Local Optimal Control of Irrigation Canals

Abstract

This paper presents a local optimal control technique (control of an individual gate) for operation of an irrigation canal with a single reach. By using the concepts of control theory, an expression for an upstream gate opening of an irrigation canal reach operated based upon a constant‐level control is obtained. In the derivation, the canal reach 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 linearized equations are then arranged to form a set of equations of the form $\mathbf{\delta }\dot{\mathbf{x}}\mathbf{/}\mathbf{\delta }\mathbf{t}=\mathbf{A}\mathbf{\delta }\mathbf{x}+\mathbf{B}\mathbf{\delta }\mathbf{u}$, which is called the state equation in control theory jargon. The linear quadratic regulator theory is applied to derive an expression of the form $\mathbf{\delta }\mathbf{u}=\mathbf{K}\mathbf{\delta }\mathbf{x}$ for the optimal gate opening to bring the system back to the equilibrium condition in the presence of disturbances. The response of the linearized system is simulated in the presence of known constant disturbances and found to be acceptable as long as the disturbances are less than 20% of the original flow rate in the canal reach. The results obtained from the optimal control theory are currently being evaluated using an unsteady open‐channel flow model.