Subspace-based Closed-loop Identification of Multirate Control System

In accordance with a class of multi-rate control systems, a subspace identification method is used to identify the discrete state-space model of the controlled object in closed-loop systems under feedback while there is no information about the controller. In order to avoid the inclusion of non-causal terms in the identified model, the generalized causal model is obtained through the analysis of causality constraints during the process of model parameterization. Then, based on the relationship of the instrumental variable, the least squares problem is developed and the state sequence estimation is solved by singular values decomposition. Meanwhile, the computation of the system matrices is given. Finally, the numerical simulation illustrates the effectiveness of the proposed method.