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The interactions between inputs and outputs in the multi input multi output (MIMO) systems yield responses from closed‐loop off‐diagonal elements. To characterize these responses through modeling, a systematic approach is followed to derive analytical expressions for relay feedback responses on multivariable systems. Time domain analytical expressions are helpful in deriving boundary conditions to estimate the parameters of MIMO systems. Unknown system parameters are identified using limit cycle data of off‐diagonal closed‐loop relay response curves obtained from single relay feedback test on these MIMO systems. Developed models are found to be in close agreement with real time system, and the parametric identification procedure is also efficient. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1672–1681, 2014

A novel approach to model the off-diagonal closed-loop transfer function of 2-by-2 multi input multi output (MIMO) system in time domain using ideal as well as biased relay feedback tests are presented. Analytical expressions are derived, for transfer function models of 2-by-2 MIMO system having individual transfer function elements of first-order plus dead time (FOPDT) nature, using ideal and biased relay feedback tests in time domain and have been validated on 2-by-2 multivariable distillation column examples from the literature as well as on coupled tanks liquid level experimental set-up. The results show that the derived expression matches with the original undesired relay response even without approximation of time delay in the denominator of closed-loop transfer function of 2-by-2 MIMO system. These analytical expressions are useful to identify unknown system parameters.

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