Robust energy shaping for mechanical systems with dissipative forces and disturbances

This paper presents a novel energy shaping-based integral action for mechanical systems with unknown dissipative forces and matched disturbances. The proposed approach builds on the simultaneous interconnection and damping assignment method and takes advantage of the representation of the dissipative forces in the port-Hamiltonian dynamics. We consider dissipative forces that cannot be written in the classical dissipation structure of the port-Hamiltonian systems. We show that the proposed design ensures the stability of the equilibrium and is robust against dissipative force uncertainty, and rejects constant matched disturbances. Two case studies are presented, and simulation results show the closed-loop performance.