Total energy shaping for underactuated mechanical systems

摘要

This paper considers the application of a new formulation of Passivity Based Control, known as Interconnection and Damping Assignment or IDA-PBC, to the problem of stabilization of underactuated mechanical systems, which as is well-known requires the modification of both, the potential and the kinetic energies. Our main contribution is the characterization of a class of systems for which IDA-PBC yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction. The class is given in terms of solvability of a certain partial differential equation. As illustration we design an asymptotically stabilizing IDA-PBC for the classical ball and beam system.