Closed-Loop System Identification with Recursive Modifications of the Instrumental Variable Method

The instrumental variable (IV) method is one of the most renowned methods for parameter estimation. Its bigger advantage is that it is applicable for open-loop as well as for closed-loop systems. The main difficulty in closed-loop identification is due to the correlation between the disturbances and the control signal induced by the loop. In order to overcome this problem, additional excitation signal is introduced. Non-recursive modifications of the instrumental variable method for closed-loop system identification on the base of a generalized IV method have been developed (Atanasov and Ichtev, 2009; Gilson and Van den Hof, 2001; Gilson and Van den Hof, 2003). In this paper, recursive algorithms for theses modifications are proposed and investigated. A simulation is carried out in order to illustrate the obtained results.