Predictive Control of the Iron Ore Beneficiation Process Based on the Hammerstein Hybrid Model

Porkuian, Olga; Morkun, Vladimir; Morkun, Natalia; Serdyuk, Oleksandra

doi:10.2478/ama-2019-0036

Abstract

Non-linear, dynamic, non-stationary properties characterize objects of the iron ore beneficiation line. Therefore, for their approximation, it is advisable to use models of the Hammerstein class. As a result of comparing the three models of Hammerstein: simple, parallel and recursive-parallel, it was shown that the best result for identifying the considered processes of magnetic beneficiation of iron ore by the minimum error criterion was obtained using the Hammerstein recursive-parallel model. Hence, it is recommended for the identification of beneficiation production objects.

References

1. Abba S.I., Nourani V., Elkiran G. (2019), Multi-parametric modeling of water treatment plant using AI-based non-linear ensemble, Aqua, 68 (7), 547–561.10.2166/aqua.2019.078
Search in Google Scholar Back to article
2. Abonyi J., Nagy L., Szeifert F. (2000), Hybrid fuzzy convolution modelling and identification of chemical process systems, International Journal of Systems Science, 31, 457–466.10.1080/002077200291046
Search in Google Scholar Back to article
3. Babuska R. (1998), Fuzzy Modeling for Control, Kluwer Academic Publishers, Boston.
Search in Google Scholar Back to article
4. Babuska R., Roubos J.A., Verbruggen H.B. (1998), Identification of MIMO systems by input-output TS fuzzy models, Proceedings FUZZ-IEEE’98, Anchorage, Alaska, 57–69.
Search in Google Scholar Back to article
5. Botto M. Ayala, van den Boom T.J.J., Krijgsman A., S’a da J. (1999), Costa Constrained nonlinear predictive control based on input-output linearization using a neural network, International Journal of Control, 72(17), 1538–1554.10.1080/002071799220038
Search in Google Scholar Back to article
6. Chen H., Ding F. (2015), Hierarchical least-squares identification for Hammerstein nonlinear controlled autoregressive systems, Circuits, Systems and Signal Processing, 34(1), 61–75.10.1007/s00034-014-9839-9
Search in Google Scholar Back to article
7. Chen J., Wang X. (2015), Identification of Hammerstein systems with continuous nonlinearity, Information Processing Letters, 115(11), 822–827.10.1016/j.ipl.2015.06.004
Search in Google Scholar Back to article
8. Clarke D. W., Tuffs P.S., Mothadi C. (1989), Generalized predictive control – part I. the basic algorithm, Automatica, 23, 137–148.10.1016/0005-1098(87)90087-2
Search in Google Scholar Back to article
9. Clarke D.W., Mohtadi C. (1989), Properties of generalized predictive control, Automatica, 25(6), 859–875.10.1016/0005-1098(89)90053-8
Search in Google Scholar Back to article
10. Falck T., Dreesen P., Brabanter K., Pelckmans K., De Moor B., Suykens J.A.K. (2012), Least-Squares Support Vector Machines for the identification of Wiener–Hammerstein systems, Control Engineering Practice, 20(11), 1165–1174.10.1016/j.conengprac.2012.05.006
Search in Google Scholar Back to article
11. Fruzetti K.P., Palazoglu A., McDonald K.A. (1997), Nonlinear model predictive control using Hammerstein models, Journal of Process Control, 7(1), 31–41.10.1016/S0959-1524(97)80001-B
Search in Google Scholar Back to article
12. Garcia C.E., Morari M. (1982), Internal model control: 1.A unifying review and some new results, Ind. Eng. Chem. Process Res. Dev, 21, 308–323.
Search in Google Scholar Back to article
13. Ikhouane F., Giri F. (2014), A unified approach for the parametric identification of SISO/MIMO Wiener and Hammerstein systems, Journal of the Franklin Institute, 351(3), 1717–172710.1016/j.jfranklin.2013.12.016
Search in Google Scholar Back to article
14. Ivanov A.I. (1991), Ortogonalnaya identifikatsiya nelineynykh dinamicheskikh sistem s konechnoy i beskonechnoy pamyatyu pri odnom i neskol’kikh vkhodakh [Orthogonal identification of nonlinear dynamical systems with finite and infinite memory at one or several inputs], NIKIRET, Penza (In Russian),
Search in Google Scholar Back to article
15. Ivanov A.I. (1995), Bystryye algoritmy sinteza nelineynykh dinamicheskikh modeley po eksperimental’nym dannym [Fast algorithms for the synthesis of nonlinear dynamic models from experimental data], NPF “Kristall”, Penza (In Russian),
Search in Google Scholar Back to article
16. Junhao Shi, Sun H.H. (1990), Nonlinear system identification for cascaded block model: an application to electrode polarisation impedance, IEEE Trans. Biomed. Eng, 6, 574–587.
Search in Google Scholar Back to article
17. Kazuo T., Wang H.O. (2001), Fuzzy Control Systems Design And Analysis, John Wiley&Sons.
Search in Google Scholar Back to article
18. Le F., Markovsky I., Freeman C.T., Rogers E. (2012), Recursive identification of Hammerstein systems with application to electrically stimulated muscle, Control Engineering Practice, 20(4), 386–39610.1016/j.conengprac.2011.08.001
Search in Google Scholar Back to article
19. Leontaritis I.J. Billings S.A. (1987), Experimental design and identifiably for nonlinear systems, International Journal of Systems Science,18, 189–202.10.1080/00207728708963958
Search in Google Scholar Back to article
20. Li Yu., Shchetsen M. (1968), Opredeleniye yader Vinera-Khopfa metodom vzaimnoy korrelyatsii. Tekhnicheskaya kibernetika za rubezhom [Determination of Wiener-Hopf kernels by cross-correlation. Technical cybernetics abroad], Mashinostroyeniye, Moskow (In Russian),
Search in Google Scholar Back to article
21. Ma J., Ding F., Xiong W., Yang E. (2016), Combined state and parameter estimation for Hammerstein systems with time-delay using the Kalman filtering, International Journal of Adaptive Control and Signal Processing, 00:1–17. DOI: 10.1002/acs
Search in Google Scholar Back to article
22. Mete S., Ozer S., Zorlu H. (2016), System identification using Hammerstein model optimized with differential evolution algorithm, AEU - International Journal of Electronics and Communications, 70(12), 1667–1675.10.1016/j.aeue.2016.10.005
Search in Google Scholar Back to article
23. Morkun V., Morkun N., Pikilnyak A. (2014a), Ultrasonic phased array parameters determination for the gas bubble size distribution control formation in the iron ore flotation, Metallurgical and Mining Industry, 6(3), 28–31.
Search in Google Scholar Back to article
24. Morkun V., Morkun N., Pikilnyak A. (2014b), Ultrasonic facilities for the ground materials characteristics control, Metallurgical and Mining Industry, 6(2), 31–35.
Search in Google Scholar Back to article
25. Morkun V., Morkun N., Pikilnyak A. (2014c), The adaptive control for intensity of ultrasonic influence on iron ore pulp, Metallurgical and Mining Industry, 6, 8–11.
Search in Google Scholar Back to article
26. Morkun V., Morkun N., Pikilnyak A. (2015c), Adaptive control system of ore beneficiation process based on Kaczmarz projection algorithm, Metallurgical and Mining Industry, 2, 35–38.
Search in Google Scholar Back to article
27. Morkun V., Morkun N., Tron V. (2015a), Formalization and frequency analysis of robust control of ore beneficiation technological processes under parametric uncertainty, Metallurgical and Mining Industry, 5, 7–11.
Search in Google Scholar Back to article
28. Morkun V., Morkun N., Tron V. (2015b), Model synthesis of nonlinear nonstationary dynamical systems in concentrating production using Volterra kernel transformation, Metallurgical and Mining Industry, 10, 6–9.
Search in Google Scholar Back to article
29. Morkun V., Morkun N., Tron V., Hryshchenko S. (2018), Synthesis of robust controllers for the control systems of technological units as iron ore processing plants, Eastern European Journal of Enterprise Technologies, 1(2-91), 37–47.10.15587/1729-4061.2018.119646
Search in Google Scholar Back to article
30. Morkun V., Tcvirkun S. (2014), Investigation of methods of fuzzy clustering for determining ore types, Metallurgical and Mining Industry, 5, 11–14.
Search in Google Scholar Back to article
31. Narendra K.S., Gallman P.G. (1966), An iterative method for the identification of nonlinear systems using the Hammerstein model, IEEETrans. Automatic Control, 12, 546.10.1109/TAC.1966.1098387
Search in Google Scholar Back to article
32. Ozer S., Zorlu H., Mete S. (2016), System identification application using Hammerstein model, Sadhana, 41(6), 597–605.10.1007/s12046-016-0505-8
Search in Google Scholar Back to article
33. Piroddi L., Farina M., Lovera M. (2012), Black box model identification of nonlinear input–output models: A Wiener–Hammerstein benchmark, Control Engineering Practice, 20(11), 1109–1118.10.1016/j.conengprac.2012.03.002
Search in Google Scholar Back to article
34. Postlethwaite B.E. (1996), Building a model-based fuzzy controller, Fuzzy Sets and Systems, 79, 3–13.10.1016/0165-0114(95)00287-1
Search in Google Scholar Back to article
36. Rébillat M., Hennequin R., Corteel E., Katz B. (2010), Identification of cascade of Hammerstein models for the description of nonlinearities in vibrating devices, Journal of Sound and Vibration, 330(5), 1018–1038.10.1016/j.jsv.2010.09.012
Search in Google Scholar Back to article
37. Rossiter J.A. (2003), Model-Based Predictive Control: a Practical Approach, CRC Press.
Search in Google Scholar Back to article
38. Sanches J.M.M., Rodellar J. (1996), Adaptive predictive control: from the concepts to plant optimization, Prentice Hall International (UK) Limited.
Search in Google Scholar Back to article
39. Sjoberg J., Zhang Q., Ljung L., Benveniste A., Deylon B., Glorennec P-Y., Hjalmarsson H., Juditsky A. (1995), Nonlinear black-box modeling in system identification: a unified overview, Automatica, 31, 1691–1724.10.1016/0005-1098(95)00120-8
Search in Google Scholar Back to article
40. Stoica P. (1981), On the convergence of an iterative algorithm used for Hammerstein system identification, IEEETrans. Automatic Control, 26, 967–969.10.1109/TAC.1981.1102761
Search in Google Scholar Back to article
41. Tobi T., Hanafusa T. (1991), A practical application of fuzzy control for an airconditioning system, International Journal of Approximate Reasoning, 5, 331–348.10.1016/0888-613X(91)90016-F
Search in Google Scholar Back to article
42. Verhaegen M., Westwick D. (1996), Identifying MIMO Hammerstein systems in the context of subspace model identification, International Journal of Control, 63, 331–349.10.1080/00207179608921846
Search in Google Scholar Back to article
43. Wills A., Ninness B. (2012), Generalised Hammerstein–Wiener system estimation and a benchmark application, Control Engineering Practice, 20(11), 1097–1108.10.1016/j.conengprac.2012.03.011
Search in Google Scholar Back to article
44. Young A.D. (1977), State of the art and trends in computers and control equipment, 2-nd IFAC Symp. “Automat. Mining, Miner. and Metal. Proc.”, Pretoria, 41–46.
Search in Google Scholar Back to article
45. Yucai Z. (1999), Parametric Wiener model identification for control, Proceedings IFAC World Congress, Bejing, China, 3a–02–1, 34–46.
Search in Google Scholar Back to article
46. Zubov D.A. (2006), Passifikatsiya i sintez algoritma avtomaticheskogo upravleniya odnim klassom SISO-obyektov ugleobogashcheniya s ispolzovaniyem algebry Li [Passification and synthesis of an automatic control algorithm for one class of SISO objects for coal enrichment using Lie algebra], Zbagachennya korisnikh kopalin, 24(65), 80–87 (In Russian),
Search in Google Scholar Back to article

Predictive Control of the Iron Ore Beneficiation Process Based on the Hammerstein Hybrid Model

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