In this paper, we present a new identification method based on the fictitious reference iterative tuning (which is abbreviated to as FRIT in the following). FRIT is one of the parameter tuning methods for controllers based on the direct use of the experimental data without mathematical models, particularly, this method enables one to obtain the optimal parameter with only one-shot experiment. Motivated by such practical advantages, we expand this method to a facile and fast-track identification by using only one-shot experiment data of the closed loop implemented with the existing controller in the one-degree of freedom control system. As one of the real systems in which it is effective for such an identification method to be applied, we consider the identification of the opening-and-closing speed dynamics of an elevator door. For this system, it is important to obtain the actual state of an elevator door for retaining a safety and quick motion. Thus, an identification of this dynamics is one of the most important factors for an effective maintenance. However, it is difficult to obtain the actual parameter because of the fact that there are many cases in which an experiment for the identification spends much time and it is undesirable to use sufficiently excited signals for the identification. We apply our identification method to solve these practical problems. Finally, in order to show the validity of our result in this paper, we also give an experimental result on the identification of the opening-and-closing speed dynamics of the door of an elevator.