Adaptive IDA‐PBC for Underactuated Mechanical Systems With Unknown Time‐Varying Disturbances

ABSTRACT Interconnection and Damping Assignment Passivity‐Based Control (IDA‐PBC) has been one of the most employed algorithms to stabilize underactuated port‐Hamiltonian systems. However, IDA‐PBC cannot handle input disturbances. Disturbances can cause a drift in the desired equilibrium and can generate unstable behaviors. In this paper, we propose to include an adaptive term to estimate the disturbance in the IDA‐PBC for underactuated mechanical systems. Under the assumption that the disturbance is composed of a finite sum of sinusoidal functions with unknown frequencies and amplitudes, we design an estimation algorithm that is based on the internal model for which we estimate, exponentially, the frequencies and the magnitudes of the disturbances. As it is typical in IDA‐PBC, we show that the desired control objective is achieved provided that the desired output is detectable.