In this paper, a method of auto-tuning of PID (Proportional-Integral-Derivative) and PIDA (Proportional-Integral-Derivative-Acceleration) controllers is proposed that can be applied to a time-delayed second order model. The proposed identification method is based on step responses, but it can be easily automated rising digital controller unlike the existing graphical identification methods. We provide a ways to yield parameter identifications which is independent to initial values of the plants. The tuning rule is based on the pole-placement strategy and is formulated so that it can be implemented using a digital controller with ease.