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Subspace Hammerstein Model Identification under Periodic Disturbance

机译:周期性扰动下的亚空间哈默斯坦模型辨识

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In this paper, a subspace identification method is proposed for Hammerstein systems under periodic disturbance. By using the linear superposition principle to decompose the periodic disturbance response from the deterministic system response, an orthogonal projection is established to eliminate the disturbance effect. The unknown disturbance period can be estimated by defining an objective function of output prediction error for minimization. Correspondingly, a singular value decomposition (SVD) based algorithm is given to estimate the observability matrix and the lower triangular block-Toeplitz matrix. The state matricesAandCare subsequently retrieved from the estimated observability matrix via a shift-invariant algorithm, while the input matrixBand the nonlinear input function parameters are retrieved from the estimated lower triangular block-Toeplitz matrix by an SVD approach. Consistent estimation of the observability matrix and the lower triangular block-Toeplitz matrix is analyzed. An illustrative example is shown to demonstrate the effectiveness of the proposed identification method.
机译:本文提出了一种周期性扰动下的Hammerstein系统子空间辨识方法。通过使用线性叠加原理将周期性干扰响应从确定性系统响应中分解出来,建立了正交投影以消除干扰影响。可以通过定义输出预测误差的目标函数来最小化未知扰动周期。相应地,给出了基于奇异值分解(SVD)的算法来估计可观察性矩阵和下三角块-托普利兹矩阵。随后,通过移位不变算法从估计的可观察性矩阵中检索状态矩阵A和C,而通过SVD方法从估计的下三角块-Toeplitz矩阵中检索输入矩阵B和非线性输入函数参数。分析了可观察性矩阵和下三角块-Toeplitz矩阵的一致估计。显示了一个说明性示例,以证明所提出的识别方法的有效性。

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