Closed-loop Subspace Model Identification Using Innovation Estimation and Orthogonal Projection
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摘要: 针对闭环控制系统提出一种基于新息估计和正交投影的闭环子空间模型辨识方法.首先采用最小二乘法对VARX模型（Vector autoregressive with exogenous inputs model）进行计算得到新息估计值，然后通过将由观测输入输出数据构造的Hankel矩阵正交投影到新息数据的正交补空间以消除噪声影响，从而在无噪声的输入输出数据奇偶空间中提取得到扩展可观测矩阵和下三角形Toeplitz矩阵.最后采用平移变换法得到系统矩阵.对该算法严格分析和证明了实现一致估计的条件.通过仿真实例验证了本文方法的有效性和优越性.Abstract: In this paper, a closed-loop subspace model identification method using innovation estimation and orthogonal projection is proposed for closed-loop control systems. Firstly, a least-squares algorithm is adopted to estimate the innovation matrix via the vector autoregressive with exogenous inputs (VARX) model. Then, by performing an orthogonal projection of the observed input-output Hankel matrix onto the orthogonal complement space of innovation Hankel matrix to eliminate the influence from noise, the extended observability matrix and lower triangular block Toeplitz matrix are derived from the parity space of noise-free input-output data. Finally, the system matrices are retrieved by using a shift-invariant approach. The consistent estimation conditions are analyzed with a strict proof. A simulation example is shown to demonstrate the effectiveness and merit of the proposed method.
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图 1 系统设定输入激励为白噪声的系统极点估计平均值
Fig. 1 Mean value of estimated poles for white noise setpoint excitation
图 2 系统设定输入激励为白噪声的系统极点估计标准方差
Fig. 2 Standard deviation of estimated poles for white noise setpoint excitation
图 3 系统设定输入激励为相关序列的系统极点估计平均值
Fig. 3 Mean value of estimated poles for correlated quasi-stationary setpoint excitation
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