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  • Print publication year: 2014
  • Online publication date: June 2014

11 - Estimation of Five Parameters of Unstable SOPTD Model with a Zero


Using a single relay feedback test, a method is proposed to identify all the five parameters of an unstable second order plus time delay model with a zero (SOPTDZ):

Gp = kp(1±τ1s) exp(-Ds)/[(τ2s±1)(τ3s-1)]. In the present work, 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). All the five parameters of the SOPTDZ model are estimated with adequate accuracy. Performance of the controller designed for the identified model is compared with that of the controller designed on the actual transfer function model. The method gives a closed loop performance closer to that of the actual system. The methods are given for an asymmetric relay test. A simulation example of a third order non-linear CSTR system is also given.


Identification of transfer function models from experimental data is essential for model-based controller design. Often derivation of a mathematical model is difficult due to the complex nature of chemical processes. Hence system identification is a valuable tool to identify models based on input-output data.

Luyben (1987) suggested the use of relay testing for identifying a transfer function model. Using the values of ku and ωu in the phase angle and amplitude criteria for first order plus time delay (FOPTD) model, we get two equations relating the three parameters (kp, τand D).

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