• modelling;
  • relay feedback;
  • identification;
  • auto tuning;
  • multi input multi output


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. © 2012 Canadian Society for Chemical Engineering