A generalized relay identification method for time delay and non-minimum phase processes

A generalized relay identification method is proposed in this paper for time delay and non-minimum phase processes. A distinct merit of the proposed method is that the process gain can be uniformly derived from a single run of the relay test, independent of the relay type being unbiased or biased. An analytical relay response expression is derived for assessing the process response under an unbiased or biased relay test. A frequency response algorithm is also derived for estimating the multiple frequency response points of the process. By categorizing cases of the model parameters to be identified, the corresponding identification algorithms are developed using fitting conditions established for the process response at the oscillation frequency. Based on the improved estimation of multiple frequency response points, a recursive least-squares identification algorithm is then proposed for obtaining further enhanced fitting accuracy over a user specified frequency range, e.g., the low frequency range often concerned in practical controller tuning. Illustrative examples from the recent literature are given to demonstrate the effectiveness and merits of the proposed algorithms.