Boundary control of hyperbolic conservation laws using a frequency domain approach

Author

Litrico, Xavier ; Fromion, Vincent

Author_Institution

Cemagref, Montpellier

fYear

2006

fDate

13-15 Dec. 2006

Firstpage

5341

Lastpage

5346

Abstract

The paper uses a frequency domain method for boundary control of hyperbolic conservation laws. We show that the transfer function of the hyperbolic system belongs to the Callier-Desoer algebra, for which the Nyquist theorem provides necessary and sufficient conditions for input-output closed-loop stability. We examine the link between input-output stability and exponential stability of the state. Specific results are then derived for the case of proportional boundary controllers. The results are illustrated in the case of boundary control of open-channel flow

Keywords

Lyapunov methods; Nyquist criterion; algebra; asymptotic stability; channel flow; closed loop systems; distributed parameter systems; flow control; frequency-domain synthesis; transfer functions; Callier-Desoer algebra; Nyquist theorem; boundary control; exponential stability; frequency domain approach; hyperbolic conservation law; hyperbolic system; input-output closed-loop stability; open-channel flow; transfer function; Control systems; Equations; Frequency domain analysis; Hydraulic systems; Irrigation; Proportional control; Stability; Sufficient conditions; Transfer functions; USA Councils;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2006 45th IEEE Conference on

Conference_Location

San Diego, CA

Print_ISBN

1-4244-0171-2

Type

conf

DOI

10.1109/CDC.2006.377703

Filename

4177853