Active control of compressor stall inception: A bifurcation-theoretic approach
type: Item
instance of: scholarly article
title: Active control of compressor stall inception: A bifurcation-theoretic approach
zbMATH Open document ID: 0847.93049
DOI: 10.1016/0005-1098(95)00096-8
author: Der-Cherng Liaw
author: Eyad H. Abed
published in: Automatica
publication date: 1996-10-07T00:00:00Z
review text: Active control of the onset of stall instabilities in axial flow compression systems is pursued using bifurcation analysis of a dynamical model proposed by Moore and Greitzer. The state variables of this model are the mass flow rate, pressure rise, and the amplitude of the first-harmonic mode of the asymmetric component of the flow. A subcritical pitchfork bifurcation is found to occur at the inception of stall, resulting in a large-amplitude instability and associated hysteresis behavior. Using the throttle opening of the compression system for actuation, it is found that the eigenvalue that becomes zero at the onset of stall is linearly uncontrollable. This, along with uncertainty of the post-stall linearized model, motivates a consideration of nonlinear feedback control laws for mitigation of the jump and hysteresis behavior occurring at stall onset. Following previous bifurcation control calculations introduced by Abed and Fu, it is found that feedback incorporating a term quadratic in the first-harmonic flow asymmetry variable renders the pitchfork bifurcation supercritical. This introduces a new stable equilibrium near the nominal equilibrium after the nominal equilibrium itself has lost stability, thus eliminating the undesirable jump and hysteresis behavior of the uncontrolled system.
Mathematics Subject Classification ID: 93C95
Mathematics Subject Classification ID: 93B52
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 867808
zbMATH Keywords: compressors
zbMATH Keywords: stall instabilities
zbMATH Keywords: axial flow compression systems
zbMATH Keywords: subcritical pitchfork bifurcation
MaRDI profile type: Publication
full work available at URL: 0005-1098(95)00096-8
OpenAlex ID: W2050361604
cites work: Local feedback stabilization and bifurcation control. I. Hopf bifurcation
cites work: Local feedback stabilization and bifurcation control. II: Stationary bifurcation
cites work: Q3948194
cites work: Q4749133
cites work: Q3995741
Wikidata QID: Q126781092
description: scientific article; zbMATH DE number 867808