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This paper discusses the estimation of the parameters of a first order plus dead-time process model using the closed-loop step response data of the process under proportional plus integral (PI) control. The proportional gain and the integral time, in the PI controller, are chosen such that the closed-loop step response exhibits an under-damped response. From this response data, five characteristic points are used to determine a second order plus dead-time model and subsequently, the frequency response of the closed-loop system. Knowing the dynamics of the closed-loop system and the dynamics of the controller, the open-loop dynamics of the process can be determined by separating the dynamics of the controller from the closed-loop dynamics.
Kealy, Tony and O'Dwyer, Aidan : Closed loop identification of a first order plus dead-time process model under PI control. Proceedings of the Irish Signals and Systems Conference, pp. 9-14, University College Cork, June, 2002. doi:10.21427/78gg-f417