Nominal Performance Recovery of a Disturbance Observer-based Control System With Respect to the Time Constant of Q-filters

This paper provides an analysis of the disturbance and uncertainty compensation performance of a disturbance observer-based control system with respect to the time constant of a Q-filter. Assuming that the time constant is sufficiently small, it was shown that the disturbance observer can compensate disturbances and recover the nominal performance designed for nominal models without considering the plant uncertainties and disturbances based on the singular perturbation theory. The explicit bound of the time constant needed for achieving robust stability for the disturbance observer-based control system has not been provided. Thus, in this paper, we provide its explicit bound and the relationship between the nominal performance recovery and the time constant using Lyapunov stability analysis. Finally, the simulation results of the mechanical systems were presented to validate the proposed analysis.