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Fractional order controllers for throughput and product quality control in a grinding mill circuit. (English) Zbl 1429.93169

Summary: This paper presents the design and application of a multiple-input-multiple-output fractional order proportional-integral (MIMO FOPI) controller to a grinding mill circuit. The MIMO FOPI controller parameters are tuned using an off-line optimization process based on particle swarm optimization (PSO). Its performance is compared to a single-input-single-output fractional order proportional-integral (SISO FOPI) controller designed and tuned using the same procedure based on PSO. The results show that the MIMO FOPI achieves better results compared to the SISO FOPI controller in most of the cases simulated, even in the presence of hardness and composition variations in the processed ore, and also in the presence of process noise.

MSC:

93C35 Multivariable systems, multidimensional control systems
93C83 Control/observation systems involving computers (process control, etc.)
93C15 Control/observation systems governed by ordinary differential equations
34A08 Fractional ordinary differential equations

Software:

Ninteger; CRONE
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References:

[1] Aguila-Camacho, N.; Duarte-Mermoud, M. A., Fractional adaptive control for an automatic voltage regulator, ISA Trans., 52, 807-815 (2013)
[2] Aguila-Camacho, N.; Roux, J. D.L.; Duarte-Mermoud, M. A.; Orchard, M. E., Control of a grinding mill circuit using fractional order controllers, J. Process Control, 53, 80-94 (2017)
[3] Chen, X.; Li, Q.; Fei, S., Constrained model predictive control in ball mill grinding process, Powder Tech., 186, 31-39 (2008)
[4] Chen, X.; Zhai, J.; Li, S.; Li, Q., Application of model predictive control in ball mill grinding circuit, Minerals Eng., 20, 1099-1108 (2007)
[5] Coetzee, L. C., Robust nonlinear model predictive control of a closed run-of-mine ore milling circuit (2009), University of Pretoria, PhD. thesis
[6] Coetzee, L. C.; Craig, I. K.; Kerrigan, E., Robust nonlinear model predictive control of a run-of-mine ore milling circuit, IEEE Trans. Control Syst. Tech., 18, 222-229 (2010)
[7] Constrained particle swarm optimization, http://www.mathworks.com/matlabcentral/fileexchange/25986-constrained-particle-swarm-optimization (2017).
[8] I.K. Craig, C. Aldrich, R. Braatz, F. Cuzzola, E. Domlan, S. Engell, J. Hahn, V. Havlena, A. Horch, B. Huang, M. Khanbaghi, A. Konstantellos, W. Marquardt, T. McAvoy, T. Parisini, S. Pistikopoulos, T. Samad, S. Skogestad, N. Thornhill, J. Yu, The impact of control technology: control in the process industries, www.ieeecss.org (Last accessed on 2016-06-28).
[9] Duarte-Mermoud, M. A.; Castillo, A.; Sepúlveda, F.; Contreras, A.; Giménez, P.; Castelli, L., Multivariable control of grinding plants: a comparative simulation study, ISA Trans., 41, 57-79 (2002)
[10] Duarte-Mermoud, M. A.; Sepúlveda, F.; Castillo, A.; Contreras, A.; Lazcano, V.; Giménez, P.; Castelli, L., A comparative experimental study of five multivariable control strategies applied to a grinding plant, Powder Tech., 104, 1-28 (1999)
[11] Duarte-Mermoud, M. A.; Suárez, A.; Bassi, D., Control of grinding plants using predictive multivariable neural control, Powder Tech., 115, 193-206 (2001)
[12] Hulbert, D. G.; Craig, I. K.; Coetzee, M. L.; Tudor, D., Multivariable control of a run-of-mine milling circuit, J. South African Inst. Min. Metal., 90, 173-181 (1990)
[13] Ordóñez Hurtado, R. H., Aplicación de la técnica PSO a la determinación de funciones de Lyapunov cuadráticas comunes y a sistemas adaptables basados en modelos de error (2012), University of Chile, PhD. thesis
[14] Ordóñez Hurtado, R. H.; Duarte-Mermoud, M. A., Finding common quadratic Lyapunov functions for switched linear systems using particle swarm optimization, Int. J. Control, 85, 12-25 (2012) · Zbl 1282.93216
[15] Kilbas, A.; Srivastava, H.; Trujillo, J., Theory and Applications of Fractional Differential Equations (2006), Elsevier · Zbl 1092.45003
[16] IEEE-SMC, Lille, France
[17] Moradi, M., A genetic-multivariable fractional order PID control to multi-input multi-output processes, J. Process Control, 24, 336-343 (2014)
[18] Muresan, C. I.; Dulf, E. H.; Copot, C.; De Keyser, R.; Ionescu, C., Design and analysis of a multivariable fractional order controller for a non-minimum phase system, J. Vib. Control, 22, 2187-2195 (2016)
[19] Muresan, C. I.; Dulf, E. H.; Ionescu, C., Robustness evaluation of a multivariable fractional order PI controller for time delay processes, Control Intell. Syst., 42, 112-118 (2014)
[20] Olivier, L. E.; Craig, I. K.; Chen, Y. Q., Fractional order and BICO disturbance observers for a run-of-mine ore milling circuit, J. Process Control, 22, 3-10 (2012)
[21] Oustaloup, A., La Commande CRONE: Commande Robuste d’ordre Non Entier (1991), Hermes, Paris · Zbl 0864.93003
[22] Petrás, I., Tunning and implementation methods for fractional-order controllers, Fract. Calc. Appl. Anal., 15, 282-303 (2012) · Zbl 1269.93039
[23] Podlubny, I. S., Fractional Differential Equations (1999), Academic Press: Academic Press San Diego, CA · Zbl 0924.34008
[24] Pomerleau, A.; Hodouin, D.; Desbiens, A.; Gagnon, E., A survey of grinding circuit control methods: from decentralized PID controllers to multivariable predictive controllers, Powder Tech., 108, 103-115 (2000)
[25] Ramasamy, M.; Narayanan, S.; Rao, C., Control of ball mill grinding circuit using model predictive control scheme, J. Process Control, 15, 273-283 (2005)
[26] Le Roux, J. D.; Craig, I. K., Reducing the number of size classes in a cumulative rates model used for process control of a grinding mill circuit, Powder Tech., 246, 169-181 (2013)
[27] Le Roux, J. D.; Craig, I. K.; Hulbert, D. G.; Hinde, A. L., Analysis and validation of a run-of-mine ore grinding mill circuit model for process control, Miner. Eng., 43-44, 121-134 (2013)
[28] Le Roux, J. D.; Olivier, L. E.; Naidoo, M. A.; Padhi, R.; Craig, I. K., Throughput and product quality control for a grinding mil circuit using non-linear MPC, J. Process Control, 42, 35-50 (2016)
[29] Le Roux, J. D.; Padhi, R.; Craig, I. K., Optimal control of grinding mill circuit using model predictive static programming: a new nonlinear MPC paradigm, J. Process Control, 24, 29-40 (2014)
[30] Shah, P.; Agashe, S., Review of fractional PID controller, Mechatronics, 38, 29-41 (2016)
[31] Song, X.; Chen, Y. Q.; Tejado, I.; Vinagre, B. M., Multivariable fractional order PID controller design via LMI approach, Proceedings of the Eighteenth IFAC World Congress (2011), Milano: Milano Italy
[32] Suárez, J.; Vinagre, B. M.; Chen, Y. Q., A fractional adaptation scheme for lateral control of an AGV, J. Vib. Control, 14, 9-10, 1499-1511 (2008) · Zbl 1229.70086
[33] Tejado, I.; HosseinNia, S. H.; Vinagre, B. M., Adaptive gain-order fractional control for network-based applications, Fract. Calc. Appl. Anal., 17, 462-482 (2014) · Zbl 1303.93104
[34] Valerio, D.; Costa, J. S.D., Ninteger: a non-integer control toolbox for matlab, Proceedings of the Fractional Derivatives and Applications. IFAC (2004), Bordeaux: Bordeaux Italy
[35] Vinagre, B. M.; Petrás, I.; Podlubny, I.; Chen, Y. Q., Using fractional order adjustment rules and fractional order reference models in model-reference adaptive control, Nonlinear Dyn., 29, 269-279 (2002) · Zbl 1031.93110
[36] Wei, D.; Craig, I. K., Economic performance assessment of two ROM ore milling circuit controllers, Miner. Eng., 22, 826-839 (2009)
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