Closed-loop Subspace Identification Methods Based On Prior Information And Principal Component Analysis

As a powerful tool for state-space estimation,subspace identification methods(SIMs)with the advantage of simple numerical computation without nonlinear optimization,strong robustness,and applicable to multi-input and multi-output system,hence it have drawn much attention in the field of control,sign processing and process identification and from the 1990s.With the development of subspace identification in both theory and industrial application,the accuracy of identification model is required to be improved.Like most other system identification methods,the accuracy of subspace identification model can easily affected by data quality.It has been proven that these problems can be solved by integrating prior information about the system into an open-loop identification procedure.However,there are very few studies in closed-loop conditions.To solve this problem,this paper proposed two new closed loop subspace identification algorithms with prior information to improve the accuracy of identification model.The first algorithm is a closed loop subspace algorithm based on prior knowledge and principal component analysis(PCA).In this algorithm,first estimate the noise term by instrumental variables,and then construct the relational equation of impulse response and coefficient matrix by singular value decomposition and linear rearrangement,finial integrate the prior information into the process of calculate system matrices through the constrained least squares.The second algorithm is a recursive subspace identification methods for closed-loop system based on prior information and orthogonal projection.Which first uses QR decomposition to achieve the orthogonal projection and update the QR decomposition online through a bona-fide recursive algorithm,and finial solve systems matrices by integrating prior knowledge through eigenvalue decomposition and constrained least square method.In this paper,some simulations are performed for the proposed two new subspace identification algorithms with prior information,and the numerical simulation results show that the proposed algorithm can effectively improve the identification accuracy and stability of the traditional algorithm,and can be applied to the closed loop systems.