Abstract: In view of the fact that it is difficult to gather the open-loop data of the control system in practice, a direct identification method of impulse response model based on subspace approach from closed loop data is presented. An orthogonal decomposition is first used to estimate the deterministic components of the joint input-output process. Then, closed loop identification problem can be converted to identify the plant with the deterministic components of the joint input-output process under open loop circumstance. Through exploiting the low triangular structure of Toeplitz matrix, the subspace matrix consisting of impulse response coefficients is estimated row by row. The impulse response model is derived by averaging elements of the estimated subspace matrix. Three simulation examples of SISO numerical simulation, MIMO numerical simulation and Wood-Berry distillation process are used to compare the proposed method、PBSID_OPT and CVA. Results of several simulations show the good performance of the proposed method. The results of this paper have actual significance of reference and guidance for the application of subspace identification method in the modeling of actual industrial process.

Key words: impulse response model, subspace identification, closed loop identification, modeling

摘要： 针对实际情况中难以采集控制系统开环数据的问题，对脉冲响应模型的闭环辨识问题进行了研究，提出了一种基于正交分解理论的脉冲响应模型闭环子空间辨识方法。通过使用正交分解得到联合输入输出信号的确定部分（Deterministic Components），把闭环问题转化成开环问题。利用Toeplitz矩阵下三角结构形式，对由脉冲响应模型系数组成的子空间矩阵分块分解，通过求取子空间矩阵元素的平均值来获取脉冲响应模型参数的估计。通过采用PID控制器的单输入单输出（SISO）数值仿真、多输入多输出（MIMO）数值仿真和Wood-Berry蒸馏过程仿真实验3个仿真实例，对比研究了所提方法与PBSID_OPT、CVA三种方法。仿真结果表明了所提出的方法具有良好的辨识性能。对于实际工业过程的建模问题，该研究所提的闭环子空间辨识方法具有实际的参考价值和一定的指导意义。

关键词: 脉冲响应模型, 子空间辨识, 闭环辨识, 建模