DC Motor Control Using the Lambert W Function Approach

A new design method for proportional-plus integral (PI) and proportional-plus velocity (PV) control for DC motors to regulate angular velocity and position considering time-delays, is presented. Time-delays inherent in plants can arise from signal processing and actuation and can lead to undesired system performance including instability. Thus, time-delays should be considered in designing controllers. In this paper, a method based on the Lambert W function is used to address such problems caused by time-delays. The method enables one to find the rightmost (i.e., dominant) characteristic roots in the infinite eigenspectrum. Then, PI and PV control gains are obtained by assigning the rightmost eigenvalues to desired positions in the complex plane. The assignment can be achieved thanks to a novel property of the Lambert W function. System performance can be improved as well as successfully stabilized. Effectiveness of the presented method is verified through simulations and experiments. Also, sensitivity analysis of the rightmost eigenvalues with respect to delay mismatches is conducted to compare the proposed approach to a prediction-based method.