Integral passivity‐based control of underactuated mechanical systems with state‐dependent matched disturbances

This work investigates the energy shaping control of a class of underactuated mechanical systems subject to state-dependent linearly parameterized matched disturbances. To this end, a new integral interconnection and damping-assignment passivity-based design is proposed. The controller design is developed for systems subject to either momenta-dependent disturbances or position-dependent disturbances or to both simultaneously. The effectiveness of the proposed approach is demonstrated with numerical simulations on three examples: an Acrobot system with nonlinear friction; a ball-on-beam system with constant and position-dependent disturbances; a disk-on-disk system with a complete set of state-dependent disturbances. In all examples, the proposed controller shows better performance compared to previous implementations.