To overcome the influence from load disturbance with unknown transient and periodic dynamics, as often encountered when performing identification tests in engineering applications, a bias-eliminated subspace model identification method is proposed to realize consistent estimation, which can be used for both open- and closed-loop systems. By decomposing the output response into disturbed and undisturbed components, an oblique projection is subtly introduced to eliminate the disturbance and noise impact so as to obtain unbiased estimation on the deterministic system state matrices, while the disturbance response dynamics could be estimated. In particular, a specific algorithm based on minimizing the output prediction error is given to find out the disturbance period if exists, such that the disturbance effect can be eliminated by the above projection regardless of the disturbance waveform and magnitude. A shift-invariant approach is then given to retrieve the deterministic state matrices. Consistent estimation on the deterministic system matrices is analyzed with a proof. A benmark example from the literature and an industrial injection molding process are used to demonstrate the effectiveness and merit of the proposed method.
Bibliographical noteThis work is supported in part by the NSFC Grants 61633006, 61473054 and 61020106003, the Fundamental Research Funds for the Central Universities of China (DUT18ZD201), National Key RD Program of China under Grant 2017YFA0700300, SAPI State Key Lab Fundamental Research Funds (2013ZCX02-01), and the Oversea Changjiang Scholar Program of China.
- consistent estimation
- deterministic system response
- load disturbance
- oblique projection
- Subspace identification