Control design and analysis of an inner-formation flying system

Modeling of the dynamics and disturbances and designing of the precise formation controller are two major problems for the inner-formation flying system (IFFS). This paper introduces a nonlinear, nonautonomous formation dynamics model for IFFS in a general elliptic orbit. This model integrates the newly developed formation dynamics and the detailed disturbance models, including atmospheric drag, solar radiation pressure, and J2 effects. Furthermore, this paper establishes a coupled self-gravitational attraction model for IFFS. After considering such a comprehensive dynamics model, the precise formation control problem of IFFS is researched in detail. By referring to the averaging system, Hurwitz matrix, Lyapunov stability theorem, Matrosov's theory, and Barbalat's lemma as preliminaries, four possible controllers are designed, i.e., feedback-linearization plus proportional-derivative (PD) controller, Lyapunov-based controller, virtual potential-based controller, and velocity-free virtual potential-based controller. These controllers are all analyzed by the corresponding stability theories. Some simulations are carried out to testify these controllers, and the results show the effectiveness. By comparing the convergence time and fuel consumption, the velocity-free virtual potential-based controller is proven to be a more advantageous controller.