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

Abstract

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.

KEYWORDS:

• Subspace identification
• Hammerstein-type nonlinear system
• periodic disturbance
• orthogonal projection
• consistent estimation

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jie Hou http://orcid.org/0000-0001-8611-4778

Tao Liu http://orcid.org/0000-0003-1243-4546

Qing-Guo Wang http://orcid.org/0000-0002-3672-3716

Additional information

Funding

This work is supported in part by the NSF China [grant number 61633006] and [grant number 61473054], and the Fundamental Research Funds for the Central Universities of China [DUT18ZD201].