  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.
