Challenges in the stabilization of a satellite using Controlled Lagrangians I: Unbalance

We discuss the stabilization of an unbalanced satellite in a gravitational field using the method of Controlled Lagrangians. The considered system can be classified as an Euler-Poincare mechanical system. Therefore, for the purpose of stabilization, we employ the stability analysis of Euler-Poincare mechanical systems that was extended to systems with non-zero potential energies in Part I of this paper. The effectiveness of the stabilizing law is verified through simulations. In addition, we demonstrate the capability of the method of Controlled Lagrangians to cope with the issue of actuator saturation.