Subspace Hammerstein Model Identification under Periodic Disturbance

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 matrices A and C are subsequently retrieved from the estimated observability matrix via a shift-invariant algorithm, while the input matrix B and 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.
QC 20190403