# Integrated Magnetic Management of Stored Angular Momentum in Autonomous Attitude Control Systems
## 3 System Performance  
The proposed integrated magnetic control method for the management of the stored angular momentum was developed for applications in operative space software and hardware. Then, the verification of the control performancewas carried out with numerical model-in-the-loop simulations, exploiting a functional engineering simulator (FES) developed for satellite applications in Earth orbits. At first, after the preliminary analyses of the linearized system dynamics, the final tuning of the control system was performedon an ideal spacecraft model, without the inclusion of system disturbances (e.g., attitude determination errors and actuator inaccuracies). Various reference attitude states were considered: inertial pointing, nadir pointing, and target tracking modes.  
Figure 3 shows the results in the case of a system aligned with a reference inertial direction, where the plots report the quaternion and the error quaternion evolution over time. Note that only the quaternion vector part is shown, being the scalar part immediately available from the unit norm constraint. In this simulation, the system quickly converges to the reference state, and it reaches the complete steady-state condition in less than \(15\,\mathrm{min}\). However, the most important result is reported in Figure 4, where the stored angular momentum is plotted with respect to time. For a more immediate visualization, the figure also reports the reaction wheels' angular velocity. The angular momentum initially increases because of the required attitude maneuver to point in the reference direction, but it is quickly dumped out by the integrated magnetic momentum management control. In about \(3\,\mathrm{h}\), the reaction wheels are slowed to almost \(10\%\) of their maximum momentum capacity. Note that the simulation was initialized with the 4 reaction wheels at around \(75\%\) of the maximum storable angular momentum. This is achieved due to the integrated magnetic control law, which is commanded at the same time as the reaction wheels. The required magnetic dipole is reported in Figure 5, showing that a continuous magnetic torque is actuated. In the presented analysis, the maximum available magnetic dipole is \(0.3\,\mathrm{Am}^{2}\), and the maximum momentum capacity of each reaction wheel is \(2\times 10^{-2}\,\mathrm{Nms}\). It can be highlighted how the continuous angular momentum management loads the magnetic torquers in the order of \(30\%\) of their maximum capabilities. Moreover, it is worth noticing how the pointing performance is not affected by the integrated control law.  
Similar results were also obtained in the tracking mode of a time-varying reference attitude. In this case, a generic slew maneuver is commanded to follow a predefined attitude profile. The system follows the time-varying reference for the initial \(1.5\,\mathrm{h}\); then, it maintains the final steady-state condition. Figure 6 reports the time evolution of the attitude in terms of quaternions, together with the error with respect to the reference target state. Additionally, in this case, the attitude performance is demonstrated by a quick convergence to the desired state, followed by a good maintenance of the time-varying attitude profile. The integrated magnetic management of the stored angular momentum is capable of dissipating the reaction wheels' spin rates, as shown in Figure 7, without affecting the attitude control performance. Note that the oscillation in the reaction wheels' speed, similar to the previous case, is due to the periodic trend in the external environmental perturbations. The magnetic torquers' load is again about \(30\%\) of the maximum actuator capacity, as evident from Figure 8.  
Figure 3: Inertial pointing control.  
Figure 4: Stored angular momentum evolution in inertial pointing control.  
Figure 5: Actuated magnetic dipole in inertial pointing control.  
Figure 6: Reference attitude tracking control.