Learning PID structures in an introductory course of automatic control

Proportional-integral-derivative (PID) controllers are described in most automatic control textbooks. The application of PID controllers is widely spread in automation of mechanical processes where control of motors is of concern. This paper focuses on implementation of the PID control when used for regulation of dc motors. Two basic PID structures for position regulation of armature-controlled de motors are studied: the classical structure based on PI position loop plus velocity feedback, and a hierarchical two-loop feedback structure invoking a velocity proportional-integral (PI) inner loop. It is shown that the latter requires simpler stability conditions than the former. Basic concepts from automatic control are evoked in this study, namely, transfer function, characteristic polynomial, stability, and Routh-Hurwitz criterion. Experiments on a direct-drive motor are provided to illustrate the PID control performance.