Application of H ∞ Control to Wave Generators in a Canal

We study the problem of designing a feedback controller for wave generators in a canal. The goal is to obtain a progressive wave at the surface by acting on plane generators at each side of a rectangular canal. The model of such a system is given by a classical linear model of shallow waters which leads to an hyperbolic equation. We formulate the problem within the additive uncertainty framework for Callier-Desoer systems and we use the standard algorithm of Doyle et al. to obtain a finite dimensional controller that ensures robust stability of the closed loop system and a prespecified performance level in a narrow frequency band. Numerical results show that we are able to create and maintain a progressive wave on the surface of the canal with this controller. We also give as a benchmark numerical and experimental results on the open loop approach of this problem.