Control relevant identification of ill-conditioned systems: Estimation of gain directionality

Abstract

In this paper, we investigate identification of a multi-variable system gain matrix with emphasis on the gain directionality. It is demonstrated that the accuracy of gain directionality has a stronger influence on the closed-loop performance of a model-based controller than that of the individual gain elements. It is also shown that a model accurately fitting all the elements of the gain matrix and its inverse is guaranteed to have accurate gain directionality. Motivated by this finding, we present an experimental procedure, which enables direct identification of the elements of the gain matrix inverse through a closed-loop experiment. Finding model gains that best fit both the open-loop data and closed-loop data can be formulated as a least-squares optimization. Case studies involving 2 x 2 and 3 x 3 distillation column control problems reveal that the models identified through the new procedure lead to superior closed-loop performance when compared with the models obtained through the conventional open-loop, single-input single-output identification method.