Model Development for Reagent Dosing Control of a Flotation Bank Using Model Predictive Control

Abstract

Flotation reagents are one of the highest costs in the concentrating stage of mining operations. Overuse of reagents can increase these costs. The inflation of reagent costs is one way that profitability is decreased. Alternatively, the inaccurate dosage of reagents can result in poor mineral recovery and grade, which decreases the value of the final concentration product. In addition, the overuse of flotation reagents leads to the excess reagents being carried away in the wastewater, which is an environmental hazard. Model Predictive Control is a technology that can be utilised to optimise reagent dosage. Research has showcased that the current models employed for reagent dosing MPC strategies are linear models. These linear models fail to explain the nonlinear effect of reagent dosage on the grade for a full operating range. Nonlinear models are required to incorporate the nonlinear behaviour of reagents. The performance of a parametric nonlinear auto-regressive with exogenous outputs (NLarx) model was compared to the performance of two linear parametric models, namely a state space model and a linear, Autoregressive Exogenous Inputs, ARX, model. Data collected from the Mt Isa Lead Zinc Concentrator site was used to train and validate the models that represent a rougher bank of the Zinc circuit. The inputs used in model development consisted of reagent flow rates, rougher feed mineral compositions, total airflow rate and the pulp level. Whereas the model outputs were the rougher bank’s Zinc and Pb concentrate grade. The model development results show that the state space models fit the training data better than the NLarx model. However, the NLarx models fit the testing data better than the linear models, providing an improved prediction of unseen data. The linear ARX model and the nonlinear ARX model were used to create linear and nonlinear MPC controllers. These controllers were compared to one another in a simulated environment. The control objective of simulations was to maintain the Zn % in Conc and Pb % in Conc readings at the respective setpoints. Two sets of simulations were used to assess the controller's performance. The first set of simulations was used to evaluate the controller's setpoint tracking performance. The Zn % in Conc and Pb % in Conc setpoints were either stepped up or stepped down in the simulations. The second set of simulations was used to assess the disturbance rejection of the controller. The disturbance variables were altered in these simulations. The simulation results showcase that the nonlinear controller performed better than the linear controller with setpoint tracking. The nonlinear controller executes better setpoint tracking than the linear controller for Zn % in Conc and Pb % in Conc readings when the Pb % in Conc setpoint change is implemented in the simulation. Similarly, the nonlinear controller performs better than the linear controller with setpoint tracking when the Zn % in Conc setpoint is changed. Overall, the nonlinear controller performed better than the linear controller with setpoint tracking. The disturbance rejection results showcased that the nonlinear controller performs better than the linear controller. The nonlinear controller was able to maintain the Zn % in Conc and Pb % in Conc at the setpoint for all simulations when the disturbance variable values were changed. However, the linear controller was not able to maintain the Zn % in Conc and Pb % in Conc at the setpoint for all scenarios.