Abstract
Column flotation is an efficient method commonly used in the mineral industry to separate useful minerals from ores of low grade and complex mineral composition. Its main purpose is to achieve maximum recovery while ensuring desired product grade. This work addresses a model predictive control design for a mineral column flotation process modeled by a set of nonlinear coupled heterodirectional hyperbolic partial differential equations (PDEs) and ordinary differential equations (ODEs), which accounts for the interconnection of well-stirred regions represented by continuous stirred tank reactors (CSTRs) and transport systems given by heterodirectional hyperbolic PDEs, with these two regions combined through the PDEs’ boundaries. The model predictive control considers both optimality of the process operations and naturally present input and state/output constraints. For the discrete controller design, spatially varying steady-state profiles are obtained by linearizing the coupled ODE–PDE model, and then the discrete system is obtained by using the Cayley–Tustin time discretization transformation without any spatial discretization and/or without model reduction. The model predictive controller is designed by solving an optimization problem with input and state/output constraints as well as input disturbance to minimize the objective function, which leads to an online-solvable finite constrained quadratic regulator problem. Finally, the controller performance to keep the output at the steady state within the constraint range is demonstrated by simulation studies, and it is concluded that the optimal control scheme presented in this work makes this flotation process more efficient.
Highlights
Since its first commercial application in the 1980s [1], column flotation has attracted the attention of many researchers
This paper proposes and develops a model predictive control design for the column flotation process, considering the process state/output and input control constraints
Model predictive control algorithms are developed for the column flotation process that take into account the input and state/output constraints as well as the input disturbance
Summary
Since its first commercial application in the 1980s [1], column flotation has attracted the attention of many researchers. One of its major advantages is that it can explicitly handle constraints while dealing with multiple-input multiple-output process setting [17] This ability comes from its model-based prediction of the future dynamic behaviour of the system. This paper proposes and develops a model predictive control design for the column flotation process, considering the process state/output and input control constraints. The steady-state profiles are utilized to linearize the original nonlinear system, and the discrete model is realized by the Cayley–Tustin time discretization transformation [18,19,20] By using this method, the continuous linear infinite-dimensional. The paper is organized as follows: Section 2 develops the model of the column flotation process, and the discrete version of the system is obtained by using the Cayley–Tustin time discretization transformation.
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