Paper:

# A Control System for the Ball Mill Grinding Process Based on Model Predictive Control and Equivalent-Input-Disturbance Approach

## Mingxing Fang, Dezhi Zheng, Xiaoxiao Qiu, and Youwu Du

College of Physics and Electronic Information, Anhui Normal University

Wuhu Anhui 241000, China

Stable control of the ball mill grinding process is very important to reduce energy losses, enhance operation efficiency, and recover valuable minerals. In this work, a controller for the ball mill grinding process is designed using a combination of model predictive control (MPC) with the equivalent-input-disturbance (EID) approach. MPC has been researched and applied widely as one of the multi-variable control algorithms for grinding. It is used to decouple in real time. The controller design does not deal with the disturbances directly. However, strong disturbances such as those caused by ore hardness and feed particle size exist in the ball mill grinding. EID estimates the equivalent disturbance of the grinding circuit in the control input channel and integrates this disturbance directly into the control law in order to suppress disturbances promptly and effectively. This results in good disturbance suppression performance. Simulation results demonstrate that the combination of MPC with EID for controlling the ball mill grinding circuit yields better performance in terms of disturbance rejection, rapid response, and strong robustness as compared to the performance of the MPC and proportional-integral (PI) decoupling control.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.20, No.7, pp. 1152-1158, 2016.

- [1] J. Yang, S. H. Li, X. S. Chen, and Q. Li, “Disturbance rejection of ball mill grinding circuits using DOB and MPC,” Powder Technology, Vol.198, No.2, pp. 219-228, 2010.
- [2] T. A. Apelt and N. F. Thornhill, “Inferential measurement of SAG mill parameters V: MPC simulation,” Minerals Engineering, Vol.22, No.12, pp. 1045-1052, 2009.
- [3] A. Pomerleau, D. Hodouin, A. Desbiens, and E. Gagnon, “A survey of grinding circuit control methods: from decentralized PID controllers to multivariable predictive controllers,” Powder Technology, Vol.108, No.2-3, pp. 103-115, 2000.
- [4] A. V. E. Conradie and C. Aldrich, “Neurocontrol of a ball mill grinding circuit using evolutionary reinforcement learning,” Minerals Engineering, Vol.14, No.10, pp. 1277-1294, 2001.
- [5] T. Chai, L. Zhai, and H. Yue, “Multiple models and neural networks based decoupling control of ball mill coal-pulverizing systems,” J. of Process Control, Vol.21, No.3, pp. 351-366, 2011.
- [6] Y. Umucu, V. Deniz, V. Bozkurt, and Fatih çauglar M., “The evaluation of grinding process using artificial neural network,” Int. J. of Mineral Processing, Vol.146, pp. 46-53, 2016.
- [7] X. S. Chen, S. H. Li, Z. Y. Zhai, and Q. Li, “Expert system based adaptive dynamic matrix control for ball mill grinding circuit,” Expert Systems With Applications, Vol.36, No.1, pp. 716-723, 2009.
- [8] N. Virivinti and K. Mitra, “Fuzzy Expected Value Analysis of an Industrial Grinding Process,” Powder Technology, Vol.268, pp. 9-18, 2014.
- [9] S. W. Lu, P. Zhou, T. Y. Chai, and W. Dai, “Modeling and Simulation of Whole Ball Mill Grinding Plant for Integrated Control,” IEEE Trans. on Automation Science and Engineering, Vol.11, No.4, pp. 1004-1019, 2014.
- [10] X. S. Chen, J. Y. Zhai, S. H. Li, and Q. Li, “Application of model predictive control in ball mill grinding circuit,” Minerals Engineering, Vol.20, No.11, pp. 1099-1108, 2007.
- [11] M. Ramasamy, S. S. Narayanan, and C. Rao, “Control of ball mill grinding circuit using model predictive control scheme,” J. of Process Control, Vol.15, No.3, pp. 273-283, 2005.
- [12] T. J. Besselmann, S. Almèr, and H. J. Ferreau, “Model Predictive Control of Load-Commutated Inverter-Fed Synchronous Machines,” IEEE Trans. on Power Electronics, Vol.31, No.10, pp. 7384-7393, 2016.
- [13] J. Wilson, M. Charest, and R. Dubay, “Non-linear model predictive control schemes with application on a 2 link vertical robot manipulator,” Robotics and Computer-Integrated Manufacturing, Vol.41, pp. 23-30, 2016.
- [14] M. Jalali, A. Khajepour, S. J. Chen, and B. Litkouhi, “Integrated stability and traction control for electric vehicles using model predictive control,” Control Engineering Practice, Vol.54, pp. 256-266, 2016.
- [15] M. Canale, S. Casale-Brunet, E. Bezati, et al. “Dataflow Programs Analysis and Optimization Using Model Predictive Control Techniques,” J. of Signal Processing Systems, pp. 1-11, 2015.
- [16] M. Nauman and A. Hasan, “Efficient Implicit Model-Predictive Control of a Three-Phase Inverter With an Output LC, Filter,” IEEE Trans. on Power Electronics, Vol.31, No.9, pp. 1-1, 2016.
- [17] M. Fang, L. Wu, J. Cheng, Y. Du, and J. She, “Active Structural Control Based on Integration of H∞ Control and Equivalent-Input-Disturbance Approach,” J. Adv. Comput. Intell. Intell. Inform. (JACIII), Vol.20, No.2, pp. 197-204, 2016.
- [18] F. Gao, M. Wu, J. She, and W. Cao, “Disturbance rejection in nonlinear systems based on equivalent-input-disturbance approach,” Applied Mathematics & Computation, Vol.282, pp. 244-253, 2016.
- [19] J. H. She, M. Fang, Y. Ohyama, H. Hashimoto, and M. Wu, “Improving disturbance-rejection performance based on an equivalent-input-disturbance approach,” IEEE Trans. on Industrial Electronics, Vol.55, No.1, pp. 380-389, 2008.
- [20] L. Sun, L. Donghai, and X. Jiang, “Automatic disturbance rejection control for power plant ball mill,” J. of Tsinghua University, Vol.43, No.6, pp. 779-781, 2003.
- [21] Q. M. Cheng and Z. Yong, “Control System of Multi-model PID Neuron Network for Ball Mill,” Proc. of the Csee, Vol.28, No.2, pp. 103-109, 2008.
- [22] P. Tian, P. Ma, and Y. Jiang, “Multi-model control in ball mill process,” Automation of Electric Power Systems, Vol.24, No.13, pp. 41-44, 2000.
- [23] Q. Cheng, X. Du, R. Guo, and Y. Zheng, “Decoupling Compound Control Method Based on Least Squares Vector Machines Multivariable Inverse System and Its Application,” Proc. of the CSEE, Vol.28, No.35, pp. 96-101, 2008.

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