Closed-loop identification using switched controllers

It is well known that one necessary condition to obtain identifiability in closed-loop experiments is to switch between several controllers, where the minimal number of controllers depends on the number of inputs and outputs of the system to identify. However, some questions still remain to be answered when designing experiments with these characteristics. This paper analyses the properties of models obtained in this manner, limited to direct identification of scalar (SISO) systems using prediction error methods (PEM). The main result of this contribution establishes a relationship for the controllers used in the experiment to ensure consistency, even when the noise model is under parameterized.