A general boundary feedback control design for an open canal

This paper deals with the regulation of water flow in an open channel with arbitrary cross sections modeled by the nonlinear Saint-Venant equations. The characteristic form of the Saint-Venant initial-boundary value problem is established in terms of Riemann invariants. In order to develop the boundary control laws for a canal with arbitrary cross sections, a general boundary control design approach is proposed. The simplest boundary conditions are presented to satisfy the stability conditions. According to these boundary conditions, a set of boundary feedback controls is deduced for a canal with arbitrary cross sections and with various control gates. Finally, a canal with several typical types of cross sections is studied.