Estimation of SOPTD Transfer Function Model

Abstract

In this chapter, using a single asymmetric relay feedback test, a method proposed by Ramakrishnan and Chidambaram (2003) is reviewed to identify four parameters of a transfer function model. The proposed method is used to identify all the parameters in a second order plus time delay model (SOPTD). The parameters estimated are of adequate accuracy for designing suitable controllers. The estimated SOPTD model has a step response behavior matching with that of the actual process. The method can also be used for identifying open loop unstable transfer function models. For unstable systems, the closed loop step responses are compared. Simulation results are given for four case studies. Introduction Identification of dynamic transfer function models from experimental data is essential for model-based controller design. Often derivation of rigorous models is difficult due to the complex nature of chemical processes. Hence, system identification is a valuable tool to identify low order models, based on input–output data, for controller design. As stated earlier in Chapter 1, Astrom and Hagglund (1984) suggested the relay feedback test to generate sustained oscillations of the controlled variable and get the ultimate gain ( K u ) and ultimate frequency ( ω u ) directly from the experiment. Since only process information K u and ω u are available, the additional information such as steady-state gain or time delay should be known a priori in order to fit a typical transfer function model such as first order plus time delay (FOPTD).