Unknown-input observation techniques for infiltration and water flow estimation in open-channel hydraulic systems

This paper addresses a problem of state and disturbance estimation for an open-channel hydraulic system. Particularly, a cascade of n canal reaches, joined by gates, is considered. The underlying Saint-Venant system of PDEs is managed by means of a collocation-based finite-dimensional approximation. The resulting nonlinear systems' dynamics are linearized, and an estimation algorithm is designed by combining a conventional linear unknown-input observer (UIO) and a nonlinear disturbance observer (DO) based on the sliding-mode approach. By using measurements of the water level in three points per reach, the suggested algorithm is capable of estimating, both, the time varying infiltration and the discharge variables in the middle point of the reaches. The UIO and DO design procedures are constructively illustrated throughout the paper, and simulation results are discussed to verify their effectiveness.