Application of BELS based methods in direct identification of linear systems from closed loop data

This paper is concerned with direct identification of linear systems in closed-loop operation. By introducing a weighting matrix, a new version of bias-eliminated least-squares (BELS) method is developed. The introduction of the weighting matrix allows for the new BELS method to contain various forms of the BELS based methods in its class. Analysis is made of the relationship between the new BELS method and the instrumental variable (IV) methods in more general setting. The developed method can provide an easy and effective approach for constructing the instrumental variables, thus broadening the application of the IV methods. Moreover, the substantial difference between the new BELS method and the prefiltering based BELS method is also illustrated in terms of construction of the weighting matrix. Computer simulations study is made to assess the performance of the developed method in various scenarios.