Data driven latent variable adaptive control for nonlinear multivariable processes

Abstract

This article aims at a new partial least squares (PLS) control design and analysis in a data-driven framework for nonlinear multivariable processes whose mechanistic models are completely unknown. First, a general nonlinear autoregressive moving average with the exogenous input (NARMAX) model is used as the dynamic nonlinear PLS model. Then, by introducing a dynamic linearisation approach in each latent variable (LV) space, the unknown NARMAX-based PLS model is transformed to a linear dynamic PLS data model (dPLSDM), which can be improved in real time by estimating its unknown parameter using the latent input and output (I/O) data. Next, a data-driven latent variable adaptive control (DDLVAC) is proposed in each LV loop. By virtue of the dPLSDM, the multivariable nonlinear process is decoupled into multiple single-loop systems and the high dimensions of the process data are reduced such that the corresponding DDLVAC is simplified. Further, the DDLVAC only depends on the I/O data without requiring any model information of the original process. Theoretical analysis confirms the validity of the DDLVAC. The simulation study demonstrates the advantages of the DDLVAC such as less storage space, smaller computation burden, less control cost, as well as more robustness against uncertainties.

Keywords:

• Data-driven control
• latent variable control
• dynamic PLS
• dynamic linearisation
• nonlinear multivariable processes

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China (62273192, 62003097, 62203245, 62003183), the Talent Introduction and Cultivation Plan for Youth Innovation of Universities in Shandong Province.