Vibration control and well-posedness analysis for a flexible spacecraft with pinned-end boundary input

This paper addresses the vibration control problem for a spacecraft with flexible appendages and boundary disturbance. The flexible spacecraft is modeled by a partial differential equation combined with boundary conditions. The control objective is to steer the flexible spacecraft to the desired angular position and simultaneously suppress vibrations by only applying control forces at the hub of the flexible spacecraft. To achieve the above objective, this paper proposes a novel boundary controller that acts at the pinned end and utilizes only the signals from the pinned end. With a disturbance observer, the boundary disturbance estimation is achieved. Then, based on operator semigroup, Lyapunov method, and LaSalle’s invariance principle, the well-posedness and asymptotic stability of the closed-loop system are guaranteed. Finally, the effectiveness and superiority of the designed boundary controller are verified through simulations.