Integrals of relay feedback responses for extracting process information

Relay feedback methods have been widely used in tuning proportional- integral-derivative controllers automatically. Previous approaches usually use specific point data such as the oscillation amplitude and period of the relay response. In this article, we propose new identification methods, which use integrals of the relay response instead of the point data. The proposed methods guarantee better accuracy and advantages in obtaining the ultimate information of process as well as parametric models compared with previous approaches, because effects of the high order harmonic terms are suppressed significantly using the integrals of the relay responses.