Vibration suppression of smart nonlinear flexible appendages of a rotating satellite by using hybrid adaptive sliding mode/Lyapunov control

In this paper, a hybrid adaptive sliding mode/Lyapunov controller is designed for both the rotational maneuver and the vibration control of smart flexible appendages of a satellite moving in a circular orbit. The satellite is considered as a rigid hub and two flexible appendages with attached piezoelectric layers as sensors and actuators. Each appendage is considered as a nonlinear beam undergoing large deflection. These governing equations of motion are obtained using a Lagrange–Rayleigh–Ritz technique and assumed mode method. The dynamic equations of motion are nonlinear and coupled due to the large angle trajectory and appendages large deflection. A through look at the resulting equations shows that the flexible satellite dynamics including the vibrations of the appendages and their rigid maneuver occur in two different time scales. Using the singular perturbation theory, the dynamics of the flexible satellite are divided into two slow and fast subsystems, the former associated with rigid-body maneuver, while the latter is a result of the vibrations of the appendages. Use of this hybrid controller allows us to cope with parameters uncertainty and disturbances of the system. The stability of the hybrid controller is studied by using the Lyapunov approach. Finally, the whole system is modeled and the simulation results show the efficient performance of the proposed hybrid controller.