Design of Global Control Algorithm for Irrigation Canals

Abstract

The problem of irrigation canal regulation under demand delivery operation was formulated as an optimal control problem. To apply the linear optimal control theory, the Saint-Venant equations of open-channel flow were linearized using the Taylor series after using a finite-difference approximation on the original nonlinear, partial differential equations. A proportional-plus-integral (PI) controller was developed using the concepts of linear optimal control theory. Since the order of the controller gain matrix was large, an optimal observer (Kalman filter) was designed to estimate values for the variables that were not measured. An example irrigation canal with five pools was considered. With the finite-difference technique used, there was a total of 45 state variables and five control variables (gates) in the problem. With two measurements per pool, values for 35 state variables were estimated using the observer. By subjecting the canal to random disturbances of up to 40% of the initial inflow rate into the canal, the simulated performance of the global feedback control algorithm along with the Kalman filter was found to be acceptable in terms of achieving either a constant-volume control or a constant-level control in the canal pools in the presence of random disturbances in lateral flow rates.