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IQC arguments for analysis of the 3-state Moore-Greitzer compressor system

Shiriaev, Anton S.; Freidovich, Leonid B.; Robertsson, A. LU ; Andersson, Alina LU and Johansson, R. LU (2015) In IFAC-PapersOnLine 28(11). p.252-257
Abstract

The Integral Quadratic Constraint (IQC) framework developed by Professor Yakubovich and his co-workers, see Yakubovich et.al. (2004), is one of few available constructive tools for establishing robust stability of nonlinear systems. An explicit format of stability conditions, procedures for computing a Lyapunov function and developed libraries IQCs for common nonlinearities in dynamics, all together have made the approach unique and at the same time so to say automatic for recovering stability conditions for many applications: in the process of analyzing a dynamical system, an engineer is just required to search for a sufficiently rich set IQCs describing nonlinearities in the dynamics so that such nonlinearities can be substituted in... (More)

The Integral Quadratic Constraint (IQC) framework developed by Professor Yakubovich and his co-workers, see Yakubovich et.al. (2004), is one of few available constructive tools for establishing robust stability of nonlinear systems. An explicit format of stability conditions, procedures for computing a Lyapunov function and developed libraries IQCs for common nonlinearities in dynamics, all together have made the approach unique and at the same time so to say automatic for recovering stability conditions for many applications: in the process of analyzing a dynamical system, an engineer is just required to search for a sufficiently rich set IQCs describing nonlinearities in the dynamics so that such nonlinearities can be substituted in analysis by quadratic constraints, which they satisfy. The power of the methodology becomes also its weak part in an analysis of concrete systems. Searching IQCs is the difficult task in new examples, where a lack of a rich set of IQCs for concrete nonlinearities makes the method inconclusive or too rough to detect (in)-stability. The paper is aimed at a discussion of such an example of a nonlinear dynamical system (the classical 3-state Moore-Greitzer compressor model) augmented with the dynamical feedback controller, whose parameters should be adjusted to meet a stability condition. The closed-loop system has several nonlinearities and searching the corresponding IQCs to meet the stability conditions for this example is rather involved. To overcome the problem, we have previously described by different methods a set of parameters for which any solution of the closed loop system, if bounded, will converge to the origin and that the origin is locally asymptotically stable. However, the proof is incomplete without showing a boundedness of all solutions. To solve the task we have re-used some of the IQC framework ideas, where the method has been utilized and the corresponding IQCs have been found only for unbounded trajectories, if they would be present in closed loop system. The arguments have allowed completing the proof of stability and illustrating deliberate use of the IQC framework aimed at analysis of behavior specific trajectories.

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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
'Frequency' condition, 3-state Moore-Greizer compressor model, Dynamic feedback controller design, Integral Quadratic Constraint, Nonlinear control systems
in
IFAC-PapersOnLine
volume
28
issue
11
pages
6 pages
publisher
IFAC Secretariat
external identifiers
  • scopus:84992513280
DOI
10.1016/j.ifacol.2015.09.193
language
English
LU publication?
yes
id
5cc344f8-0ca4-4cef-8e4d-a902df8c3dbb
date added to LUP
2017-02-17 08:45:13
date last changed
2017-05-03 13:33:30
@article{5cc344f8-0ca4-4cef-8e4d-a902df8c3dbb,
  abstract     = {<p>The Integral Quadratic Constraint (IQC) framework developed by Professor Yakubovich and his co-workers, see Yakubovich et.al. (2004), is one of few available constructive tools for establishing robust stability of nonlinear systems. An explicit format of stability conditions, procedures for computing a Lyapunov function and developed libraries IQCs for common nonlinearities in dynamics, all together have made the approach unique and at the same time so to say automatic for recovering stability conditions for many applications: in the process of analyzing a dynamical system, an engineer is just required to search for a sufficiently rich set IQCs describing nonlinearities in the dynamics so that such nonlinearities can be substituted in analysis by quadratic constraints, which they satisfy. The power of the methodology becomes also its weak part in an analysis of concrete systems. Searching IQCs is the difficult task in new examples, where a lack of a rich set of IQCs for concrete nonlinearities makes the method inconclusive or too rough to detect (in)-stability. The paper is aimed at a discussion of such an example of a nonlinear dynamical system (the classical 3-state Moore-Greitzer compressor model) augmented with the dynamical feedback controller, whose parameters should be adjusted to meet a stability condition. The closed-loop system has several nonlinearities and searching the corresponding IQCs to meet the stability conditions for this example is rather involved. To overcome the problem, we have previously described by different methods a set of parameters for which any solution of the closed loop system, if bounded, will converge to the origin and that the origin is locally asymptotically stable. However, the proof is incomplete without showing a boundedness of all solutions. To solve the task we have re-used some of the IQC framework ideas, where the method has been utilized and the corresponding IQCs have been found only for unbounded trajectories, if they would be present in closed loop system. The arguments have allowed completing the proof of stability and illustrating deliberate use of the IQC framework aimed at analysis of behavior specific trajectories.</p>},
  author       = {Shiriaev, Anton S. and Freidovich, Leonid B. and Robertsson, A. and Andersson, Alina and Johansson, R.},
  keyword      = {'Frequency' condition,3-state Moore-Greizer compressor model,Dynamic feedback controller design,Integral Quadratic Constraint,Nonlinear control systems},
  language     = {eng},
  month        = {07},
  number       = {11},
  pages        = {252--257},
  publisher    = {IFAC Secretariat},
  series       = {IFAC-PapersOnLine},
  title        = {IQC arguments for analysis of the 3-state Moore-Greitzer compressor system},
  url          = {http://dx.doi.org/10.1016/j.ifacol.2015.09.193},
  volume       = {28},
  year         = {2015},
}