Real-Time Pressure Control in Water Distribution Networks: Stability Guarantees via Gain-Scheduled Internal Model Control

Abstract

This article proposes a novel scheme for the real-time control (RTC) of service pressure in water distribution networks (WDNs), which is beneficial in terms of leakage reduction, energy recovery, pipe burst abatement, and extension of infrastructure lifetime. Compared with the other schemes previously proposed in the scientific literature, this novel scheme combines regulatory performance with proven guarantee of stability, which is obtained by framing gain scheduling in the context of internal model control (IMC) of linear parameter-varying (LPV) systems. Previous works relying on gain scheduling only prove stability for fixed scheduling parameter values, which is only a necessary condition for stability in case of possibly fast, time-varying parameters. The proposed RTC scheme guarantees instead stability of the closed loop for any admissible trajectory of the scheduling parameter. The novel control scheme is tested numerically against challenging operating conditions in a benchmark WDN, including two different demand patterns and four hydrant activation scenarios.