Vibration control for a flexible satellite with input constraint based on Nussbaum function via backstepping method

In this paper, the vibration control for a flexible satellite subject to input constraint and external disturbance is considered. The symmetrical flexible solar panels are described as symmetrical Euler-Bernoulli beams modelled as partial differential equations (PDEs). By using the backstepping method, a vibration control scheme is designed to regulate the satellite's vibration. An auxiliary system based on a smooth hyperbolic function and a Nussbaum function is designed to satisfy the constrained input. In order to overcome external disturbance, a robust item is introduced. It is proved that the vibration, the constrained input and external disturbance can be handled simultaneously. Simulations results are demonstrated for illustration.