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.
- combined sewer overflow (CSO)
- model predictive control (MPC)
- Predictive control
- Predictive models
- Probabilistic logic
- Stochastic processes
- urban drainage system (UDS)