Biased relay feedback with PD controller for identification of unstable processes with large time delay

It is difficult to identify the unstable processes with time delay, especially with large time delay. In this paper, a new relay feedback identification method for open-loop unstable processes with time delay is proposed. The exact expressions for the periods and amplitudes of limit cycles under the biased relay feedback are derived for unstable processes which can be modeled by first-order plus dead-time dynamics. Furthermore, for the unstable processes with large time delay, an additional PD controller is incorporated in the relay feedback system to relax the constraint on the ratio of delay to the unstable time constant, so that the exact model parameters of unstable processes can be identified. The numerical simulation examples demonstrate the validity of the proposed identification method.