Identification of the second order system based on hybrid time and frequency domain response

It is challenging to identify the time constants of the second order system via the sole step response, especially in the presence of the measurement noise. It is revealed that the responses behaves quite close to each other provided that the sum of time constants is fixed. To this end, this paper aims to develop a hybrid identification method that combines the characteristics in both time and frequency domain. The starting point has been the non-dimensionalization of the open-loop step response. A critical time at which the scaled amplitude equals 0.7 is chosen as the first characteristic parameter. The frequency at which the phase lag equals 90° is chosen as the second characteristic parameter. The time constants can be readily obtained by solving the equations describing the characteristic parameters. Illustrative examples show the superiority of the proposed hybrid method over the conventional time-domain “two-point” method.