Identification of low-order unstable process model from closed-loop step test

Based on a closed-loop step response test, control-oriented low-order model identification algorithms are proposed for unstable processes. By using a damping factor to the closed-loop step response for realization of the Laplace transform, an algorithm for estimating the process frequency response is developed in terms of the closed-loop control structure used for identification. Correspondingly, two model identification algorithms are derived analytically for obtaining the widely used low-order process models of first-order-plus-dead-time (FOPDT) and second-order-plus-dead-time (SOPDT), respectively. Illustrative examples from the recent literature are used to demonstrate the effectiveness and merits of the proposed identification algorithms.