System identification using balanced parametrizations

Some general issues in the “black-box” identification of multivariable systems are first discussed. It is then suggested that balanced parametrizations can be used to give identifiable forms. A particular advantage is that balanced parametrizations are known for several useful classes of linear dynamic models, including stable minimal models, minimum-phase models, positive-real models, and normalized coprime factor models. Before optimizing the parameters of balanced parametrizations, an initial model must be found. We use realization-based methods and so-called “subspace” methods for this purpose. These methods are very effective at finding accurate initial models without preliminary estimation of various structural indexes. The paper ends with two simulation examples, which compare the use of balanced parametrizations with more traditional ones, and three “real” examples based on practical problems: a distillation column, an industrial dryer, and the (irrational) spectrum or sea waves