Relay feedback identification for processes under drift and noisy environments

Relay feedback identification methods are widely used to find the process ultimate information and tune proportional-integral-derivative controllers. The conventional relay feedback method has several disadvantages, which include poor estimates of the process ultimate information for low-order processes, chattering of relay for noisy environments, and asymmetric relay responses for constant biases or slow drifts in the process outputs. Methods to mitigate each of the above disadvantages are available. However, a systematic method to treat all of them has not been studied yet. Here, simple relay feedback methods that resolve these problems by introducing band-pass filters in the feedback loop are proposed. The high-pass filter part in band-pass filter removes a constant bias or low frequency drift, and the low-pass filter part removes high frequency noise and high-order harmonic terms in the relay feedback oscillation, resulting better estimates of the process ultimate information. Because filters used for the proposed methods are able to reject constant biases, the process steady state gains can be estimated without disturbing the relay feedback oscillations and first order plus time delay (FOPTD) models can be obtained by combining the process steady state gains with the relay oscillation information.