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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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This study analyzes with the technology of auto tuning using relay feedback test for non-square MIMO system through process modeling, identification, input-output pairing and control strategies. However, the control configuration selection based on conventional steady-state Relative Gain Array (RGA) matrix sometimes degrades the loop performance and it needs attention. This study also deals with the real challenges in time domain modeling and appropriate pairing of loops for non-linear chemical processes. The choice of input-output pairing for square system has been extended to non-linear chemical processes. This ensures the system’s stability by selecting an appropriate manipulated-controlled variable pairing in non-linear chemical processes and the same is also tested for benchmark of non-linear chemical processes. In this study, two types of non-square systems are considered: one is systems with excess input than output variables and the other is systems with excess output than input variables. Some benchmark non-linear chemical processes, such as processes with mild nonlinearity, moderate to high nonlinearity and highly nonlinearity, are also taken for this study. Three standard benchmark processes are used in analysis of nonlinear chemical processes, namely: (1) Continuous Stirred Tank Reactor (CSTR) process; (2) hydrogen-ion- concentration (pH) process and (3) distillation column and this procedure is illustrated via simulation of 3-by-2 and 2-by-3 non-linear chemical processes.

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