Robust control of irrigation canals

The design of irrigation water delivery systems involves decisions about siting, dimensions, and characteristics of facilities for conveyance, regulation, monitoring, and diversion of flow. The characteristics of all there individual system components work together to determine the performance of the entire irrigation water delivery system. With the ever increasing demand for water due to population growth and competition from non-agricultural demands, there is an urgent need for efficient management of irrigation resources. Improvements in the operation and maintenance of an irrigation delivery system can translate into better overall management in an irrigation project, and automation of irrigation canals can be an effective way to achieve such improvements. Automation of irrigation distribution canals improves water-delivery service to farmers, reduce operating cost and improve distribution efficiency. The conveyance and distribution performance of irrigation canals can be improved to better meet the requirements of farmers by providing modern methods of canal control. Therefore, to avoid overflows and always be able to satisfy the demand, the irrigation canal system must be controlled and robust to maintain desired flow rates and water surface elevations. The goal of the canal controls is to match the actual flow in the canal to the required flow for that day while maintaining water surface elevations within allowable limits. Canal control systems must provide timely deliveries to customers with little or no waste use of water and power under predicted and unknown demands (perturbations). Because of that the design of highly accurate control systems in the presence of significant system uncertainty requires the designer to seek a robust control system. A robust control system exhibits low sensitivities to unknown demands (disturbances) and is stable over a wide range of disturbance variations.; This research aims at strengthening the distribution link through the development of a robust control algorithm to provide for automatic control of a MIMO (multi-input, multi-output) water distribution system under unknown external perturbations. In the derivation, the canal between two gates is divided into N nodes, and the finite-difference forms of the continuity and the momentum equations are written for each node. The Taylor series is applied to linearize the equations around the initial steady state or equilibrium conditions. The Linear Quadratic Regulator (LQR) is designed to generate control input (optimal gate opening) u( k). With a known control input, measured depth and density matrices, a Kalman filter is designed to provide an optimal estimate of the state vector, x(k). The Separation Theorem is applied to combine LQR and Kalman filter as a Linear Quadratic Gaussian (LQG) controller. With combination of LQR and Kalman filter, there is some loss of robustness. To improve the robustness of the control algorithm, Loop Transfer Recovery (LTR) loop shaping technique is used. Loop shaping technique is an adjustment of the singular values of return ratio matrices to achieve desired closed-loop robustness and stability. To analyze the robustness of the controller, two robustness analysis methods are conducted: Singular Values and Bode Diagrams.