Modeling and Attitude Control of Spacecraft With an Unbalanced Rotating Device

Design of an Active Balancing System for Rotating Orbital Devices

“…The above assumption is reasonable as the magnitude of the unbalance force and torque are dependent on the rotor speed, as shown next, and in a plausible scenario the rotor will be spun up slowly to avoid the risks associated with large unbalances. Moreover, based on the results of [10], a properly designed and tuned attitude control system for the spacecraft base can keep the attitude stable in the presence of a rotating unbalanced device, with guaranteed convergence to the desired attitude for vanishing unbalances. Small mismatches with respect to the perfect stabilization condition embedded in Assumption 1 will be treated as disturbance terms acting on the nominal model.…”

“…It is worth underlying that the approximation introduced through Assumption 2 essentially splits the overall motion of the spacecraft into the orbital motion of a point having the total mass of the system and a superimposed relative motion, as if the spacecraft is floating without gravity. As shown next, Assumption 1 and Assumption 2 allow for the development of a decoupled control architecture in which the ABS control design can be carried out independently of the spacecraft attitude control, the latter being considered in [10]. ⌟…”

“…Let us focus on the translational dynamics first. By substituting (10) into the left-hand side of (8), we have:…”

“…Further assuming that the orbital acceleration times the mass of the payload is mostly balanced by the gravity force, i.e., 𝑚 𝑝 𝑖 𝑣 𝑖 𝑂 ≈ 𝑓 𝑔 (we embed the mismatch into the disturbance term Δ 𝑓 𝑒 ), using (10), ( 14) and ( 12) the interface force can be approximated by the following expression:…”

“…The proposed approach assumes a decoupled control architecture, wherein the attitude of the spacecraft is controlled through the actuators of the spacecraft base while the ABS controller tries to cancel out the effects of inertial unbalances in the rotor by moving the masses at suitable locations. In this regard, it has been recently shown in [10] that a properly tuned PD-like controller is capable of keeping a stable attitude in the presence of inertial unbalances in the rotating device and ensures convergence to the desired attitude for vanishing unbalances, thereby allowing for balancing operations to be carried out safely. In this work, assuming that the spacecraft controller keeps the attitude close to the desired one, we show that through suitable assumptions the rotating device can be considered as fixed on the ground when designing the control algorithm of the ABS.…”