Adaptive reference control for pressure management in water networks

Water scarcity is an increasing problem worldwide and at the same time a huge amount of water is lost through leakages in the distribution network. It is well known that improved pressure control can lower the leakage problems. In this work water networks with a single pressure actuator and several consumers are considered. Under mild assumptions on the consumption pattern and hydraulic resistances of pipes we use properties of the network graph and Kirchhoffs node and mesh laws to show that simple relations exist between the actuator pressure and critical point pressures inside the network. Subsequently, these relations are exploited in an adaptive reference control scheme for the actuator pressure that ensures constant pressure at the critical points. Numerical experiments underpin the results.