**5. Conclusions**

This paper proposes a multi-point feeding strategy for aluminum reduction cell based on distributed subspace predictive control. This method combines the subspace method with the idea of distributed model predictive control using process data and designs a distributed controller through the input and output data. Therefore, it overcomes the shortcomings of centralized control and decentralized control and achieves the performance optimization of the entire complex large system at a lower cost. Compared with traditional methods, the proposed control strategy has the following advantages:

(1) Each feeding device is controlled by an independent controller, and the distributed control method which combines the advantages of centralized and decentralized control is adopted, overcoming their shortcomings.

(2) The mutual influence between the various subsystems and the influence of sudden interference are considered. For example, when the feeding amount is inaccurate, the controller can also control the concentration of alumina well to ensure the stability of the reduction cell.

Compared with traditional control strategies, the method developed in this paper can control the uniform distribution of alumina concentration more effectively, improve the production efficiency of aluminum plants and save production costs. However, in the actual production process, with the passage of time, the change of aluminum reduction cell health status will affect the accuracy of the prediction model and further affect the control accuracy. Therefore, combining the distributed subspace predictive control with the adaptive idea and improving the adaptability of the method by updating the parameters of the predictive model are the key avenues of research future.

**Author Contributions:** Conceptualization, J.C. and Q.L.; methodology, P.W. and X.L.; software, P.W.; validation, R.H. and H.L.; formal analysis, J.C.; investigation, P.W.; resources, Q.L. and B.C.; data curation, J.C.; writing—original draft preparation, P.W.; writing—review and editing, J.C. and X.L.; visualization, P.W. and J.C.; supervision, Q.L. and R.H.; project administration, H.L. and B.C.; funding acquisition, J.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the China Postdoctoral Science Foundation, gran<sup>t</sup> number 2021M690798; Guizhou Province Science and Technology Plan Project, gran<sup>t</sup> number [2021] General 085; National Natural Science Foundation of China, gran<sup>t</sup> number 61603034; The Fundamental Research Funds for the Central Universities, gran<sup>t</sup> number FRF-DF-20-14.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
