Irkutsk National Research Technical University (Irkutsk, Russia):

Burdonov A. E., Associate Professor, Candidate of Engineering Sciences, slimbul@inbox.ru
Lukyanov N. D., Associate Professor, Candidate of Engineering Sciences, Lukyanov.n@gmail.com

The article discusses an approach aimed at developing an application methodology for the principles and models used in the theory of process control automation. The problems solved in the article are as follows: to try and represent the gravity concentration process (centrifugal concentration) in the form of a transfer function and to establish its parameters. In this case, the limited amount of data obtained in the course of the experiments is the main limitation for building models in the form of differential equations. An original processing and application methodology is proposed for the averaged data used when designing the model. This approach may be applicable to other ore preparation and processing stages as it involves equipment operation using the black box principle. The study is based on replacement of instantaneous characteristics of the input stream with their averaged values and subsequent integration, allowing the creation of a numerical model that coincides with the actual data. Transfer functions and their parameters for tailings and concentrate were established separately. MatLAB software with the Simulink package was used to verify the calculations. As a result, the transfer function was found for a KC-CVD6 device used at a gold deposit and satisfactory simulation results were obtained. The work uses automatic systems identification, system analysis, and mathematical modeling methods, namely, numerical solutions of differential equations using the MatLAB desktop environment with the Simulink package.

1. Pelikh V. V., Salov V. M., Burdonov A. E., Lukyanov N. D. Application of Knelson CVD technology for beneficiation of gold-lead ore. Obogashchenie Rud. 2019. No. 1. pp. 3–11. DOI: 10.17580/or.2019.01.01
2. Murthy Y. R., Tripathy S. K. Process optimization of a chrome ore gravity concentration plant for sustainable development. Journal of the Southern African Institute of Mining and Metallurgy. 2021. Vol. 120. pp. 261–268.
3. Ma L., Wei L., Zhu X., Xu D., Pei X., Xue H. Numerical studies of separation performance of Knelson concentrator for beneficiation of fine coal. International Journal of Coal Preparation and Utilization. 2021. Vol. 41. pp. 40–50.
4. de Freitas Marques Araújo P., Silva P. M. P., do Carmo A. L. V., Gonçalves M. V. L., da Costa R. V., de Melo C. C. A., Lucheta A. R., Montini M. Gravity methods applied to bauxite residue for mineral pre-concentration. Minerals, Metals and Materials Series. 2021. Vol. 6. pp. 68–76.
5. Nayak A., Jena M. S., Mandre N. R. Application of enhanced gravity separators for fine particle processing: An overview. Journal of Sustainable Metallurgy. 2021. Vol. 7. pp. 315–339.
6. Pelikh V. V., Salov V. M., Burdonov A. E., Lukyanov N. D. Establishment of technological dependence of KCCVD6 concentrator operation by means of the argument group accounting method. Izvestiya Tomskogo Politekhnicheskogo Universiteta. Inzhiniring Georesursov. 2020. Vol. 331, No. 2. pp. 139–150.
7. Dehaine Q., Foucaud Y., Kroll-Rabotin J.-S., Filippov L. O. Experimental investigation into the kinetics of Falcon UF concentration: Implications for fluid dynamicbased modelling. Separation and Purification Technology. 2019. Vol. 215. pp. 590–601.
8. Pelikh V. V., Salov V. M., Burdonov A. E., Lukyanov N. D. Model of extraction of baddeleyite from the waste products of the apatite-baddeleyite processing plant at the CVD6 concentrator. Zapiski Gornogo Instituta. 2021. Vol. 248, No. 2. pp. 281–289.

9. Chen Q., Yang H., Tong L., Liu Z., Chen G., Wang J. Analysis of the operating mechanism of a Knelson concentrator. Minerals Engineering. 2020. Vol. 158. DOI: 10.1016/j.mineng.2020.106547.
10. Chen Q., Yang H.-Y., Tong L.-L. Processing a gold ore from Hainan province using Knelson gravity concentration–flotation. Journal of Northeastern University. 2020. Vol. 41. pp. 413–417, 451.
11. Oney O., Samanli S., Niedoba T., Pięta P., Surowiak A. Determination of the important operating variables on cleaning fine coal by Knelson concentrator and evaluation of the performance through upgrading curves. International Journal of Coal Preparation and Utilization. 2020. Vol. 40. pp. 666–678.
12. Basnayaka L., Albijanic B., Subasinghe N. Performance evaluation of processing clay-containing ore in Knelson concentrator. Minerals Engineering. 2020. Vol. 152. DOI: 10.1016/j.mineng.2020.106372.
13. Chen Q., Yang H.-Y., Tong L.-L., Niu H.-Q., Zhang F.-S., Chen G.-M. Research and application of a Knelson concentrator: A review. Minerals Engineering. 2020. Vol. 152. DOI: 10.1016/j.mineng.2020.106339.
14. Perepelkin M. A., Sklyanov V. I. Dynamic modeling of mineral bed mobility in centrifugal concentrators. Gornaya Promyshlennost'. 2021. No. 2. pp. 114–119.
15. Fedotov P. K., Senchenko A. E., Fedotov K. V., Burdonov A. E. A study of gold ore for processability by gravity separation techniques. Tsvetnye Metally. 2021. No. 2. pp. 8–16. DOI: 10.17580/tsm.2021.02.01
16. Pilov P. I., Kirnarsky A. S. Industrial use of single parameters as a tool to improve separation selectivity. Obogashchenie Rud. 2020. No. 2. pp. 21–28. DOI: 10.17580/or.2020.02.04
17. Koyzhanova A. K., Kenzhaliev B. K., Magomedov D. R., Abdyldaev N. N. Development of a combined processing technology for low-sulfide gold-bearing ores. Obogashchenie Rud. 2021. No. 2. pp. 3–8. DOI: 10.17580/or.2021.02.01
18. Petrov S. V., Bederova L. L., Borozdin А. P. Upon the method of reliable determination of noble metals grades in samples with high occurrence of native metals. Obogashchenie Rud. 2015. No. 4. pp. 44–48. DOI: 10.17580/or.2015.04.08
19. Das A., Sarkar B. Advanced gravity concentration of fine particles: A review. Mineral Processing and Extractive Metallurgy Review. 2018. Vol. 39. pp. 359–394.
20. Fatahi M. R., Farzanegan A. Computational modelling of water flow inside laboratory Knelson concentrator bowl. Canadian Metallurgical Quarterly. 2019. Vol. 58. pp. 140–155.
21. Ghaffari A., Farzanegan A. An investigation on laboratory Knelson concentrator separation performance. Part 3: Multi-component feed separation modelling. Minerals Engineering. 2018. Vol. 122. pp. 185–194.
22. Ghaffari A., Farzanegan A. An investigation on laboratory Knelson concentrator separation performance. Part 1: Retained mass modelling. Minerals Engineering. 2017. Vol. 112. pp. 57–67.
23. Ghaffari A., Farzanegan A. An investigation on laboratory Knelson concentrator separation performance. Part 2: Two-component feed separation modelling. Minerals Engineering. 2017. Vol. 112. pp. 114–124.
24. Brito G., Jerez O., Gutierrez L. Incorporation of rheological characterization in grinding and tailings slurries to optimize the CMP magnetic separation plant. Minerals. 2021. Vol. 11. DOI: 10.3390/min11040386
25. Cheng J., Ren T., Zhang Z., Jin X., Liu D. Influence of two mass variables on inertia cone crusher performance
and optimization of dynamic balance. Minerals. 2021. Vol. 11. DOI: 10.3390/min11020163
26. Malanchuk Y., Khrystyuk A., Moshynskyi V., Denisyuk P., Malanchuk Z., Korniienko V., Martyniuk P. Regularities in the distribution of granulometric composition of tuff while crushing. Mining of Mineral Deposits. 2021. Vol. 15. pp. 66–74.
27. Lee I., Choi K. K., Noh Y., Lamb D. Comparison study between probabilistic and possibilistic methods for problems under a lack of correlated input statistical information. Structural and Multidisciplinary Optimization. 2015. Vol. 47. pp. 175–189.
28. Chanturiya V. A. Innovation-based processes of integrated and high-level processing of natural and technogenic minerals in Russia. Proc. of the 29^th International mineral processing congress IMPC. 2018. pp. 3–12.
29. Nikolić M., Do X. N., Ibrahimbegovic A., Nikolić Ž. Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model. Computer Methods in Applied Mechanics and Engineering. 2018. Vol. 340. pp. 480–499.
30. Sebbouh O., Dossal C. H., Rondepierre A. Convergence rates of damped inertial dynamics under geometric conditions and perturbations. SIAM Journal on Optimization. 2020. Vol. 30. pp. 1850–1877.
31. Xing X. Automatic control theory virtual experiment system based on MATLAB GUI. Journal of Theoretical and Applied Information Technology. 2013. Vol. 49, Iss. 1. pp. 155–160.