Rigorous numerical method for irrigation canal system dynamics and control

Water canals for water delivery or irrigation provide a challenging system dynamics and control problem for distributed parameter plants. Canals are formed by a sequence of pools separated by gates. Output variables are the pool level at certain points, manipulated variables are the position of the gates and disturbances are the outlet water flows for agricultural use. Water pool dynamics are derived from the shallow water equations (also called Saint-Venant equations in its one-dimensional form) that are a set of hyperbolic partial differential nonlinear equations. Gate opening produces a water wave that travels through the pool which is partially reflected back in the next gate, the remainder crosses the gate and propagates to the next pool. Rigorous numerical methods that are able to capture water wave dynamics in canals are difficult to achieve. In this case a numerical routine was designed from a finite volume method for hyperbolic systems of conservation laws with source terms using a semi-discrete MUSCL flux reconstruction linear wellbalanced scheme (Kurganov and Tadmor central scheme with superbee limiter). Time integration was done with a Runge-Kutta method. The numerical method was used to simulate water dynamics in the first two pools with withdraws of an existing irrigation canal in Vila Nova de MilFontes, Portugal, including PI controlled gates movement to compensate for wave disturbances.