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On Boundedness of Solutions of Three-State Moore–Greitzer Compressor Model with Nonlinear Proportional–Integral Controller for the Surge Subsystem

Shiriaev, Anton ; Freidovich, Leonid ; Shepeljavyi, Aleksandr ; Robertsson, Anders LU and Johansson, Rolf LU orcid (2026) In Systems & Control Letters 216.
Abstract
The work focuses on Lagrange stability of the origin for the three-state Moore–Greitzer compressor model in closed loop with a nonlinear PI controller, tuned only to stabilize a lower-dimensional invariant surge dynamics subsystem. The linearization of the system is not stabilizable but the static nonlinearity satisfies a sector condition, and together with a structural property of the stall-dynamics subsystem, this plays an essential role in the analysis. The main contribution provides explicit conditions on the controller parameters together with analytical arguments that guarantee boundedness of all solutions of the closed-loop system. The analysis employs a non-standard application of Circle-Criterion-based arguments. Together with the... (More)
The work focuses on Lagrange stability of the origin for the three-state Moore–Greitzer compressor model in closed loop with a nonlinear PI controller, tuned only to stabilize a lower-dimensional invariant surge dynamics subsystem. The linearization of the system is not stabilizable but the static nonlinearity satisfies a sector condition, and together with a structural property of the stall-dynamics subsystem, this plays an essential role in the analysis. The main contribution provides explicit conditions on the controller parameters together with analytical arguments that guarantee boundedness of all solutions of the closed-loop system. The analysis employs a non-standard application of Circle-Criterion-based arguments. Together with the additional arguments developed in the work, this stability test also shows that the closed-loop system is robust to certain perturbations and model uncertainties. (Less)
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author
; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Nonlinear systems, Circle Criterion, Integral Quadratic Constraints, 3-state Moore–Greitzer compressor model, Stability
in
Systems & Control Letters
volume
216
article number
106510
pages
7 pages
publisher
Elsevier
external identifiers
  • scopus:105043604156
ISSN
0167-6911
DOI
10.1016/j.sysconle.2026.106510
project
RobotLab LTH
THE FUTURE OF DRONES: TECHNOLOGIES, APPLICATIONS, RISKS AND ETHICS
Active Control 2013-2015
language
English
LU publication?
yes
id
11d2ae74-8fde-48e1-9f09-bde8ba4f5ae3
date added to LUP
2026-07-01 16:56:07
date last changed
2026-08-18 15:41:50
@article{11d2ae74-8fde-48e1-9f09-bde8ba4f5ae3,
  abstract     = {{The work focuses on Lagrange stability of the origin for the three-state Moore–Greitzer compressor model in closed loop with a nonlinear PI controller, tuned only to stabilize a lower-dimensional invariant surge dynamics subsystem. The linearization of the system is not stabilizable but the static nonlinearity satisfies a sector condition, and together with a structural property of the stall-dynamics subsystem, this plays an essential role in the analysis. The main contribution provides explicit conditions on the controller parameters together with analytical arguments that guarantee boundedness of all solutions of the closed-loop system. The analysis employs a non-standard application of Circle-Criterion-based arguments. Together with the additional arguments developed in the work, this stability test also shows that the closed-loop system is robust to certain perturbations and model uncertainties.}},
  author       = {{Shiriaev, Anton and Freidovich, Leonid and Shepeljavyi, Aleksandr and Robertsson, Anders and Johansson, Rolf}},
  issn         = {{0167-6911}},
  keywords     = {{Nonlinear systems; Circle Criterion; Integral Quadratic Constraints; 3-state Moore–Greitzer compressor model; Stability}},
  language     = {{eng}},
  month        = {{07}},
  publisher    = {{Elsevier}},
  series       = {{Systems & Control Letters}},
  title        = {{On Boundedness of Solutions of Three-State Moore–Greitzer Compressor Model with Nonlinear Proportional–Integral Controller for the Surge Subsystem}},
  url          = {{http://dx.doi.org/10.1016/j.sysconle.2026.106510}},
  doi          = {{10.1016/j.sysconle.2026.106510}},
  volume       = {{216}},
  year         = {{2026}},
}