Identification of unstable transfer model with a zero by optimization method

A method is proposed for closed loop identification of an unstable first-order plus time delay with a zero transfer function model using the step response of a PI or PID-controlled system. A standard optimization method is used to estimate the model parameters to match the closed loop response of the model with that of the actual response. A simple method is proposed for initial guesses of the transfer function model parameters (time delay, time constant, gain and the value of zero). The method is applied to unstable transfer function models with a positive or negative zero, and to a CSTR to identify an unstable FOPTD (first-order plus time delay) with a zero. It gives good results in all the simulation case studies considered. The effect of measurement noise and controller settings on the identification of transfer function model is studied.