Feedback control of water waves in a tube with moving boundary

Abstract

Non-collocated feedback control of water waves in a tube with moving boundary described by the one-dimensional Saint-Venant equations is considered. Two control approaches are developed both relying on a measurement of the water level at the non-actuated boundary. Firstly, a flatness based approach for a partially linearized model of the system is introduced. Secondly, a non-linear collocated Lyapunov based feedback law relying on a non-linear collocated observer is considered. Both approaches are studied and compared in simulations and experimental studies.