Convex, Real-Time Koopman Model Predictive Control of Activated-Sludge Aeration: Constraint-Aware Operation With an Explicit Energy-Nitrous-Oxide Operating Frontier.

Aeration is the largest energy consumer in activated-sludge treatment and a principal control over nitrous oxide (N2O), a dominant contributor to a plant's carbon footprint, while effluent limits remain nonnegotiable. This paper develops a convex Koopman-operator model predictive controller (MPC) for that three-way trade-off. Extended dynamic mode decomposition identifies a linear predictor of the nonlinear process, N2O included; successive linear programming reduces each control step to a strictly convex quadratic program with explicit ammonia and total-nitrogen constraints, an offset-free correction and an influent forecast, solved in about 9 ms against a 15-min interval. The predictor accounts for 96.7% of output variance one step ahead and 73.4% at the 90-min horizon, against 71.9% and 39.8% for local linearization. On the single-reactor reference model the controller eliminated effluent-ammonia violation over 10 identification and noise realizations, against 7.5 and 15.4 h for fixed-dissolved-oxygen and ammonia-cascade baselines at indistinguishable aeration energy, and sweeping the emission weight traced a monotone frontier along which each per cent of N2O abatement costs about 2.4% of aeration energy. Transferred without modification to a five-tank Activated Sludge Model No. 1 cascade manipulating aeration and internal recirculation, it removed ammonia violation from 69 h to none and lowered the nitrogen-load effluent index by 38% at N2O parity. A component-wise ablation identifies the lifted predictor and the offset-free correction, not the influent preview, as the sources of compliance. Run unchanged on an independently structured evaluation plant, the compliance and energy results transferred but the emission magnitudes and the ranking of the controllers on N2O did not, which bounds what the emission results license.