Robust control approach for handling matched and/or unmatched uncertainties in port‐controlled Hamiltonian systems

This study considers the problem of robust interconnection and damping assignment passivity‐based control approach (IDA‐PBC) for underactuated mechanical systems from two points of view. First, the robustness of IDA‐PBC in the presence of non‐vanishing matched and unmatched uncertainties is analysed and sufficient conditions are derived to ensure ultimate boundedness of system. Second, the robust control design is provided by adding a new control input to the former controller designed by IDA‐PBC, such that asymptotic stability of the closed‐loop system in the face of non‐vanishing matched uncertainties is fulfilled. Finally, the proposed robust controller is evaluated through simulations of two practical examples, i.e. an inertia wheel pendulum and a single‐link elastic joint robot. The simulation outcomes clearly reveal the effectiveness of the presented robust controller.