Statistical Change-point Methods for Closed-loop Delay Estimation

The input-output delay of a process is an important parameter for control design and closed-loop identification. This paper proposes new methods for estimating the delay of a transfer function model in closed-loop based on statistical change-point detection methods. A Bayesian change-point approach, a sequential probability ratio test (SPRT), and a cumulative sum (CUSUM) approach are proposed and compared against a recently proposed Laguerre polynomial-based method. The first two methods assume that the correct orders of the closed-loop ARMA model description are known, while the last one (the CUSUM approach) does not make such assumption. Two simulation examples and a sensitivity analysis are presented for comparison purposes. It is shown that the SPRT method performs best overall and is easy to tune depending on the dynamical response of the process. It is also shown that a CUSUM applied to the observed measurements, which does not require a parametric model of the closed-loop process, performs better than existing methods.