Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances

The problem of robustification of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) for underactuated mechanical system vis-à-vis matched, constant, unknown disturbances is addressed in the paper. This is achieved adding an outer-loop controller to the IDA-PBC. Three designs are proposed, with the first one being a simple nonlinear PI, while the second and the third ones are nonlinear PIDs. While all controllers ensure stability of the desired equilibrium in spite of the presence of the disturbances, the inclusion of the derivative term allows us to inject further damping enlarging the class of systems for which asymptotic stability is ensured.