# Integrated Magnetic Management of Stored Angular Momentum in Autonomous Attitude Control Systems
## 3 System Performance
### Model-in-the-Loop Verification  
After the preliminary results on the ideal case, the presented system performance was also validated with realistic simulations exploiting the FES models. In this context, the assumed scenario was well defined to better describe the actual performance of the proposed method. Table 1 summarizes the main simulation parameters. The spacecraft considered in the verification campaign has moments of inertia in the order of \(1\times 10^{-1}\,\mathrm{kgm}^{2}\), and the actuators are analogous to those in the previous simulations. The system is orbiting in LEO on a Sun-synchronous orbit (SSO) with an altitude of 550 km and local time of ascending node (LTAN) at 06:00 a.m. The system was simulated considering an attitude determination performance model with an average determination error of 3 deg. The actuator's functional models consider all the internal dynamics and errors, and they are representative of real spacecraft hardware. The reference attitude state was in nadir-pointing mode. The MIL results were analyzed and discussed in terms of pointing performance and stored angular momentum, which is the primary objective of the proposed control system. The initial conditions were randomly dispersed to better generalize the results, which were also verified in a similar simulation scenario and with alternative initial states. Finally, to facilitate the reader comprehension, it is stated that the integrated magnetic angular momentum management control has a bandwidth in the order of 5 Hz, while the three-axis attitude control is around 50 Hz. Figure 8: Actuated magnetic dipole in reference attitude tracking control. Figure 7: Stored angular momentum evolution in reference attitude tracking control. Figure 9 shows the dynamics' evolution of the spacecraft in the considered mission scenario along a 24 h simulation. The periodic trend in the quaternion components is due to the nadir-pointing mode, and the pointing error value confirms the positive achievement of the proposed control system. Indeed, the residual error is mainly due to the attitude determination errors, while the small oscillation is associated with the reaction wheels' jitter. The management of the angular momentum is effective even in the real case, with the average storage level in the low range of the plot, as shown in Figure 10. The initial build-up of the momentum is positively dumped out in less than 30 min, and the average reaction wheels' spin rate is about 10% of the saturation value. This is due to the fact that below this threshold, the integrated magnetic control is not active in maintaining the actuators far from the zero-velocity level, with a beneficial effect on the reaction wheels disturbances. Indeed, a minimum spin rate of the rotors minimizes the friction in the bearings and the vibrations due to the zero-crossing dead band. To further prove the positive impact of the proposed integrated control system, the same simulation was repeated with the continuous reaction wheels' desaturation switched off. \begin{table}
\begin{tabular}{l c c} \hline
**Specification** & **Value** & **Units** \\ \hline Spacecraft’s Principal Moments of Inertia & [0.1067 0.1068 0.0455] & kgm\({}^{2}\) \\ Reaction Wheels’ Torque Capacity & \(2\times 10^{-3}\) & Nm \\ Reaction Wheels’ Momentum Capacity & \(2\times 10^{-2}\) & Nms \\ Magnetic Torquers’ Maximum Dipole & 0.3 & Am\({}^{2}\) \\ Simulation Time & 24 & h \\ Spacecraft Orbit & SSO at 06:00 AM LTAN & N/A \\ Orbit Altitude & 550 & km \\ Initial Attitude & Random & N/A \\ Initial Angular Velocity & \(\mu=0\,\mathrm{deg/s}\), \(\sigma=0.1\,\mathrm{deg/s}\) & N/A \\ Initial Reaction Wheels’ Spin Rate & \(\mu=0\,\mathrm{deg/s}\), \(\sigma=0.3\,\omega_{R}^{Max}\) & N/A \\ Attitude Mode & Nadir Pointing & N/A \\ Attitude Determination Average Error & 3 & deg \\ \hline \end{tabular}
\end{table} 
Table 1: Model-in-the-loop verification parameters. Figure 9: MIL simulation of nadir-pointing control.