Time Data-Based Iterative Method for Frequency-Domain Multivariable Systems Identification by Optimized Expansion of Rational Functions

This paper proposes a deterministic iterative method to obtain a linear time-invariant model of a multivariable plant from time-domain measured data. Model identification is based on frequency response matrices computed from time input–output signals which can be also measured during the normal system operation, possibly without the need of introducing special classes of input signals. Quality of computed frequency response is improved as a new data set is considered at each iteration. The iterative process runs as a filter for noises introduced by system or sensors. Once a frequency response matrix is obtained, a matrix function model is estimated by computing a sequence of optimal and analytical solutions to a convex problem based on a quadratic criterion and an optimized expansion of rational functions. Final identified models are chosen considering a trade-off between small cost and low complexity (small order). Numerical examples are used to evidence advantages and limitations of the method.