Studies On Closed-loop System Identification Based On Covariance And Subspace Method

For security and high-quality control,most of industrial processes are carried out under closed-loop condition.The identification methods for these systems also requires to develop under closed-loop condition.Subspace identification methods(SIMs)can built the state-space models for multi-input multi-output(MIMO)systems.Closed-loop systems identification based on SIMs have been widely studies.Compared to other closed-loop SIMs,the covariance Based SIMs(CoBSIMs)for closed-loop systems eliminate the effects of the noise via correlation with an instrument before identifying the system matrices.The CoBSIMs can identify the system metrices with less computational efforts,which also can effectively resist the noises under high noises levels.The CoBSIMs for closed-loop systems is becoming a hotspot.The dissertation focuses on the research of relevant problems in closed-loop CoBSIMs.The main contents include:(1)An optimal weighting CoBSIM is proposed to improve the classical CoBSIM estimation performance.Firstly,the estimation error of the extended observability matrix about the noises terms is obtained.Then,by minimize the variance of the estimation error of the extended observability matrix,an optimal weighting matrix is obtained in term of miniming the variance of the projection error of the extended observability matrix,which may reduce the variance of the estimated system matrices.The simulation results show that the proposed method can reduce the variance of the estimated system matrices compared to classical CoBSIM.(2)A recursive CoBSIM is proposed for online identification for closed-loop systems.Firstly,the recursive forms of covariance of system data is obtained.Secondly,a recursive least-square method is used to estimate the system Markov parameters,then the Hankel matrix of the system Markov parameters is obtained.Finally,the system matrices can be estimated by performing SVD for the Hankel matrix of the system Markov parameters.Convergence property of the proposed method is analyzed.The simulation results show that the proposed method can accurately estimate the system matrices.(3)An orthogonal projection based CoBSIM is proposed for closed-loop systems with non-zeros mean noises.The proposed method eliminate the effects of the noise by performing orthogonal projection of the covariance of system data into the orthogonal the covariance of noise terms.The proposed method can give consistent estimations of system matrices.Meanwhile a corresponding recursive method of the orthogonal projection based CoBSIM is proposed for online identification for closed-loop systems.The simulation results show that the proposed method can accurately estimate the closed-loop systems with non-zeros mean noises.