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Publication# Dynamical Behavior and Stability Analysis of Hydromechanical Gates

Abstract

This study revisits the stability of hydromechanical gates for upstream water surface regulation, also known as AMIL gates. AMIL gates are used in irrigation canals, where they are often installed in series. From the regulation perspective, instabilities are undesired because they generate waves and fluctuations in the discharge. A mathematical model for an AMIL gate is described as a nonlinear dynamical system, which permits analyzing the dynamic interaction between the local water level and the gate position. The feedback effect of the gate on the water level is introduced by considering a storage volume of length l. In the derived model, waves are simplified to fluctuations of the flat water surface of the storage volume. Although previous studies used the same model, none has clarified the sensitivity of the model to the parameter l. The role of this parameter is investigated and it is calibrated with experimental measurements. The precision of the regulation is described by the decrement, the range of the water level around the target level. Based on the mathematical model, a relationship for calibration of the gate and precision of regulation is presented. The subsequent stability analysis of the dynamical system focuses on five control parameters and sheds light on their influence on the gate behavior. Hopf bifurcations are identified, which separate stable equilibrium solutions from stable periodic solutions. Further work might consider the implications of the periodic solutions on gates that work in series, as well as envision the innovative use of such gates outside of the domain of irrigation canals to obtain dynamic environmental flows in hydropower systems. (C) 2017 American Society of Civil Engineers.

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Related concepts (2)

Mathematical model

A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).

Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.