Extremum seeking control to optimize mineral recovery of a flotation circuit using peak air recovery

Abstract

A flotation circuit is controlled in simulation using an extremum seeking control (ESC) approach to keep the cells operating at the optimal operating point, as represented by peak air recovery. It is assumed that optimal performance is achieved at this operating point where the froth layer is stable, and the mineral recovery of the flotation cell is maximized. 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 compared on the flotation circuit to steer the plant through an unknown static map towards the peak in air recovery. The three ESCs can respectively optimize the flotation circuit 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 and adapt to an external disturbance. Although the three ESC methods are not dependent on a process model to optimize the plant, their convergence times are relatively slow. The ESCs are ideally suited for model-independent long-term automated optimization of a flotation circuit with a slow time-varying optimal operating point.