The speed regulation problem with only speed measurement is investigated in this paper for a permanent magnet direct current (DC) motor driven by a buck converter. By lumping all unknown matched/unmatched disturbances and uncertainties together, the traditional active disturbance rejection control (ADRC) approach provides an intuitive solution for the problem under consideration. However, for such a higher-order disturbed system, the increase of poles for the extended state observer (ESO) therein will lead to drastically growth of observer gains, which causes severe noise amplification. This paper aims to propose a new model-based disturbance rejection controller for the converter-driven DC motor system using output-feedback. Instead of estimating lumped disturbances directly, a new observer is constructed to estimate the desired steady state of control signal as well as errors between the real states and their desired steady-state responses. Thereafter, a controller with only speed measurement is proposed by utilizing the estimates. The performance of the proposed method is tested through experiments on dSPACE. It is further shown via numerical calculations and experimental results that the poles of the observer within the proposed control approach can be largely increased without significantly increasing magnitude of the observer gains.