Relay feedback methods for noisy processes

If there is noise in the original relay feedback system, because of chattering, it is not easy to obtain accurate ultimate information. To prevent chattering of the original relay output, hysteresis relay feedback method could be used. However, its relay output switching time is fluctuant and the average of switching time is different from the ultimate period. Thereby, here, we propose a chattering-free method using the integral signal of process output. This method is very simple and shows results that an obtained ultimate gain is pretty accurate.