Boundary control of linearized Saint-Venant equations oscillating modes

The Saint-Venant equations describe the dynamics of one dimensional open-channel flow. The paper investigates linearized Saint-Venant equations modes and their control. We show that it is possible to suppress the oscillating modes over all the canal pool by a well-designed boundary dynamic controller using only the water level measurement at the downstream end of the pool. This controller is infinite dimensional, and also not strictly proper, which makes it difficult to implement on a real canal. However, a static control of the oscillating modes can be performed with a well-designed hydraulic structure. We therefore study the specific case of a constant proportional controller on the oscillating modes and show that they can be asymptotically attenuated by using a controller that depends only on local flow characteristics. Experimental results on a laboratory canal pool show the effectiveness of the proposed control.