Robust multi-variable identification: Optimal experimental design with constraints

Model identification for use in the design of multi-variable controllers should utilize an experimental design that optimizes the resulting robust control stability and performance, irrespective of the eventual controller structure or tuning. Previous research has shown that a key factor is to identify a steady-state gain matrix with minimal mismatch in the multi-variable gain directionality. In particular, for ill-conditioned systems, precise estimation of the weak process directions is essential.This research extends prior work to provide two alternative design formulations for robust multi-variable identification that allow seamless inclusion of any linear inequality constraints in the inputs, outputs or combinations thereof. These designs, based on D-optimality theory, produce highly correlated input sequences, and accommodate the input and output constraints by using highly unbalanced replications at the various input condition support-points.The superior effectiveness of the proposed designs over prior methods in the literature is demonstrated on a two-input, two-output binary distillation case study. In addition, the seamless extension of the method to higher-order systems is exhibited via a four-input, four-output fluid catalytic cracking example.Uncertainty in the prior estimate of the steady-state gain matrix and in design implementation is addressed in both of the proposed formulations. Furthermore, the second formulation provides a single tuning parameter to balance the efficacy of robust identification versus minimizing sensitivity to uncertainty. Finally, guidelines are presented for the extension of these methods to non-square systems.