Stochastic Optimal and Suboptimal Control of Irrigation Canals

Abstract

The Saint-Venant equations of open-channel flow were linearized using the Taylor series and a finite-difference approximation of the original nonlinear, partial differential equations. Using the linear optimal control theory, a proportional-plus-integral (PI) controller was developed for an irrigation canal with five pools. Since the order of the controller gain matrix was large, the Kalman filter was designed to estimate values for the state variables that were not measured. For this problem, there were a total of 45 state and five control variables. With two flow depth measurements per pool, values for the remaining 35 state variables were estimated using the Kalman filter. The simulated canal dynamics with the regional PI controllers along with the local Kalman filter were compared with the performance of the global control algorithms for achieving a constant-volume control and a constant-level control of an example irrigation canal. The performance of the regional constant-volume control algorithms was found to be as good as the performance of the global control algorithm, whereas the performance of the regional constant-level control algorithm was marginally acceptable.