Abstract
The problem of robustness improvement, vis a 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.
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