Modeling Unsteady Open-Channel Flow for Controller Design

An approximated linear model of unsteady open-channel flow is necessary to design the water-level controller for irrigation open channels. Toward this end, this paper presents the matrix approach to derive the linear model of open-channel system in analytical form mainly according to the Saint Venant equations and the backwater profile at the steady state of open channel. The hydraulic model of the check structure at the downstream end of open channel is also incorporated into the linear model. A practical example indicates that the frequency response of the open-channel system can be accurately analyzed with the linear model. The simulation results in the time domain show that the dynamic behavior of the linear model approximates to that of the nonlinear model of the open-channel system. Finally, the limitations of the linear model are discussed.