IQC arguments for analysis of the 3state MooreGreitzer compressor system
(2015) In IFACPapersOnLine 28(11). p.252257 Abstract
The Integral Quadratic Constraint (IQC) framework developed by Professor Yakubovich and his coworkers, 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 coworkers, 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 3state MooreGreitzer compressor model) augmented with the dynamical feedback controller, whose parameters should be adjusted to meet a stability condition. The closedloop 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 reused 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.
(Less)
 author
 Shiriaev, Anton S.; Freidovich, Leonid B.; Robertsson, A. ^{LU} ; Andersson, Alina ^{LU} and Johansson, R. ^{LU}
 organization
 publishing date
 20150701
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 'Frequency' condition, 3state MooreGreizer compressor model, Dynamic feedback controller design, Integral Quadratic Constraint, Nonlinear control systems
 in
 IFACPapersOnLine
 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
 5cc344f80ca44cef8e4da902df8c3dbb
 date added to LUP
 20170217 08:45:13
 date last changed
 20181121 21:29:56
@article{5cc344f80ca44cef8e4da902df8c3dbb, abstract = {<p>The Integral Quadratic Constraint (IQC) framework developed by Professor Yakubovich and his coworkers, 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 3state MooreGreitzer compressor model) augmented with the dynamical feedback controller, whose parameters should be adjusted to meet a stability condition. The closedloop 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 reused 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,3state MooreGreizer compressor model,Dynamic feedback controller design,Integral Quadratic Constraint,Nonlinear control systems}, language = {eng}, month = {07}, number = {11}, pages = {252257}, publisher = {IFAC Secretariat}, series = {IFACPapersOnLine}, title = {IQC arguments for analysis of the 3state MooreGreitzer compressor system}, url = {http://dx.doi.org/10.1016/j.ifacol.2015.09.193}, volume = {28}, year = {2015}, }