Identification of Multivariable System Using Relay Tuning

G. S. Dombe and M. Chidambaram

Abstract
In this paper, the recently proposed method by Ramakrishnan and Chidambaram (2003)6 on identifying SOPTD transfer function model by asymmetric relay tuning method is extended to identify a multivariable system. The decentralized relay feedback method suggested by Wang et. al. (1997)11 is applied for the m × m system and m relay tests are required for identifying the entire transfer function matrix. Although, most of the processes can be adequately approximated by a FOPTD model, some of the processes are under-damped and higher order processes can be better incorporated by a SOPTD than a FOPTD model. Certain higher order stable models when approximated to a FOPTD model give a negative time constant, hence, identifying a second order model is necessary. The proposed method is applied to a 2 × 2 transfer function matrix. The multivariable IMC controllers are designed for the identified model and the closed loop performance of the actual and identified model is compared.

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Keywords
Relay tuning, multivariable system, IMC