Robustifying energy shaping control of mechanical systems

The problem of robustness improvement, vis à vis external disturbances, of energy shaping controllers for mechanical systems is addressed in this paper. First, it is 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, additional damping and gyroscopic forces terms must be added to reject matched disturbances and, moreover, enforce the property of integral input-to-state stability with respect to matched disturbances. Finally, the stronger property of input-to-state stability, this time with respect to matched and unmatched disturbances, is ensured with further addition of nonlinear damping.