Simplifying Robust Energy Shaping Controllers for Mechanical Systems via Coordinate Changes

The problem of robustness improvement, vis a vis external disturbances, of energy shaping controllers for mechanical systems was addressed by the authors in a previous paper. It was shown that—if the inertia matrix is constant—constant disturbances (both, matched and unmatched) can be rejected simply adding a suitable integral action. For systems with non-constant inertia matrix and non-constant disturbances the controller, that adds nonlinear damping and gyroscopic forces terms, is quite complicated. The purpose of this paper is to show that, including a partial change of coordinates, the controller can be significantly simplified, achieving the same robustness property of input-to-state stability with respect to matched disturbances of the previous controller.