Design of optimal experiments for dynamic MIMO identification

A new experiment design procedure for identification of dynamic multiple-input multiple-output (MIMO) systems is presented. The implementation of the design is similar to previously proposed rotated input designs based on an estimate of the static gain matrix of the system. However, in the new design procedure, dynamics and input constraints can be explicitly taken into account if an approximate dynamic model is available.

The design problem is formulated as a convex optimization problem, where constraints are handled by linear matrix inequalities (LMIs). The objective is to produce uncorrelated outputs with maximum variance, subject to constraints, in order to maximize identifiability. Standard input designs, where the inputs are perturbed simultaneously in an uncorrelated way, or rotated input designs based on a static gain matrix, do not generally produce outputs with the desired distribution.

Other design procedures to include dynamics and constraints have been suggested, but the proposed procedure is significantly simpler than the previous ones. Because standard software can be used for the design, it is well suited for practical applications. The method is illustrated by application to a distillation column model.