Bias-eliminated subspace model identification under time-varying deterministic type load disturbance

• Bias-eliminated subspace identification against deterministic load disturbance.
• Consistent estimation on the plant state-space model by using an orthogonal projection approach.
• Disclose the rank condition for performing the orthogonal projection.
• A uniform transformation approach is given for variance analysis of the identified state matrices.

Unexpected or time-varying deterministic type load disturbances are often encountered when performing identification tests in practical applications. A bias-eliminated subspace identification method is proposed in this paper by developing an orthogonal projection approach to guarantee consistent estimation on the deterministic part of the plant, in combination with a Maclaurin time series approximation on the output response arising from deterministic type load disturbance. The rank condition for such an orthogonal projection is disclosed in terms of the state-space model structure adopted for identification. Using principal component analysis (PCA), the extended observability matrix and the lower triangular Toeplitz matrix of the state-space model are explicitly derived. Accordingly, the plant state-space matrices can be retrieved from the above matrices through a shift-invariant algorithm. A benchmark example from the literature and an illustrative example of industrial injection molding are used to demonstrate the effectiveness and merit of the proposed identification method.