Estimation of Five Parameters of an Unstable SOPTD Model with a Zero Using a Single Relay Feedback Test

Abstract

A method is suggested to identify the five parameters of an unstable second-order plus time delay model with a zero (SOPTDZ): G p=k p(1±τ 1s) exp(−τ d s)/[(τ 2s±1)(τ 3s − 1)]. Three simulation examples are given (delay system with one unstable pole, one stable pole and a negative zero; delay system with one unstable pole, one stable pole and a positive zero; delay system with two unstable poles and one negative zero). The five parameters of the SOPTDZ model are estimated adequately. The performance of the controller designed using the identified model is compared with that of the controller designed using the actual transfer function model. The method gives a good closed loop performance. The methods are given for an asymmetric relay test. A simulation example of a third-order nonlinear continuous stirred tank reactor system is also given.