(184u) Modelling and MPC Design of Mineral Column Flotation Process

Column Flotation is a commonly used separation method in the mineral processing industry, it can effectively separate useful minerals from ore with low grade and complex mineral composition and has been widely used in industry for decades. Since it was first used in the commercial application of mineral separation in 1980s [1], the modelling and/or control of the column flotation processes have attracted the attention of many researchers and gradually become a popular research field. Its main purpose is to ensure maximum recovery of minerals while ensuring products (concentrates) grade, the optimization of the flotation process through control effects could improve recovery and product grades for greater benefits [2].

The column flotation process is a highly nonlinear distributed parameter system (DPS) consisting of gas, water and solid three-phases flows, with multiple inputs and various important parameters are highly interrelated, there are also various sub-process occur during the flotation process. After many years of research and development, flotation process is still not fully understood and production is still relatively inefficient [3].

Motivated by the above, in this work, a three-phase dynamic model and model predictive control design of column flotation process is developed. Based on the process description and conservation of mass, the overall system is described by a set of nonlinear coupled hyperbolic PDEs and ODEs of interface, froth and collection regions, these three subsystems are connected through the boundaries. The steady-state profiles are utilized to linearize the original nonlinear model. The structured preserving Cayley-Tustin time discretization transformation [4] is utilized for the discrete controller design which renders discrete infinite dimensional system without spatial discretization or any model reduction. The model predictive controller is designed by solving the optimization problem to minimization the open-loop objective function at sampling time K [5]. By adding constraints to future inputs, outputs or state variables, the constraints can be explicitly expressed in an online solving quadratic programming. The controller performance to keep the output at the steady state within the constraint range by adjusting the input is demonstrated by simulation studies.

[1] Finch, J. A., and G. S. Dobby. "Column flotation" (1990).

[2] McKee, D. J. "Automatic flotation control-a review of 20 years of effort." Minerals Engineering 4.7-11 (1991): 653-666.

[3] Shean, B. J., and J. J. Cilliers. "A review of froth flotation control." International Journal of Mineral Processing 100.3-4 (2011): 57-71.

[4] Xu, Qingqing, and Stevan Dubljevic. "Linear model predictive control for transport‐reaction processes." AIChE Journal 63.7 (2017): 2644-2659.

[5] Muske, Kenneth R., and James B. Rawlings. "Model predictive control with linear models." AIChE Journal 39.2 (1993): 262-287.