Switched control of fluid networks

Abstract

A switched-control technique for fluid distribution systems is presented. It is based on a compartment model of the distribution network consisting of a number of interconnected reservoirs. The unforced flows among reservoirs and environment only depend (non-linearly) on the stored water levels (state variables), which are also influenced by the water demands (disturbances) and by the forced flows of the water pumped into or out of the reservoirs (controlled variables). The control objective is to drive the system to the equilibrium state and keep it there. This goal can be achieved by means of a state-feedback control, which entails switching the controlled inputs among given values according to the current system state. Necessary and sufficient stabilizability conditions are provided. The global asymptotic stability of the overall control system is proved by resorting to a suitable control-Lyapunov function. An experiment is worked out to show the performance of the adopted control policy.