Silva, Datta, and Bhattacharyya (in the above paper) have studied the feedback control system, provided with a proportional-integral-derivative (PID) controller and relative to a first-order plant with a time delay, and have determined the range of the PID controller parameters suitable for the stability by means of a version of the Hermite-Biehler theorem. The purpose of this note is to find the same results in a simpler way by means of the classical Nyquist's stability criterion.