On the model order reduction of a direct current motor

Abstract

Neglecting the armature inductance, La, is a common approach for model order reduction for a class of brush DC motors. Some authors, however, make a partial or incomplete interpretation for neglecting La, leading students to wrong results and misunderstandings. The existing conditions in the literature and in introductory control systems textbooks are either based on the time constant of the mechanical system being greatly larger than that of the electrical system, or La ≈ 0. These conditions are not supported analytically and no corresponding error analysis of any kind is provided. This paper analyzes and criticizes the eligibility of these conditions and provides an error model that corresponds to the model order reduction associated with neglecting La, and another that corresponds to neglecting the non-dominant pole. Experimental results are included to illustrate the suitability of the proposed error models and the suitability of employing such models in basic control designs.