Flatness-Based Control Design for the Saint-Venant Equations with Experimental Results

Abstract

Control design for a fluid in a pipe with arbitrary cross-sectional area is considered. The position (resp. the velocity) of a piston moving within the tube acts as control input. The system dynamics are described by the so-called Saint-Venant equations defined on a varying spatial domain. The flatness-based approach is utilized in order to parameterize rest-to-rest transitions of the system by means of the water level at the uncontrolled boundary. This way the contribution extends previous results to systems with moving boundary. The proposed control scheme is validated in experimental studies.