Closed loop control of gas flow in a pipe: Stability for a transient model Regelung des Gasflusses in einer Pipeline: Stabilität eines transienten Modells

Martin Gugat, Falk M. Hante, Li Jin

Research output: Contribution to journalArticlepeer-review

Abstract

This contribution focuses on the analysis and control of friction-dominated flow of gas in pipes. The pressure in the gas flow is governed by a partial differential equation that is a doubly nonlinear parabolic equation of p-Laplace type, where p = 3 2 p=\frac{3}{2}. Such equations exhibit positive solutions, finite speed of propagation and satisfy a maximum principle. The pressure is fixed on one end (upstream), and the flow is specified on the other end (downstream). These boundary conditions determine a unique steady equilibrium flow. We present a boundary feedback flow control scheme, that ensures local exponential stability of the equilibrium in an L 2 {L^{2}}-sense. The analysis is done both for the PDE system and an ODE system that is obtained by a suitable spatial semi-discretization. The proofs are based upon suitably chosen Lyapunov functions.

Original languageEnglish (US)
Pages (from-to)1001-1010
Number of pages10
JournalAutomatisierungstechnik
Volume68
Issue number12
DOIs
StatePublished - Nov 18 2020

Keywords

  • Lyapunov function
  • boundary feedback
  • closed loop control
  • exponential stability
  • friction dominated model

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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