}{**ITSE**} & \multicolumn{2}{c}{**IAE**} & \multicolumn{2}{c}{**ITAE**} \\ \hline LMT & A-PI & PID & A-PI & PID & A-PI & PID & A-PI & PID \\ \hline \(\alpha\) & 0.18 & 0.50 & 44.90 & 164.07 & 7.26 & 11.43 & 1837.85 & 3346.27 \\ \(\beta\) & 0.07 & 0.12 & 23.16 & 31.89 & 3.73 & 5.87 & 1030.41 & 1614.24 \\ \hline ALMA & & & & & & & & \\ \(\alpha\) & 0.66 & 1.17 & 151.75 & 457.35 & 14.27 & 20.35 & 3980.25 & 7077.22 \\ \(\beta\) & 0.37 & 0.77 & 139.38 & 322.41 & 8.81 & 13.68 & 2904.12 & 4687.09 \\ \hline IRO & & & & & & & & \\ \(\alpha\) & 0.0008 & 0.10 & 0.13 & 8.54 & 0.38 & 2.60 & 65.96 & 297.57 \\ \(\beta\) & 0.06 & 0.14 & 5.60 & 21.73 & 2.52 & 4.71 & 325.84 & 863.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance rating A-PI and PID controllers for closed–loop trajectory generation. Figure 7: LEO tracking simulation with closed–loop trajectories and A-PI control, for three different geolocations. Subfigures that plot 6 colors represent the corresponding response of each degree of freedom: 1 for red, 2 for green, 3 purple, 4 for yellow, 5 for dark blue, 6 for light blue. Subfigure that plot 2 colors represents orange for azimuth, and dark blue for elevation. Notice that the point–to–point tracking window are (see Table 2): 7:10 min for LMT, 8:52 min for the ALMA and 3:56 min for IRO, and the periods before and after correspond to the initial and go–to–home phases, respectively. the downlinking capacity of the system (phase two). The negative azimuth for IRO station is due to the satellite trajectory passed through the west from such location, in contrast to the LMT station location; see Figure 1. Altitude among stations also affect final trajectories, including distance to satellite trajectories. * _Row 3:_ Leg extensions trajectories in configuration space are shown in the third row, where curves exhibit consistency with the trajectory generation block policy. Notice that both the extension and the force of the pistons remain within the operating ranges provided by the manufacturer. * _Row 4:_ The aerodynamic force shows the importance to compensate for drag force along \(x\)-direction, particularly at the beginning and at the end of the point-to-point tracking phase, where antenna plate tends to an almost vertical pose, producing the highest wind disturbance, moreover with low lift and slip force components.