Closed-loop System Identification Based On Subspace Methods

Closed-loop system identification is greatly significant for the engineering practice. On the one hand, for the security, quality control, or the system instability, etc., the system identification must be carried out under the closed-loop condition; On the other hand, as the rise and the development of the researches related to control oriented identification, the design of the model-based control system also requires to identify the plant in the closed-loop. Subspace identification method (SIM) is a new class of state-space model identification methods. Compared to other traditional identification methods, SIM needs less a prior knowledge of the model structure, has the numerical robustness, and is especially suitable for the multivariable system. Based on this new theoretical tool, the dissertation focuses on the research of relevant problems in the closed-loop system identification. The main contents include:1. For the traditional closed-loop subspace identification methods result in biased estimates under colored noises of large variances, the framework of SIM is extended from traditional input/output data to correlation function and a closed-loop subspace identification method based on correlation function estimates is proposed. The basic idea of the proposed method is to carry out the identification process into two steps. In the first step, the M-sequence is used to be the external input signal of the closed-loop system and to compute correlation function estimates sequences, and then the state-space equations of the identified object based on correlation function are obtained; In the second step, the null-space projection is developed to estimate the extended observability matrix based on the shifted-invariant of the correlation function. The simulation results show that the proposed method can effectively resist the noises of different variances in order to achieve unbiased estimates, especially colored noises of large variances.2. For most of recursive subspace identification methods (RSIMs) are not suitable to the closed-loop system, a closed-loop RSIM based on the orthogonal decomposition is proposed which can realize the recursive update of the identified model under the closed-loop condition. Firstly, through the orthogonal decomposition of the input-output process, the deterministic state-space realization of the identified model is obtained which effectively avoids the influence of the correlation between the observed input and the noise in closed-loop. After that, the newly sampled data is sequentially and recursively processed and the extended observability matrix is recursively obtained based on subspace tracking technique to realize the update of the model. The simulation results show that the proposed method dose not require any information of the controller and a priori knowledge of the identified object in the closed-loop system and can obtain more accurate estimates of the identified model than other closed-loop recursive subspace identification methods.3. Consider a class of the multirate system with the input-output non-uniformly sampled, a closed-loop subspace identification method based on the innovation estimates is proposed. The proposed method can determine the discrete state-space model of the identified object under the feedback. During the process of the identification parameterization, the causal constraint due to the lifting technique is fully considered. So the each row of the specific matrix is transformed into the triangular structure. Then the innovation sequences are computed row by row and the obtained innovations are included into the regression variables. Finally the state sequence is estimated by the appropriate weighting matrices. The simulation results show that the proposed method can effectively determine not only the paramters of the discrete state-space model of the identified object in the multirate closed-loop system, but also the order of the model by the singular values decomposition of the state sequences.