A gain scheduling approach to improve pressure control in water distribution networks

Highlights

• Stability issues affect real time pressure control in water distribution networks.

• Problems are caused by strong process gain nonlinearity and resonance peaks.

• Nonlinearity inversion and gain scheduling allow compensating the nonlinearity.

• Gain scheduling can improve the overall control performances.

• Gain scheduling avoids heavy regulator retuning when applied to the plant.

Abstract

Real time pressure control is a common technique adopted to face the problem of leakage reduction in water distribution networks. Recently, in the context of Water 4.0, the spread of wired water distribution networks has opened new possibilities in terms of sensing and communication, resulting in the possibility of adopting higher sampling rates and consequently higher closed-loop bandwidths for the control system. While this could be exploited to improve the performance, it has also drawn the attention of the fundamental question of closed-loop stability, which was seldom considered in a systematic way, especially in the hydraulic community. This works aims to combine some recent results in term of design of frequency domain controllers with a gain scheduling approach, to account and compensate for the main nonlinearities affecting the system under control, and to preserve stability and robustness of the closed-loop in a wide operating region. The approach is validated by means of simulated experiments performed on a detailed dynamic model of the water distribution network. In addition, the gain scheduling approach can improve the overall performance of the control scheme and allows avoiding heavy retuning of the regulator when applied to the nonlinear system.

Introduction

Real Time Control (RTC) of service pressure plays a fundamental role in the context of Water Distribution Networks (WDNs) management, allowing for leakage reduction (Creaco and Walski, 2017, Farley and Trow, 2003), pipe burst abatement (Creaco and Walski, 2017, Lambert et al., 2013, Thornton and Lambert, 2006) and overall infrastructure life extension. The WDN is first subdivided in homogeneous pressure zones (Walski et al., 0000). On this basis, hierarchical control schemes are developed, with high-level optimal controllers defining the pressure setpoints for the different pressure zones, according to an economic cost–benefit evaluation over the whole network, and RTC controllers working as low-level controllers to ensure regulation to the assigned setpoint (Cembrano et al., 2000, Grosso, Maestre, et al., 2014, Grosso, Ocampo-Martínez, et al., 2014, Grosso et al., 2017, Ocampo-Martinez et al., 2012, Ocampo-Martinez et al., 2013, Toro et al., 2011). Recently, the spread of wired water distribution networks, promoted by the Water 4.0 approach, is attracting new interest on the design of low level controllers. In fact, in wired WDNs, sensors and actuators are connected by wire to control units: this allows developing new control approaches working with high sampling rates. Some recent works (Fontana, Giugni, Glielmo, Marini, and Verrilli, 2017, Fontana, Giugni, Glielmo, Marini, and Zollo, 2017, Galuppini et al., 2019) try to investigate this approach and compare it to more traditional control strategies (Campisano et al., 2009, Campisano et al., 2016, Campisano et al., 2011, Creaco et al., 2018, Creaco and Franchini, 2013), to understand how to exploit the new communication possibilities at best. The design of such control algorithms results particularly challenging, due to the complexity of the nonlinear system under control, and the topic of guaranteed closed-loop stability, which was previously disregarded by the hydraulic community, is getting more and more attention (Galuppini et al., 2020, Janus and Ulanicki, 2017, Janus and Ulanicki, 2018). In particular, Fontana, Giugni, Glielmo, Marini, and Verrilli (2017) and Galuppini et al. (2019) propose a model-based frequency domain approach, with regulators based on a linear, local model of the system dynamics around the working point. The issue of stability is faced by providing robustness margins against gain and phase variations. Galuppini et al. (2020) further investigates the problem of stability, and demonstrates that a poor description of the high frequency behaviour of the system, together with the strong gain nonlinearity affecting the Pressure Control Valves (PCVs) exploited as actuators, may result in highly overestimated robustness margins and, eventually, in closed-loop instability as the process moves from its nominal working point. The aim of this paper is to improve the design methodology originally developed in Galuppini et al. (2019), to explicitly account and compensate for the main static nonlinearities characterising the process under control. This is achieved by means of a proper choice of the control variable (inspired by Creaco, 2017), a nonlinearity inversion block, and a gain scheduling approach. The gain scheduling policy is further extended to better manage the regulation error vs cost of control trade-off at different operating points of the system. The correctness of the approach is verified by means of closed-loop simulations, performed on a detailed model of two different WDN topologies and different user demand scenarios. This paper is organised as follows: Section 2 describes the different case studies adopted for simulations while Section 3 reports the details of their numerical modelling; Section 4 discusses the control methodology and Section 5 its application to the case studies. Finally, a detailed discussion of the results, including a comparison with similar algorithms, is given in Section 6, while the conclusions are reported in Section 7.