Adaptive and Optimal Control of the Water Gate of a Dam Using a Finite Element Method

Abstract

Abstract A methodology for flood control by operating a dam gate, based on the hydraulic model and adaptive control, is presented in this paper. The purpose of this method is to reduce the water elevation of a reservoir. The dam model is introduced by using the shallow-water equation, which is discretized by the finite element method. Optimal and adaptive control theories are used to obtain optimal control of the volume of flow at the water gate of the dam. There are many numerical control methods, i.e. dynamic programming, conjugate-gradient method, etc. which have been previously presented. Among those, the Fletcher-Reeves and the Sakawa-Shindo methods are used as solution procedures for the deterministic problem, in which it is assumed that an inflow discharge is to be disturbed by random noise. Computational time and storage cause some difficulties in the application of an optimal control method to a practical problem. Thus, this paper presents these optimal and adaptive control techniques and their application. A practical dam model is used for the numerical examples in this paper. Keywords: Finite element methodoptimal controldam controldynamic programmingclipping-off conjugate gradient methodSakawa-Shindo method