基于辅助变量的闭环系统子空间辨识

Closed-loop subspace identification based on instrumental variable

提出一种基于辅助变量的子空间辨识方法,适用于控制器信息未知以及参考输入已知的闭环系统参数辨识.通过将输入-输出数据块正交投影到辅助变量的行空间,直接得到扩展观测矩阵垂空间的估计.由此可从闭环系统中提取出对象模型信息,同时由SVD分解得到扩展观测矩阵与下三角Toeplitz矩阵的估计.给出了系统参数矩阵、噪声矩阵的计算方法.将所提出的子空间辨识方法应用于闭环动态的系统参数估计,其结果表明了该方法的有效性.

A subspace identification method based on instrumental variable is proposed for parameter estimation of closed-loop dynamic systems with known setpoint input. The proposed method is suitable for the closed-loop identification without any controller information. The orthogonal complement to the extended observability matrix can be directly estimated by projecting the future input-output block data onto the row space of the instrumental variable. Then the model process information can be extracted from the closed-loop dynamic systems. The extended observability matrix and lower triangular block-Toeplitz matrix can be estimated by the singular value decomposition. Furthermore, the computation of the system parameter matrices and the noise covariance matrix is given. Finally, a simulation example illustrates the performance of the proposed algorithm in closed-loop identification.