Identification of Forward and Feedback Transfer Functions in Closed-Loop Systems with Feedback Delay

The subject of this paper is the identification of closed-loop continuous-time systems, with delayed feedback action, from sampled input-output measurements. In particular, a method for the identification of both forward and feedback subsystems is presented that requires only the knowledge of their orders and of the time-delay introduced in the feedback loop. The identification procedure is divided in two parts. The first step captures the behavior of the whole closed-loop system, estimating its transfer function. In the second step two different approaches are presented to separate the contributions of the forward and feedback subsystems in the loop. One of these approaches exploits a system theoretical method to compute the approximate greatest common divisor between polynomials. Numerical results validate the effectiveness of the proposed technique.