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Stability Analysis of Closed Loops of non-linear Systems and PV Controllers designed using approximated Quasi-LPV Systems

Oehlschägel, Thimo and Heise , Christian and Theil, Stephan and Steffen, Thomas (2012) Stability Analysis of Closed Loops of non-linear Systems and PV Controllers designed using approximated Quasi-LPV Systems. In: 7th IFAC Symposium on Robust Control Design 2012, pp. 349-354. 7th IFAC Symposium on Robust Control Design 2012, 20-22 June 2012, Aalborg, Denmark. ISBN 9781622762262

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Abstract

This paper proposes an approach for the stability analysis of feedback con gurations consisting of a non-linear system and a linear parameter-varying (LPV) controller. The LPV controller synthesis for non-linear systems is commonly based on a Quasi-LPV representation of a non-linear system. With regard to performance oriented controller design, the approach proposed in this contribution considers the case where the controller is designed using an approximation of a Quasi-LPV representation of the non-linear system. As a consequence, the resulting controller does not necessarily stabilize the non-linear system. Therefore a method to prove the stability of the aforementioned closed loop is introduced. Since the proposed method is based on a Quasi-LPV representation of the closed loop, it results in a feasibility problem for a Quasi-LPV system globally representing the closed loop or otherwise in a simple convex optimization problem. In the latter case, the solution of the convex optimization problem de nes an estimate of the Region of Attraction (ROA) of the non-linear closed loop. In both cases the resulting program can be solved using standard tools. Finally the application to a landing vehicle controlled using a 2-DOF LPV-H1 controller shows the bene ts of the proposed method.

Item URL in elib:https://elib.dlr.de/81184/
Document Type:Conference or Workshop Item (Speech, Paper)
Title:Stability Analysis of Closed Loops of non-linear Systems and PV Controllers designed using approximated Quasi-LPV Systems
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Oehlschägel, Thimothimo.oehlschlaegel (at) dlr.deUNSPECIFIED
Heise , ChristianUNSPECIFIEDUNSPECIFIED
Theil, StephanUNSPECIFIEDUNSPECIFIED
Steffen, ThomasUNSPECIFIEDUNSPECIFIED
Date:June 2012
Journal or Publication Title:7th IFAC Symposium on Robust Control Design 2012
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Page Range:pp. 349-354
ISBN:9781622762262
Status:Published
Keywords:LPV, Robust Control, Non-Linear System
Event Title:7th IFAC Symposium on Robust Control Design 2012
Event Location:Aalborg, Denmark
Event Type:international Conference
Event Dates:20-22 June 2012
Organizer:IFAC
HGF - Research field:other
HGF - Program:other
HGF - Program Themes:other
DLR - Research area:no assignment
DLR - Program:no assignment
DLR - Research theme (Project):no assignment
Location: Bremen
Institutes and Institutions:Institute of Space Systems > Navigation and Control Systems
Deposited By: Oehlschlägel, Thimo
Deposited On:14 Feb 2013 11:52
Last Modified:14 Feb 2013 11:52

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