Stability analysis, control design, and closed-loop dynamic simulation of a two-spacecraft electromagnetic formation flying array

In this paper, we consider the equations of motion of a two-spacecraft formation flying array that uses electromagnets as relative position actuators. The relative positions of the spacecraft are controlled by the forces generated between the electromagnets on the two spacecraft, and the attitudes of the spacecraft are controlled using reaction wheels. The nonlinear equations of motion for this system are linearized about a nominal operating trajectory, taken to be a steady-state spin maneuver used for deep-space interferometric observation. The linearized equations are analyzed for stability and controllability. Although the open-loop system proves to be unstable, a controllability analysis indicates that the system is fully controllable with the given suite of actuators, and is therefore stabilizable. An optimal linear feedback controller is then designed, and the closed-loop dynamics are simulated. The simulations demonstrate that the closed-loop system is indeed stable, and that linear control is a very promising technique for electromagnetic formation flight (EMFF) systems, despite the nonlinearity of the dynamics.