A frequency domain step response identification method for continuous-time processes with time delay

Step response test is widely practiced for model identification in process industry. A frequency domain step response identification method is proposed for obtaining a continuous-time process model with time delay. By introducing a damping factor to the step response for realization of Laplace transform, a frequency response estimation algorithm is first proposed, in which only single integral is needed for computation, compared to recently developed identification methods based on multiple integral in time domain. Based on the estimated frequency response, two model fitting algorithms are developed analytically for obtaining a time delay model of first-, second-, or higher order with repetitive poles. Another two algorithms based on fitting multiple frequency response points thus estimated are proposed for obtaining a time delay model of any order, the latter of which may also be used to improve fitting accuracy over a specified frequency range interested to control design. Meanwhile, practical strategies to consolidate identification robustness against measurement noise are given based on consistent estimation analysis, together with a guideline for model structure selection to realize optimal fitting for identification of a high order process. Illustrative examples from recent references are used to demonstrate the effectiveness and merits of the proposed identification algorithms.