Constrained MIMO dynamic discrete-time modeling exploiting optimal experimental design

This article presents a new multiple input, multiple output (MIMO) constrained discrete-time modeling (DTM) approach for dynamic block-oriented processes that does not require the nonlinear steady state characteristics to be known prior to model development. This approach uses an efficient statistical experimental design to provide design points for sequential step tests. The DTM is developed from this data in two stages. In the first stage, the ultimate response (steady state) model is determined from just the ultimate response data of the sequential step tests. In the second stage, the dynamic parameters are estimated under the constraint of the fitted ultimate response model obtained in the first stage. The constrained formulation is given for MIMO Hammerstein and Wiener block-oriented systems. Comparison of the proposed constrained DTM method is made with unconstrained DTM and constrained continuous-time modeling (CTM). Prediction accuracy of the proposed method is significantly better than unconstrained DTM and comparable to constrained CTM for the process studied.