Frequency domain identification for a simple plant

A method to synthesize the transfer function of a simple plant from experimentally obtained magnitude and phase data is presented. In Hassul and Shahian (1992), the relevant formulas to estimate parameters were derived in terms of linearizing the quadratic error criterion so that students could follow the development without any mathematical difficulty. This method, however, inevitably is accompanied by a significant difference between the real and identified model especially in the low frequency region. As a method to decrease this difference in the low frequency region, a weighting function matrix that is directly related to the measured frequency data of the plant is introduced. That is, we propose an effective method to determine a weighting function based upon the results of identification. An efficient identification procedure for the proposed method is suggested to improve the quality of the model under the given circumstance. We confirm the validity of this method through several simulations and an experiment.