Conversion from Discharge to Gate Opening for the Control of Irrigation Canals

Abstract

The paper reviews several methods to convert discharge into gate opening. A control algorithm for one or several reaches of an irrigation canal sometimes uses a discharge as the control action variable even though the device to be manipulated is a gate or a weir. In this case a slave controller has to convert the discharge into a gate opening or a sill elevation in case of a weir. This is usually done by inverting the static relation between discharge and gate opening. An improved method can be based on the characteristics theory to estimate the water levels deviations. However, both methods underestimate the gate opening deviations required to deliver a desired discharge deviation, because water levels vary continuously along time when the gate is operated. The paper proposes a method to take account of this dynamic behavior of the pool-gate interaction by using a simple linear model for the pools dynamics, the IDZ model. The proposed method enables to better estimate the gate opening necessary to get a desired average discharge. The method is evaluated in simulation and on a gate of the Gignac Canal, located in the South of France. A dimensionless analysis of the problem is finally performed to evaluate the methods' applicability.

Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems

“…Multiplying both sides by e βt * , using definition (19); and noting that for the present situation (case B.1), we have t * ≤ T max , then T ≤ T max , and for t (28) with C 13 = (1 + ǫc β )e βTmax and C 14 = ǫe βTmin . For case B.2: Again integrating the r-th equation from t r to t * , and using that ξ r (t r , b) = n l=m+1 g R,j rl ξ l (t r , b) with j = σ(t r ),…”

“…These problems are of interest because hyperbolic PDE systems can model flows in networks that are monitored and controlled at the boundary nodes [16]. Examples include transportation systems [17], [18], canal systems [19], and gas distribution systems [20]. The available results for this class of problems for linear hyperbolic systems can be found in [21], [22], and more generally for quasilinear hyperbolic systems in [23], [24], [25] and [26].…”

Model predictive control and moving horizon estimation for water level regulation in inland waterways

“…The global control level must compute the optimal action and send it to the slave controller that operates the gate or weir. If the discharge is used as the control variable, the slave controller must convert the given discharge into an equivalent opening or elevation, which is not as straightforward as inverting the discharge equation [21]. Furthermore, choosing the openings and elevations allows to link them with the local discharges and the upstream and downstream water levels at the structure, thus taking into account such complex dynamics [22].…”

Automatic Tuning of PI Controllers for Water Level Regulation of a Multi-pool Open-Channel Hydraulic System

“…For this purpose, we use here the method of the characteristics used by Litrico et al [10]. This method takes into account the deviations of the upstream and downstream water levels and their impacts on the gate discharge due to change of hydraulic conditions at the gate due to its movements.…”