Convex Pollution Control of Wastewater Treatment Systems
Joshua Taylor
TL;DR
This work addresses flooding, CSO, and pollutant emissions in sewer networks by integrating storage dynamics, treatment plant kinetics, and actuated flows into a model-predictive controller. It achieves real-time feasibility by two key convexifications: a second-order cone (SOC) relaxation of microbial growth kinetics and a linearization strategy that removes bilinearities in mass flows, yielding a single second-order cone program ($SOCP$) per control period. The approach is demonstrated on a Paris-network of storage tanks, long pipes, and three treatment plants, where the pollution-based MPC reduces pollutant release by about $15\%$ while treating a comparable volume of sewage, outperforming a conventional volume-based MPC. The work demonstrates practical, scalable, convex optimization-based control for wastewater systems, with potential for significant environmental and operational benefits in urban water networks.
Abstract
We design a model-predictive controller for managing the actuators in sewer networks. It minimizes flooding and combined-sewer overflow during rain and pollution at other times. To make the problem tractable, we use a convex relaxation of the microbial growth kinetics and a physically motivated linearization of the mass flow bilinearities. With these approximations, the trajectory optimization in each control period is a second-order cone program. In simulation, the controller releases roughly 15% less pollutant mass than a conventional controller while treating nearly the same volume of flow. It does so by better balancing the flow over the treatment plants and over time.