System identification in a real world

TLDR: This paper discusses both options for identification of linear models in the presence of nonlinear distortions, including the generation of error bounds, and a double approach is proposed, using either unstructured nonlinear state space models, or highly structured block oriented nonlinear models.

Abstract: In this paper we discuss how to identify a mathematical model for a (non)linear dynamic system starting from experimental data. In the initial step, the frequency response function is measured, together with the properties of the disturbing noise and the nonlinear distortions. This uses nonparametric preprocessing techniques that require very little user interaction. On the basis of this information, the user can decide on an objective basis, in an early phase of the modelling process, to use either a simple linear approximation framework, or to build a more involved nonlinear model. We discuss both options here: i) Identification of linear models in the presence of nonlinear distortions, including the generation of error bounds; and ii) Identification of a nonlinear model. For the latter, a double approach is proposed, using either unstructured nonlinear state space models, or highly structured block oriented nonlinear models. The paper is written from a users perspective.