Nonlinear Model Predictive Control of Process Water Quality in the Closed-Loop Water Circuit of the Aktogai GOK Flotation Plant

This paper presents a simulation-based feasibility study of nonlinear model predictive control (NMPC) for process water quality management in the closed-loop water circuit of the Aktogai copper concentrator. Repeated water recirculation leads to the accumulation of total dissolved solids (TDSs), organic compounds (CODs), and suspended solids (TSSs), degrading flotation efficiency. A dynamic model of the process water pond with nine flows is combined with pseudo-first-order kinetics for H2O2 oxidation (kox = 0.003 L/(mg·h)) and polyaluminum chloride (PAC)/FeCl3 coagulation (kcoag = 0.005 L/(mg·h)). The NMPC manipulates the treated-effluent flow Q2 and the coagulant and oxidant doses over an 8 h prediction horizon, uses normalized one-sided soft constraints on water quality and a reagent cost, and is solved through sequential quadratic programming. The volume, TDSs, and TSSs are assumed to be measured online, whereas CODs are available only from laboratory analyses taken every 2–8 h with a 2 h delay. NMPC was compared with no-control, fixed dosing, a maximum-dilution policy, and a proportional–integral (PI) feedback dosing benchmark with the same manipulated variables. Under nominal disturbances, all strategies met the process limits. Under a simulated stress-test scenario (ore change and reagent overdosing), no control produced 26, 37, and 25 h of TDS, COD, and TSS violations in 72 h; maximum dilution alone removed the TDS and TSS violations but left 13 h of COD violations. With online measurements, a well-tuned PI controller performed almost as well as NMPC (1 h vs. 0 h of COD violations). With laboratory COD analyses, the PI controller incurred 4–11 h of COD violations, whereas NMPC, using a model-based COD estimate between analyses, incurred none, at the cost of 9–47% higher oxidant consumption; this advantage reflects the combined effect of model-based COD estimation and predictive optimization, not of predictive optimization alone. It persisted under up to 30% adverse parametric plant–model mismatch, and the results were insensitive to tenfold variations in the selected NMPC tuning weights. TDSs could be held below their limit only through hydraulic dilution and only while the thickener-overflow TDSs remained below about 2260 mg/L.