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Model Reduction for Linear Time-Varying Systems

Sandberg, Henrik LU (2004) In PhD Thesis TFRT-1071
Abstract
The thesis treats model reduction for linear time-varying systems. Time-varying models appear in many fields, including power systems, chemical engineering, aeronautics, and computational science. They can also be used for approximation of time-invariant nonlinear models. Model reduction is a topic that deals with simplification of complex models. This is important since it facilitates analysis and synthesis of controllers.



The thesis consists of two parts. The first part provides an introduction to the topics of time-varying systems and model reduction. Here, notation, standard results, examples, and some results from the second part of the thesis are presented.



The second part of the thesis consists... (More)
The thesis treats model reduction for linear time-varying systems. Time-varying models appear in many fields, including power systems, chemical engineering, aeronautics, and computational science. They can also be used for approximation of time-invariant nonlinear models. Model reduction is a topic that deals with simplification of complex models. This is important since it facilitates analysis and synthesis of controllers.



The thesis consists of two parts. The first part provides an introduction to the topics of time-varying systems and model reduction. Here, notation, standard results, examples, and some results from the second part of the thesis are presented.



The second part of the thesis consists of four papers. In the first paper, we study the balanced truncation method for linear time-varying state-space models. We derive error bounds for the simplified models. These bounds are generalizations of well-known time-invariant results, derived with other methods. In the second paper, we apply balanced truncation to a high-order model of a diesel exhaust catalyst. Furthermore, we discuss practical issues of balanced truncation and approximative discretization. In the third paper, we look at frequency-domain analysis of linear time-periodic impulse-response models. By decomposing the models into Taylor and Fourier series, we can analyze convergence properties of different truncated representations. In the fourth paper, we use the frequency-domain representation developed in the third paper, the harmonic transfer function, to generalize Bode's sensitivity integral. This result quantifies limitations for feedback control of linear time-periodic systems. (Less)
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author
supervisor
opponent
  • Professor Lall, Sanjay, Stanford University, Stanford, CA, USA
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Automation, robotics, control engineering, Performance limitations, Convergence analysis, Frequency-domain analysis, Error bounds, Time-varying systems, Model reduction, Linear systems, Automatiska system, robotteknik, reglerteknik
in
PhD Thesis TFRT-1071
pages
169 pages
publisher
Department of Automatic Control, Lund Institute of Technology (LTH)
defense location
Room M:B, M-building, Lund Institute of Technology
defense date
2004-12-03 10:15:00
external identifiers
  • scopus:85064378155
ISSN
0280-5316
0280-5316
language
English
LU publication?
yes
additional info
Article: Paper 1: Sandberg, H. and A. Rantzer "Balanced Truncation of Linear Time-Varying Systems." IEEE Transactions on Automatic Control, vol. 49, no. 2, pp. 217-229, February 2004. Article: Paper 2: Sandberg, H. "A Case Study in Model Reduction of Linear Time-Varying Systems." Submitted to Automatica, 2004. Article: Paper 3: Sandberg, H., E. Möllerstedt, and B. Bernhardsson "Frequency-Domain Analysis of Linear Time-Periodic Systems." Under review for IEEE Transactions on Automatic Control, 2004. Article: Paper 4: Sandberg, H. and B. Bernhardsson "A Bode Sensitivity Integral for Linear Time-Periodic Systems." Submitted to IEEE Transactions on Automatic Control, 2004.
id
4a95145a-549b-4ae0-b65e-844ef97c38e4 (old id 467645)
date added to LUP
2016-04-01 16:19:20
date last changed
2020-01-12 19:15:30
@phdthesis{4a95145a-549b-4ae0-b65e-844ef97c38e4,
  abstract     = {The thesis treats model reduction for linear time-varying systems. Time-varying models appear in many fields, including power systems, chemical engineering, aeronautics, and computational science. They can also be used for approximation of time-invariant nonlinear models. Model reduction is a topic that deals with simplification of complex models. This is important since it facilitates analysis and synthesis of controllers.<br/><br>
<br/><br>
The thesis consists of two parts. The first part provides an introduction to the topics of time-varying systems and model reduction. Here, notation, standard results, examples, and some results from the second part of the thesis are presented.<br/><br>
<br/><br>
The second part of the thesis consists of four papers. In the first paper, we study the balanced truncation method for linear time-varying state-space models. We derive error bounds for the simplified models. These bounds are generalizations of well-known time-invariant results, derived with other methods. In the second paper, we apply balanced truncation to a high-order model of a diesel exhaust catalyst. Furthermore, we discuss practical issues of balanced truncation and approximative discretization. In the third paper, we look at frequency-domain analysis of linear time-periodic impulse-response models. By decomposing the models into Taylor and Fourier series, we can analyze convergence properties of different truncated representations. In the fourth paper, we use the frequency-domain representation developed in the third paper, the harmonic transfer function, to generalize Bode's sensitivity integral. This result quantifies limitations for feedback control of linear time-periodic systems.},
  author       = {Sandberg, Henrik},
  issn         = {0280-5316},
  language     = {eng},
  publisher    = {Department of Automatic Control, Lund Institute of Technology (LTH)},
  school       = {Lund University},
  series       = {PhD Thesis TFRT-1071},
  title        = {Model Reduction for Linear Time-Varying Systems},
  url          = {https://lup.lub.lu.se/search/ws/files/4637025/8571781.pdf},
  year         = {2004},
}