A robust unknown input observer for open channel irrigation systems

In agriculture, most of the water for irrigation is transported by means of open-flow channel networks. To ensure their optimal operation, it is very important to monitor all system state variables accurately. This paper proposes a new state estimation scheme able to mitigate the effect of unknown inputs (e.g., user demands, seepage and rain) and noise based on a robust unknown input observer (RUIO) that expresses the canal control-oriented model as a one-sided Lipschitz (OSL) quadratically inner bounded (QIB) system. The modeling methodology also includes the discharges of each gate, along with a transition flow that considers the effect of potential energy (channel slope) and kinetic energy (velocity in the transport of matter and frictional losses). The performance of the proposed observer is evaluated on the Corning channel benchmark using data provided by SIC${}^2$, which is a high-fidelity simulator that solves numerically the Saint-Venant equations and thus generates data that is close to the real canal operation. The obtained results demonstrate that the RUIO is capable of estimating the upstream heights from the downstream height measurements (which are subject to noise and unknown inputs), hence showing that this strategy can lead to savings in terms of required sensors.