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Boundary feedback control of an open canal with arbitrary cross sections

机译：具有任意横截面的开放式运河的边界反馈控制

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摘要

This paper deals with the boundary feedback control of an open channel with arbitrary cross sections, which is modelled by the nonlinear Saint-Venant equations. The characteristic form of the Saint-Venant initial-boundary value problem is established in terms of Riemann invariants. In order to develop the boundary feedback control laws for a canal with arbitrary cross sections, the simplest boundary conditions are deduced to satisfy the stability conditions for the characteristic form. According to these simplest boundary conditions, a set of boundary feedback controls is derived for a canal with arbitrary cross sections. Then a unified design approach for the boundary feedback control is proposed. The control design method is illustrated with applications in a single canal with several typical types of cross sections and with various control gates.
机译：本文针对具有任意横截面的明渠的边界反馈控制，通过非线性的Saint-Venant方程建模。 Saint-Venant初边值问题的特征形式是根据黎曼不变量确定的。为了制定具有任意横截面的运河的边界反馈控制律，推导最简单的边界条件以满足特征形式的稳定性条件。根据这些最简单的边界条件，为具有任意横截面的运河导出了一组边界反馈控制。然后提出了一种统一的边界反馈控制设计方法。在具有几种典型类型横截面和各种控制浇口的一条运河中的应用中说明了控制设计方法。

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