Periodic Nonlinear Economic Model Predictive Control with Changing Horizon for Water Distribution Networks

Abstract

A periodic nonlinear economic model predictive control (EMPC) with changing prediction horizon is proposed for the optimal management of water distribution networks (WDNs). The control model of the WDN is built by means of nonlinear differential-algebraic equations in which both the hydraulic pressure and flow variables are taken into account. The model allows the controller to consider minimum pressure constraints at the demands. A periodic terminal constraint is employed in order to guarantee closed-loop stability. The prediction horizon is modified on-line in order to guarantee convergence to the optimal periodic trajectory. The proposed control strategy is verified with the case study of the Richmond water network in a realistic hydraulic simulator. Although there are modeling errors between the control model and hydraulic model, the closed-loop system converges to a sub-optimal periodic trajectory satisfying all the constraints.