This paper deals with the boundary feedback control of an open channel with arbitrary cross sections, which is modelled 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 feedback control laws for a canal with arbitrary cross sections, the simplest boundary conditions are deduced to satisfy the stability conditions for the characteristic form. According to these simplest boundary conditions, a set of boundary feedback controls is derived for a canal with arbitrary cross sections. Then a unified design approach for the boundary feedback control is proposed. The control design method is illustrated with applications in a single canal with several typical types of cross sections and with various control gates.
Keywords: Saint-Venant equations, Riemann invariants, boundary feedback control