Dynamics and control of a smart flexible satellite moving in an orbit

In this paper, the three axes maneuver control and vibration suppression of a smart flexible satellite moving in a circular orbit are studied. First, by using Lagrange-Rayleigh-Ritz technique and assumed mode method, the governing equations of a flexible satellite with PZT (lead zirconate titanate) piezoelectric patches are obtained. The flexibility of the appendages and the assumption of a large angle trajectory cause the governing equations to be nonlinear and coupled. The piezoelectric layers, attached to both sides of the appendages, are considered as sensors and actuators. A thorough look at the resulting equations reveals that the flexible satellite dynamics that include the appendage vibrations and rigid maneuver occur in two different time scales. By using the singular perturbation theory, the system dynamics is divided into two fast and slow subsystems. The slow and fast subsystems are associated with rigid motion dynamics and flexible appendages dynamics, respectively. A hybrid controller, which is proposed for use, consists of a variable structure controller (VSC) for maneuvering control of the slow subsystem, and a Lyapunov based controller for vibration suppression of the fast subsystem. The stability of the controllers is studied using the Lyapunov stability theory. Finally, the system behavior is simulated and the simulation results show the efficient performance of the proposed hybrid controller.