Boundary control of linearized Saint-Venant equations oscillating modes

The paper investigates the control of oscillating modes occurring in open-channels, due to the reflection of propagating waves on the boundaries. These modes are well represented by linearized Saint-Venant equations, a set of hyperbolic partial differential equations which describe the dynamics of one-dimensional open-channel flow around a given stationary regime. We use a distributed transfer function approach to compute a dynamic boundary controller that cancels the oscillating modes over all the canal pool. This result is recovered with a Riemann invariants approach in the case of a frictionless horizontal canal pool. The effect of a proportional boundary control on the poles of the transfer matrix is then characterized by a root locus, and we derive an asymptotic result for high frequencies closed-loop poles.