Nonlinear control of bubble size in a laboratory flotation column

Gas dispersion properties have proven to be key variables of the flotation process. Among them, bubble surface area flux (BSAF) has been reported to linearly correlate with the flotation rate constant; therefore, it is a potential variable to achieve a desired metallurgical performance. BSAF can be represented as a combination of two other gas dispersion properties: superficial gas velocity and Sauter mean bubble diameter. Thus, controlling BSAF implies controlling bubble size and superficial gas velocity. This work focuses on the nonlinear control of the Sauter mean bubble diameter. Sauter bubble mean diameter was indirectly calculated from the bubble size distribution, estimated by using a Gaussian mixture model. To improve controllability, a so-called frit-and-sleeve sparger was installed to regulate bubble size independently from superficial gas velocity. With this device, the bubble size can be modified by manipulating the water flow rate circulating through the sleeve that surrounds the porous ring. A Wiener model is used to represent the dynamic relationship between the sleeve water flow rate and Sauter mean diameter. Wiener models consist of a linear system in series with a memory-less (static) nonlinear element. An IMC controller based on the identified Wiener model was implemented in a laboratory flotation column. Tracking performance and rejection of gas velocity and unmeasured frother concentration variations were then successfully evaluated.