Closed-Loop Identification with an Unstable or Non-minimum Phase Controller

In many practical cases, the identification of a system is done using data measured on the plant in closed loop with some controller. In this paper, we show that the internal stability of the resulting model, in closed loop with the same controller, cannot always be guaranteed if this controller is unstable and/or nonminimum phase, and that the direct, indirect and joint input-output approaches of closed-loop prediction-error identification present different properties regarding this stability issue. We give some guidelines to avoid the emergence of this problem; these guidelines concern both the experiment design and the identification method.