Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop

TL;DR

This paper investigates the theoretical consistency of refined instrumental variable methods for continuous-time system identification in closed-loop settings, revealing conditions under which these methods are consistent or not.

Contribution

It provides a rigorous analysis of the consistency of SRIVC and CLSRIVC methods in closed-loop systems, highlighting the impact of continuous-time versus discrete-time controllers.

Findings

SRIVC and CLSRIVC are not generically consistent with continuous-time controllers.

Consistency can be achieved when controllers are implemented in discrete-time.

Numerical simulations support the theoretical analysis.

Abstract

Refined instrumental variable methods have been broadly used for identification of continuous-time systems in both open and closed-loop settings. However, the theoretical properties of these methods are still yet to be fully understood when operating in closed-loop. In this paper, we address the consistency of the simplified refined instrumental variable method for continuous-time systems (SRIVC) and its closed-loop variant CLSRIVC when they are applied on data that is generated from a feedback loop. In particular, we consider feedback loops consisting of continuous-time controllers, as well as the discrete-time control case. This paper proves that the SRIVC and CLSRIVC estimators are not generically consistent when there is a continuous-time controller in the loop, and that generic consistency can be achieved when the controller is implemented in discrete-time. Numerical simulations are presented to support the theoretical results.