Coprime factor perturbation models for closed-loop model validation techniques

Abstract

This paper addresses the problem of checking the consistency of experimental closed-loop frequency-domain data with uncertainty models that are structured using coprime factorizations. The uncertainty models presented in this paper use the knowledge of a stabilizing feedback controller to structure and formulate the uncertainty on a model. Subsequently, the controller dependent coprime factor uncertainty model can be used to formulate model (in)validation tests on the basis of closed-loop data. Closed-loop model validation results are developed for the cases of noise-free and noise perturbed closed-loop data. The model validation tests involve the computation of a structured singular value over a finite frequency grid. It is also shown that the computation of the structured singular value simplifies considerably when the feedback controller used for the closed-loop experiments is the same as the controller used for formulating the controller dependent coprime factor uncertainty model.