Abstract

A constrained model predictive control (MPC) strategy is proposed to deal with the problem of optimizing flotation column operation using secondary variables. Froth depth, collection zone gas hold-up and bias rate are selected as secondary variables to be controlled whereas tailing, wash-water and gas flow rate are used as manipulated variables. The control problem was formulated in order to minimize the tracking error of the gas hold-up and bias rate by maintaining gas flow rate, wash-water flow rate and bias rate within their operational limits. In particular, a strategy was conceived to optimize the column flotation process based on establishing an unreachable high set point for the gas hold-up (which is equivalent to maximizing the bubble surface area available for particle collection at a given flotation reagent dosage and thus recovery), while simultaneously satisfying operational constraints (such as ensuring a positive bias rate to prevent gangue entrainment and therefore concentrate grade deterioration). Several other operational constraints on wash water, gas rate, gas hold-up and bias rate were considered, their use being justified from a processing point of view. Since this study deals with the hydrodynamic characteristics of flotation columns, a pilot flotation column working with a two-phase system is sufficient to demonstrate the advantages of using predictive control for this process optimization.