Refined Instrumental Variable methods for closed-loop system identification

This paper describes optimal instrumental variable methods for identifying discrete-time transfer function models when the system operates in closed-loop. Several noise models required for the design of optimal prefilters and instruments are analyzed and different approaches are developed according to whether the controller is known or not. Moreover, a new optimal refined instrumental variable technique is developed to handle the identification of a linear (ARX) predictor combined with an ARMA noise model in a closed-loop framework. The proposed refined instrumental variable algorithm achieves minimum variance estimation of the process model parameters. The performance of the proposed approaches is evaluated by Monte-Carlo analysis in comparison with other alternative closed-loop estimation methods.