Closed-loop step response identification of integrating and unstable processes

Motivated by the fact that integrating and unstable processes are usually operated in a closed-loop manner for safety and economic reasons, this paper proposes a systematic closed-loop identification method based on step response test to facilitate closed-loop system operation and on-line optimization. To avoid jeopardizing the closed-loop system stability of such a process, guidelines are given for proper implementation of a closed-loop step test for model identification. By introducing a damping factor to the closed-loop step response for realization of the Laplace transform in frequency domain, a frequency response estimation algorithm is developed in terms of the closed-loop control structure used for identification. Accordingly, three model identification algorithms are derived analytically in frequency domain to obtain the widely used low-order process models of first-order-plus-dead-time (FOPDT) and second-order-plus-dead-time (SOPDT). To enhance fitting accuracy for a higher order process, in particular for a specified frequency range interested to control design and on-line tuning, a weighted least-squares fitting algorithm is also given based on the estimated process frequency response points. Illustrative examples from the recent literature are used to demonstrate the effectiveness and merits of the proposed identification algorithms.