A method for estimating the dynamics of a sampled-data system when it is operating under feedback control is proposed in this paper. This method does not require any special control action for the identification experiment. The theoretical analysis of the identifiability property of this method is also discussed. In this method, the input-output data is sampled at the frequency of which is a multiple of the control system's sampling frequency. It is proved that the condition for strong system identifiability depends only on rank of the pulse transfer function matrix of the feedback controller, for the feedback law is formulated in a periodic time-variant form in terms of the data. The model estimated from the data can be converted into the one available for the digital control of the system. It is shown that the conversion can be carried out with simple numerical operations, and a method for the fast conversion is also presented in this paper.