On Disturbance Rejection for a Class of Underactuated Hamiltonian Systems

Abstract

In this work, the problem of additive perturbations is studied for a class of port Control Hamiltonian (PCH) systems. The considered class of Hamiltonian systems includes underactuated systems, which continue to be an important open study area. The starting point of the used methodology begins by considering that a previous tracking control has already made the equilibrium point of the error dynamic system asymptotically stable. The Integral Control (IC) reported in cite{ortega2012robust} and cite{ferguson2017integral} are implemented in the PCH class system so that it can reject the constant additive perturbations and conserves the Hamiltonian system structure. The results are compared and tested in a studied case with the system application of the Permanente Magnet Synchronous Motor (PMSM), and the MATLAB Simulink simulations obtained are exposed to compare the performance of both controls.