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The problem of robustification of interconnection and damping assignment passivity-based control for underactuated mechanical system vis-à-vis matched, constant, and unknown disturbances is addressed in the paper. This is achieved adding an outer-loop controller to the interconnection and damping assignment passivity-based control. 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. Numerical simulations of the Acrobot system and experimental results on the disk-on-disk system illustrate the performance of the proposed controller.

Control of underactuated mechanical systems via energy shaping is a well-established, robust design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations (PDEs). In this paper a new, fully constructive, procedure to shape the energy for a class of mechanical systems that obviates the solution of PDEs is proposed. The control law consists of a first stage of partial feedback linearization followed by a simple proportional plus integral controller acting on two new passive outputs. The class of systems for which the procedure is applicable is identified imposing some (directly verifiable) conditions on the systems inertia matrix and its potential energy function. It is shown that these conditions are satisfied by three benchmark examples. Index Terms-Nonlinear systems, passivity-based control, mechanical systems, stabilization.0018-9286 (c)