State Estimation of a Flotation Column using Fundamental Dynamic Models

Two on-line model-based state estimators are used in a semi-batch flotation column system based on a two-phase fundamental dynamic model. The column is modeled as two interconnected plug-flow reactors, representing the pulp and the froth zones. The model accounts for the appearance and breakage of three bubble size classes. The unknown states representing the gas holdup through the column have been estimated, assuming that the gas holdup of the bubble size classes at the exit on top of the column can be measured. It is confirmed that the proposed estimator for a two-phase case well predicts the gas holdup propagation through a lab-scale two-phase semi-batch column flotation based on experimental data. The performance of the model-based ensemble Kalman filter is comparable to that of the Luenberger observer with the same operating conditions. Gas holdup propagation was better captured by the Luenberger observer for state estimation in this simplified version of a flotation system. However, the ensemble Kalman filter has an acceptable performance while being a better option than the linear Luenberger observer for state estimation of more complex cases, such as the continuous nonlinear three-phase model of a flotation column with parameter uncertainty. Thereby, the ensemble Kalman filter algorithm is used to estimate the gas holdup through the column and the concentration of attached and free minerals in the upward and downward flows in the case of a three-phase continuous flotation column.