Control Theory for Water Quality Regulation in Drinking Water Distribution Networks




Wang, Shen

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A drinking water distribution network (WDN) is designed to adequately carry quantities and qualities of potable water from treatment plants or reservoirs to consumers. To ensure safe drinking water, the most used disinfectant in WDNs is chlorine, and a minimum chlorine residual is typically maintained according to the regulations enforced by the U.S. Environmental Protection Agency (EPA). However, maintaining minimum chlorine concentrations or performing real-time water quality control (WQC) and regulation are challenging tasks due to the lack of (i) a proper control-oriented model considering complicated components in WDNs (e.g., junctions, tanks, pipes, and valves) for water quality modeling (WQM), and (ii) a corresponding scalable control algorithm that performs real-time water quality regulation.

The objective of this dissertation is to propose a control-oriented state-space representation of the water quality model that is friendly to the state-of-the-art algorithms to model, control, and estimate water quality state in WDNs. Based on the proposed state-space model, this dissertation solves two essential research challenges—optimal water quality control and sensor placement problems. Furthermore, this dissertation explores other potential ways to create more compact water quality models by reducing the system order of the proposed control-oriented water quality model and identifying system models only by data-driven methods.

In particular, water quality models depict the decay and transport of disinfectants (e.g., chlorine) in WDNs. However, traditional water quality models fail to describe the explicit relationship between inputs (chlorine dosage at booster stations) and states/outputs (chlorine concentrations in the entire network) from the perspective of control theory such that the advanced control algorithms are prohibited from being applied in WDNs. This dissertation proposes a control-oriented state-space form of water quality model that not only can describe the spatiotemporal evolution of disinfectants accurately but also is friendly for existing control algorithms. With such proposed WQM, a highly scalable model predictive control algorithm that showcases fast response time and resilience against some sources of uncertainty is developed. The goal of maintaining the minimum chlorine residual in entire WDNs, that is, the requirements of water quality control (WQC) are met.

Furthermore, real-time water quality sensors in WDNs have the potential to enable contamination event detection, closed-loop feedback control of water quality dynamics/models, and network-wide observability of water quality indicators. However, this objective is overlooked in recent research studies. Hence, this dissertation also provides a computational water quality sensor placement (WQSP) method considering improve the network-wide observability of the water quality dynamics with the assistant of the proposed WQM. This metric finds the optimal WQSP that minimizes the state estimation error via the Kalman filter for noisy water quality dynamics—a metric that quantifies WDN observability.

With the proposed WQM and solving the corresponding WQC and WQSP problems, this dissertation revisits the WQM problem and explores several methods (such as reducing system orders and identifying system dynamics using data-driven techniques) to obtain a more compact water quality model that potentially reduces computational load.

Specifically, model order reduction (MOR) methods for water quality dynamics are investigated. The presented investigation focuses on (i) reducing state-dimension by orders of magnitude while retaining the input-output relationship and stability of the MOR methods and (ii) combining the reduced-order model with model predictive control. System identification (SysID) algorithms, seeking to approximate models using only input-output data without relying on WDN parameters/typologies, are explored while overcoming several challenges. Such challenges are the complex water quality and reaction dynamics and the mismatch between the requirements of SysID algorithms and the properties of water quality dynamics. Through case studies, we demonstrate the applicability of SysID algorithms and show the corresponding performance in terms of accuracy and computational time by comparing it with the proposed WQM. Moreover, the possible factors impacting water quality model identification are explored.

In short, this dissertation is the first thorough system, network, and control-theoretic attempt at modeling water quality dynamics, controlling them, and scaling their implementation via model-free methods. Future work will focus on more complex and nonlinear multi-species models as well as feedback control problems that regulate such complex models.


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Model Order Reduction, Optimal Sensor Placement, System Identification, Water Distribution Network, Water Quality Control, Water Quality Modeling



Electrical and Computer Engineering