Model Predictive Control using Linearized Radial Basis Function Neural Models for Water Distribution Networks

It is often the case that the main operation cost of Water Distribution Networks (WDN) is due to pump actuation. Although advanced control schemes are widely available, most water utilities still use on/off control. In this study, water networks with multiple flow inlets, storage tanks and several consumers are considered. Under mild assumptions on the consumption and hydraulic resistance of pipes, a reduced model is proposed with the aim of building its mathematical structure into a data-driven control design. For identification purposes we use Radial Basis Function Neural Networks (RBFNN). We show that linearization of the identified RBFNN model in the two peak points of the daily flow demand results in a control model with good prediction accuracy. Subsequently, this time-varying model is utilized in a standard economic Model Predictive Control (MPC) scheme, considering pump flows as inputs. A numerical case study on an EPANET model and experimental results on a test setup demonstrate the proposed method.