Model Order Reduction for Water Quality Dynamics

TL;DR

This paper explores model order reduction techniques for water quality dynamics in drinking water networks to enable efficient control and estimation in large-scale systems.

Contribution

It introduces and evaluates MOR methods tailored for water quality models, focusing on reducing complexity while maintaining stability and control capabilities.

Findings

Significant reduction in model dimension achieved.

MOR methods maintain stability of water quality models.

Enhanced feasibility of model predictive control in large networks.

Abstract

A state-space representation of water quality dynamics describing disinfectant (e.g., chlorine) transport dynamics in drinking water distribution networks has been recently proposed. Such representation is a byproduct of space- and time-discretization of the PDE modeling transport dynamics. This results in a large state-space dimension even for small networks with tens of nodes. Although such a state-space model provides a model-driven approach to predict water quality dynamics, incorporating it into model-based control algorithms or state estimators for large networks is challenging and at times intractable. To that end, this paper investigates model order reduction (MOR) methods for water quality dynamics with the objective of performing post-reduction feedback control. The presented investigation focuses on reducing state-dimension by orders of magnitude, the stability of the MOR methods, and the application of these methods to model predictive control.