Boundary feedback control of open canals with a Riemann invariants approach

Abstract

This paper proposes a boundary feedback control design for open canal networks using the linearization of boundary conditions. For open canal networks with any types of cross-sections, which can be modelled by the Saint-Venant equations, the characteristic form in terms of Riemann invariants has been established. Under this established characteristic form, the stabilizing boundary control law has been developed by linearizing the boundary conditions for both a single reach and the open-channel network composed by multi-reaches in a cascade. The design of the boundary feedback control laws for both a single canal and the cascaded networks is illustrated in a unified framework, which extends the results in the literature.