Title: Boundary feedback control of an open canal with arbitrary cross sections

Authors: Lihui Cen; Yugeng Xi; Dewei Li

Addresses: Department of Control Engineering, Central South University, South of Lushan Road 932, Changsha, Hunan Province, China ' Key Laboratory of System Control and Information Processing, Ministry of Education, Dongchuan Road 800, Shanghai, China; Department of Automation, Shanghai Jiaotong University, Dongchuan Road 800, Shanghai, China ' Department of Automation, Shanghai Jiaotong University, Dongchuan Road 800, Shanghai, China

Abstract: 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.

Keywords: Saint-Venant equations; Riemann invariants; boundary feedback control; open canals; arbitrary cross sections; open channels; control gates.

DOI: 10.1504/IJSCIP.2012.052186

International Journal of System Control and Information Processing, 2012 Vol.1 No.2, pp.148 - 163

Published online: 19 Feb 2013 *

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