Evaluation and expansion of observable dynamic froth flotation models for control

Abstract

This work builds on existing observable dynamic models of froth flotation circuits, aimed at on-line parameter estimation and model-based control. The models are analysed and two main limitations are identified and addressed: the lack of explicit modelling of reagent effects and the need for dynamic validation on large-scale industrial plant data. The feasibility of expanding a froth flotation model to include reagent effects is investigated. A Sobol sensitivity analysis is used to identify the crucial parameters. The model is expanded with two different reagent effect models. Both expansions include mass balance models of the frother concentration in each cell. The first model expands an empirical parameter in the air recovery model, related to the froth height at which peak air recovery (PAR) is achieved, as a linear function of frother concentration. The second model adds a linear frother concentration term to the existing air recovery model to modify the steady-state air recovery directly. Observability analyses of the expanded models show that all states and the important time-varying model parameters are observable (and identifiable) from the available on-line measurements. Most importantly, the frother concentrations are shown to be observable without concentration measurements. Simulations of the model expansions show that the second model can qualitatively predict the impact of increased frother dosage on air recovery, grade and recovery, while the first model can only predict the correct effect under certain conditions. The implementation of a Moving Horizon Estimator (MHE) based on the model (excluding reagent effects) on data from an industrial rougher bank is investigated with the aim of validating the model and parameter estimation approach. The available plant data and its limitations are discussed and additional model analysis is conducted. An expanded observability analysis of the model identifies groups of parameters for which identifiability is linked. It is shown that without on-line compositional measurements only a reduced model that lumps all recovery mechanisms into a single empirical equation is observable. The reduced model is used to develop the MHE which is implemented on data from the Mogalakwena North Concentrator (MNC) historian. The state and parameter estimates are then used to evaluate the model prediction accuracy over a shifting control horizon, as would be done in model predictive control (MPC). Estimation results show that there are substantial amounts of unmodelled dynamics and/or disturbances. Parameter estimates compensate somewhat, but the model predictions are only accurate over some sections of the data. The lack of on-line compositional measurements as well as uncertainty regarding the validity of calculated measurements and assumptions prevented a fair evaluation of the full potential of the model, but served to highlight drawbacks and challenges that will need to be addressed in future work.