PID Passive-Based Control of Spacecraft Formation Flying in the Port-Hamiltonian Framework

The relative position and velocity control problem of spacecraft formation flight (SFF)is a classically significant problem in the field of space control. In this paper, we propose a high-precision nonlinear dynamics model for spacecraft formation flight with J2 perturbation in the framework of the port-Hamiltonian (pH) system. And through the application of the PID passive-based control method (PID-PBC), we give a new controller design method for the dynamics of SFF. Applying the leader-multi-follower spacecraft architecture, we first establish a nonlinear spacecraft formation dynamics model in the pH framework in the Earth Centered Inertial framework, and then transform it to the LVLH frame to establish a spacecraft relative motion dynamics model, and retain the nonlinear structure and
$J_{2}$
perturbation. Then a PID-PBC controller was established by constructing an additional system and designing a closed-loop Lyapunov function to ensure the stability of the target position. Numerical simulations show that the method is effective under the spacecraft formation reconfiguration mission.