Subspace identification of Hammerstein-type nonlinear systems subject to unknown periodic disturbance

In this paper, a subspace identification method is proposed for Hammerstein-type nonlinear systems subject to periodic disturbances with unknown waveforms. By separating the periodic disturbance response from the deterministic system response using the superposition principle, an orthogonal projection is established to eliminate the disturbance influence, while an instrumental variable is introduced to eliminate the noise effect for consistent estimation. The overall disturbance period could be exactly estimated by minimising an objective function of output prediction error. A singular value decomposition algorithm is developed to simultaneously estimate the observability matrix and the triangular block-Toeplitz matrix. The system matrices are subsequently retrieved via a shift-invariant algorithm. Sufficient conditions for consistent estimation of the observability matrix and the triangular block-Toeplitz matrix are established with a proof. An illustrative example is presented to demonstrate the effectiveness and merit of the proposed identification method.