Automatic Control of Canal Flow Using Linear Quadratic Regulator Theory

Abstract

An integrated approach to the design of automatic control systems for canals using Linear Quadratic Regulator theory is developed. The one‐dimensional partial differential equations (PDE) describing open channel flow (Saint‐Venant equations) are linearized about equilibrium flow conditions and discretized spatially to provide a set of approximate ordinary differential equations (ODE) which describe the effects of gate openings on depth and flow rate. Standard linear quadratic techniques are used to design a regulator. The requirement to measure all states is obviated by the construction of an observer using only measurements of depth adjacent to control gates. Simulation results are presented which show dramatic improvements in transient response over the uncontrolled case. Use of these techniques in water conveyance canals facilitates more rapid changes in discharge, and by permitting longer periods of off‐peak pumping could greatly reduce pumping costs.