Robust control of irrigation canals

A robust control algorithm was developed for the automatic control of an open-channel water distribution system under unknown disturbances (demands) acting in the canal. 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, the Linear Quadratic Regulator (LQR), assuming all the state variables (flow depths and flow rates) were available, was designed to generate control input (optimal gate opening) u(k). Since it was expensive to implement the LQR, a Kalman filter based upon two flow depth measurements per pool was used to estimate the values for the state variables that were not measured but are needed in the feedback loop. To minimize the cost of implementing feedback control algorithm, the LQR and Kalman filter were combined as a Linear Quadratic Gaussian (LQG) controller. Due to the combination, there was some loss of robustness in the system. To improve the robustness of the LQG controller, a loop shaping technique, H-2 norm minimization, was employed in the algorithm. The proposed algorithm was comprehensively verified by a numerical application on an irrigation canal, called as Harran main canal, located in Turkey. The results from stability and robustness analysis showed that the control algorithm was found to be adequate for improvement of robustness properties of the control system in case of unknown demands (withdrawals) from the canal.