Feed-Forward Control of Open Channel Flow Using Differential Flatness

This brief derives a method for open-loop control of open channel flow, based on the Hayami model, a parabolic partial differential equation resulting from a simplification of the Saint-Venant equations. The open-loop control is represented as infinite series using differential flatness, for which convergence is assessed. A comparison is made with a similar problem available in the literature for thermal systems. Numerical simulations show the effectiveness of the approach by applying the open-loop controller to irrigation canals modeled by the full Saint-Venant equations.