Optimizing flotation performance using extremum seeking control

Abstract

In this dissertation, a flotation circuit is controlled in simulation using an extremum seeking control (ESC) approach to optimize the flotation performance of the circuit using peak air recovery. Flotation is a separation process in the mineral processing chain. A comminution process such as a grinding circuit first grounds the raw ore from a mine into fine particles, then the flotation circuit is responsible for separating the valuable minerals from the waste material or gangue. A flotation process achieves this by exploiting the difference in hydrophobicity between the valuable minerals and the gangue. Air is pumped into the bottom of the flotation cell to create bubbles in the cell. Chemical reagents such as collectors are added to the slurry to ensure the valuable minerals are hydrophobic, and the gangue is hydrophilic. As the bubbles rise through the slurry, the valuable minerals attach to the bubbles and rise to a froth layer at the top of the cell, from where it overflows and can be concentrated.

The flotation process has two important performance properties: the grade is how pure the final product is, and the recovery is how much of the valuable minerals have been concentrated. Grade and recovery are inversely proportional, which creates the control challenge of selecting the optimal grade and recovery operating points. A solution to this control challenge is to maximize air recovery. Air recovery is the fraction of air introduced to the cell that overflows in unburst bubbles and has been shown to be a measure of froth stability. It is assumed that optimal performance is achieved at the operating point where the air recovery is maximized as the froth layer is stable and the mineral recovery of the flotation cell is optimized.

A model-free adaptive control strategy in the form of ESC is proposed to control the flotation circuit at the peak air recovery operating point and optimize the flotation performance. The ESC controller explores an unknown static map of the objective function and searches for the extremum. Two gradient-based ESCs, a classical perturbation-based ESC and a time-varying ESC, as well as a non-gradient-based direct search Nelder-Mead simplex ESC, are implemented on a model that simulates a flotation circuit and used to steer the plant towards the peak in air recovery. The three ESC methods do not depend on a process model to optimize the plant and only use the online measurement of the objective function to optimize the process.

Two control strategies are implemented: a single-input perturbation and a multiple-input perturbation strategy. The implemented ESC controllers are evaluated in two simulation scenarios that investigate the optimization ability of the ESC controllers and the disturbance rejection ability of the ESC controllers. The three ESCs can respectively optimize the flotation circuit in both strategies and find the peak air recovery operating point. The simplex ESC can converge quickly to the optimum but does not adapt to changing conditions. The gradient-based ESCs can track the time-varying peak air recovery operating point in the presence of an external disturbance.

The convergence time of the gradient-based controllers is relatively slow due to the time scale separation required between the flotation dynamics and the optimization rate. The multiple-input perturbation strategy resulted in slightly faster convergence in the gradient-based controllers, but with slightly worse performance compared to the single-input perturbation strategy. The convergence time of the simplex ESC becomes much slower when the second input is also perturbed due to the added complexity. The ESCs are ideally suited for model-independent long-term automated optimization of a flotation circuit with a slow time-varying optimal operating point.