LPV Model Order Reduction by Parameter-Varying Oblique Projection

Julian Theis; Peter Seiler; Herbert Werner

doi:10.1109/TCST.2017.2692744

LPV Model Order Reduction by Parameter-Varying Oblique Projection

Julian Theis, Peter Seiler, Herbert Werner

Aerospace Engineering and Mechanics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

A method to reduce the dynamic order of linear parameter-varying (LPV) systems in grid representation is developed in this paper. It consists of an oblique projection and is novel in its use of a parameter-varying nullspace to define the direction of this projection. Parameter-varying state transformations in general lead to parameter rate dependence in the model. The proposed projection avoids this dependence and maintains a consistent state space basis for the reduced-order system. This extension of the projection framework lends itself very naturally to balanced truncation and related approaches that employ Gramian-based information to quantify the importance of subspaces. The proposed method is first compared to LPV balancing and truncation on a numerical example and then used to approximate two LPV systems: the longitudinal dynamics model of an aeroservoelastic unmanned aerial vehicle and the far wake model of a wind turbine.

Original language	English (US)
Pages (from-to)	773-784
Number of pages	12
Journal	IEEE Transactions on Control Systems Technology
Volume	26
Issue number	3
DOIs	https://doi.org/10.1109/TCST.2017.2692744
State	Published - May 2018

Bibliographical note

Funding Information:
Manuscript received October 12, 2016; revised January 30, 2017; accepted February 28, 2017. Date of publication April 28, 2017; date of current version April 11, 2018. Manuscript received in final form March 14, 2017. This work was supported by NASA entitled “Lightweight Adaptive Aeroelastic Wing for Enhanced Performance Across the Flight Envelope,” under Grant NRA NNX14AL36A. Recommended by Associate Editor S. Tarbouriech. (Corresponding author: Julian Theis.) J. Theis and H. Werner are with the Institute of Control Systems, Hamburg University of Technology, 21073 Hamburg, Germany (e-mail: julian.theis@tuhh.de; h.werner@tuhh.de).

Funding Information:
This work was supported by NASA entitled "Lightweight Adaptive Aeroelastic Wing for Enhanced Performance Across the Flight Envelope," under Grant NRA NNX14AL36A. Recommended by Associate Editor S. Tarbouriech.

Publisher Copyright:
© 2017 IEEE.

Keywords

Linear parameter-varying (LPV) systems
model order reduction

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10.1109/TCST.2017.2692744

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abstract = "A method to reduce the dynamic order of linear parameter-varying (LPV) systems in grid representation is developed in this paper. It consists of an oblique projection and is novel in its use of a parameter-varying nullspace to define the direction of this projection. Parameter-varying state transformations in general lead to parameter rate dependence in the model. The proposed projection avoids this dependence and maintains a consistent state space basis for the reduced-order system. This extension of the projection framework lends itself very naturally to balanced truncation and related approaches that employ Gramian-based information to quantify the importance of subspaces. The proposed method is first compared to LPV balancing and truncation on a numerical example and then used to approximate two LPV systems: the longitudinal dynamics model of an aeroservoelastic unmanned aerial vehicle and the far wake model of a wind turbine.",

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note = "Funding Information: Manuscript received October 12, 2016; revised January 30, 2017; accepted February 28, 2017. Date of publication April 28, 2017; date of current version April 11, 2018. Manuscript received in final form March 14, 2017. This work was supported by NASA entitled “Lightweight Adaptive Aeroelastic Wing for Enhanced Performance Across the Flight Envelope,” under Grant NRA NNX14AL36A. Recommended by Associate Editor S. Tarbouriech. (Corresponding author: Julian Theis.) J. Theis and H. Werner are with the Institute of Control Systems, Hamburg University of Technology, 21073 Hamburg, Germany (e-mail: julian.theis@tuhh.de; h.werner@tuhh.de). Funding Information: This work was supported by NASA entitled {"}Lightweight Adaptive Aeroelastic Wing for Enhanced Performance Across the Flight Envelope,{"} under Grant NRA NNX14AL36A. Recommended by Associate Editor S. Tarbouriech. Publisher Copyright: {\textcopyright} 2017 IEEE.",

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LPV Model Order Reduction by Parameter-Varying Oblique Projection

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