Piece-wise linear functions-based model predictive control of large-scale sewage systems

In this study, model predictive control (MPC) of large-scale sewage systems is addressed, considering several inherent continuous/discrete phenomena (overflows in sewers and tanks) and elements (weirs) in the system. This fact results in distinct behaviour depending on the dynamic state (flow/volume) of the network. These behaviours cannot be neglected nor can be modelled by a pure linear representation. In order to take into account these phenomena and elements in the design of the control strategy, a modelling approach based on piece-wise linear functions (PWLF) is proposed and compared against a hybrid modelling approach previously suggested by the authors. Control performance results and associated computation times of the closed-loop scheme considering both modelling approaches are compared by using a real case study based on the Barcelona sewer network. Results have shown an important reduction in the computation time when the PWLF-based model is used, with an acceptable suboptimality level in the closed-loop system performance.