ON TEST DESIGN FOR SUBSPACE IDENTIFICATION OF MULTIVARIABLE ILL-CONDITIONED SYSTEMS

Ill-conditioned processes often produce data of low quality for model identification in general, and for subspace identification in particular, because data vectors of different outputs are typically close to collinearity, being aligned in the “strong” direction. One of the solution that can be adopted is the use of appropriate input signals (usually called “rotated” inputs), which must excite sufficiently the process in the “weak” direction. In this paper open-loop (uncorrelated and rotated) random signals are compared against closed-loop signals with the aim of finding the most appropriate ones to be used in multivariable subspace identification of ill-conditioned systems. As a result it is shown that closed-loop data give superior models, both in the sense of frequency response and in terms of performance when used to design a model predictive control system.