Model Predictive Control of Mineral Column Flotation Process
Abstract
:1. Introduction
2. Model Formulation of Column Flotation
2.1. Model Description
2.1.1. Model for Collection Region
2.1.2. Model for Froth Region
2.2. Linearized Model
2.3. Discretized Model
2.3.1. Time Discretization for Linear PDE
2.3.2. Time Discretization of Column Flotation System
3. Model Predictive Control Design
4. Simulation Results
5. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
Appendix A. Resolution of Operator A for Discretized Model
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Symbol | Description | Value |
---|---|---|
h | Height of froth region | 1.0 |
l | Height of collection region | 1.0 |
Bubble saturation parameter | 5 | |
Air–water interfacial area | C: 1.0; F: 0.3 | |
Water velocity of collection region | 0.8 | |
Settling/slip velocity | 1 | |
Air holdup | C: 0.3; F: 0.7 | |
Downward water holdup | 0.1 | |
Upward water holdup | C: 0.7; F: 0.2 | |
Air velocity | C: 0.1; F: 0.2 | |
Downward water velocity | 0.1 | |
Upward water velocity | C: 0.08; F: 0.1 | |
Attachment-rate parameter for downward water | C: 1.2; F: 1.0 | |
Attachment-rate parameter for upward water | 1.5 | |
Detachment rate parameter | C: 0.1; F: 0 | |
Transfer rate from upward water to downward water | 0.1 | |
k | Transfer rate from air to downward water | 0.01 |
, , | Initial-condition coefficients | , , |
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Tian, Y.; Luan, X.; Liu, F.; Dubljevic, S. Model Predictive Control of Mineral Column Flotation Process. Mathematics 2018, 6, 100. https://doi.org/10.3390/math6060100
Tian Y, Luan X, Liu F, Dubljevic S. Model Predictive Control of Mineral Column Flotation Process. Mathematics. 2018; 6(6):100. https://doi.org/10.3390/math6060100
Chicago/Turabian StyleTian, Yahui, Xiaoli Luan, Fei Liu, and Stevan Dubljevic. 2018. "Model Predictive Control of Mineral Column Flotation Process" Mathematics 6, no. 6: 100. https://doi.org/10.3390/math6060100