Closed-loop identification of transfer function model for unstable systems

A simple method of identifying first order plus time delay transfer functio n model is proposed for unstable systems. The method is based on a single e xperiment on a closed-loop system with a step change in the set point of a PI or PID controller. The step response and derived analytical formulae are used to calculate the steady-state gain, time delay and time constant of t he unstable system, Simulation results are given for transfer function mode ls and on nonlinear model equation of an unstable bioreactor. The identifie d model parameters and/or the designed PID controllers settings are compare d with those of the exact or the linearized model used. (C) 1999 The Frankl in Institute. Published by Elsevier Science Ltd. All rights reserved.