A Nonlinear Model Predictive Control Framework for Dynamic Water Network Optimization

Abstract

[EN] This paper proposes the application of nonlinear model predictive control (NMPC) strategies within an integrating framework for planning and scheduling real-time water distribution system operations. Model predictive control (MPC) refers to a class of algorithms that make explicit use of a process model to optimize the future predicted behavior of a system. Originally developed to address the control needs of power plants and petroleum refineries, over the past 30 years it has successfully been used in a very wide range of applications in industry. In addition to the predictive model, MPC consists of a performance metric reflecting the control actions, an optimization algorithm that computes a sequence of future control signals that minimizes the performance index subject to a given set of constraints, and a moving horizon strategy, according to which only the first element of the optimal control sequence is applied online. The predictive models are generally intended to represent the behavior of complex nonlinear dynamical systems and often consist of linear models that circumvent the stability and performance challenges associated with their nonlinear counterparts. Recent developments on methods to model and solve large-scale nonlinear optimization problems lead to a reconsideration of these formulations, in particular, through development of efficient large-scale barrier methods for nonlinear programming (NLP). As a result, it is now realistic to solve NLPs on the order of a million variables, for instance, with the IPOPT algorithm. These developments are leveraged here to develop an NMPC dynamic real-time optimization strategy that combines a nonlinear dynamical model of the water network with a large-scale NLP optimization algorithm, and a moving horizon strategy to determine how to exert control on the system at the pump facility and network levels. We consider a recent water utility case study to illustrate these concepts.