Model predictive control of urban drainage systems considering uncertainty

Abstract

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This brief contributes to the application of model predictive control (MPC) to address the combined sewer overflow (CSO) problem in urban drainage systems (UDSs) with uncertainty. In UDS, dealing with uncertainty in rain forecast and dynamic models is crucial due to the possible impact on the UDS control performance. Two different MPC approaches are considered: tube-based MPC (T-MPC) and chance-constrained MPC (CC-MPC), which represent uncertainty in deterministic and stochastic manners, respectively. This brief presents how to apply T-MPC to UDS, by establishing a mathematical relation with CC-MPC, and a rigorous mathematical comparison. Based on simulations using the Astlingen benchmark UDS, the strengths and weaknesses of the performance of T-MPC and CC-MPC in UDS were compared. Differences in the involved mathematical computations have also been analyzed. Moreover, the comparison in performance also indicates the applicability of each MPC approach in different uncertainty scenarios.

This work was supported in part by the Supervision and fault-tolerant control of smart infrastructures based on advanced learning and optimization (L-BEST) Project of the Spanish Agency of Research under Grant PID2020-115905RB-C21 and in part by the Real-time pollution-based control of urban drainage and sanitation systems for protection of receiving waters (RUBIES) Project of the European Commission under Grant LIFE20 ENV/FR/000179

Peer Reviewed

Postprint (author's final draft)