Relay-based critical point estimation of a process with the PID controller in the loop

The proposed procedure is implemented without breaking the loop with the controller in operation, by activating a cascade of band-pass filters in series with a relay in the inner loop and a notch filter in the outer loop. A highly accurate estimate of the critical point of a process G p ( s ) is obtained in the presence of measurement noise and load disturbance. The effectiveness of the proposed procedure is illustrated using a test batch consisting of stable, integrating and unstable processes, including dead-time.