Boundary Control of Open Channels With Numerical and Experimental Validations

The problem of the stabilization of the flow in a reach is investigated. To study this problem, we consider the nonlinear Saint-Venant equations, written as a system of two conservation laws perturbed by non-homogeneous terms. The non-homogeneous terms are due to the effects of the bottom slope, the slope´s friction, and also the lateral supply. The boundary actions are defined as the position of both spillways located at the extremities of the reach. It is assumed that the height of the flow is measured at both extremities. Assuming that the non-homogeneous terms are sufficiently small in C ¹-norm, we design stabilizing boundary output feedback controllers, i.e., we derive a new strategy which depends only on the output and which ensures that the water level and water flow converge to the equilibrium. Moreover, the speed of the convergence is shown to be exponential. The proof of this result is based on the estimation of the effects on the non-homogeneous terms on the evolution of the Riemann coordinates. This stability result is validated both by simulating on a real river data and by experimenting on a micro-channel setup.