Pid+ Tracking in a Leader-follower Spacecraft Formation

In this paper we present two PID+ solutions to the problem of relative translational and rotational tracking in a leader-follower spacecraft formation, based on the concept of integrator backstepping. By using an integrator augmentation technique, we include integral action in the controllers to account for unknown orbital perturbations. Two methods for including integral action in the control loop are presented, and the equilibrium points in the two closed-loop systems are proved to be uniformly exponentially stable and uniformly asymptotically stable, respectively. Finally, simulation results are presented to show the controller performance.