Automatic control of bubble size in a laboratory flotation column

• An adaptive Gaussian mixture model was used to track bubble size distribution.
• A frit and sleeve sparger improved bubble size controllability.
• A Wiener internal model control was used to regulate Sauter bubble mean diameter.
• Good regulation was observed against gas rate and frother concentration variations.

Gas dispersion properties play an important role on determining the metallurgical performance of flotation processes. Indeed, bubble surface area flux (Sb) has been found to correlate with the collection zone flotation rate constant and is therefore a potential variable to regulate in order to achieve a target performance. Sb can be calculated as a combination of two other gas dispersion properties, namely, gas superficial velocity and the Sauter bubble mean diameter. This communication describes the design and implementation of a feedback control system for the Sauter bubble mean diameter in an attempt towards controlling Sb. In order to track changes on bubble size, the Sauter bubble mean diameter was derived from an adaptive bubble size probability density function (PDF). A Gaussian mixture model was used to represent the bubble size PDF and its parameters were updated on-line and in real-time by a dedicated computer from sequentially incoming images. To improve bubble size controllability, a frit-and-sleeve sparging device was installed. This device allows modifying bubble size by manipulating the water flow rate circulating through a sleeve surrounding a porous ring (shear water). A Wiener model is used to represent the dynamic relationship between the shear water flow rate and the Sauter bubble mean diameter. A nonlinear control, based on the internal model control (IMC) structure, was designed and implemented. Tracking and regulation performance against gas velocity and unmeasured frother concentration variations were then successfully evaluated in a two-phase system.

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