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Linear Time-Varying Systems: Modeling and Reduction

Sandberg, Henrik LU (2002)
Abstract
Linear time-invariant models are widely used in the control community. They often serve as approximations of nonlinear systems. For control purposes linear approximations are often good enough since feedback control systems are inherently robust to model errors. In this thesis some of the possibilities for linear time-varying modeling are studied. In the thesis it is shown that the balanced truncation procedure can be applied to reduce the order of linear time-varying systems. Many of the attractive properties of balanced truncation for time-invariant systems can be generalized into the time-varying framework. For example, it is shown that a truncated input-output stable system will be input-output stable, and computable simple worst-case... (More)
Linear time-invariant models are widely used in the control community. They often serve as approximations of nonlinear systems. For control purposes linear approximations are often good enough since feedback control systems are inherently robust to model errors. In this thesis some of the possibilities for linear time-varying modeling are studied. In the thesis it is shown that the balanced truncation procedure can be applied to reduce the order of linear time-varying systems. Many of the attractive properties of balanced truncation for time-invariant systems can be generalized into the time-varying framework. For example, it is shown that a truncated input-output stable system will be input-output stable, and computable simple worst-case error bounds are derived. The method is illustrated with model reduction of a nonlinear diesel exhaust catalyst model. It is also shown that linear time-periodic models can be used for analysis of systems with power converters. Power converters produce harmonics in the power grids and give frequency coupling that cannot be modeled with standard time-invariant linear models. With time-periodic models we can visualize the coupling and also use all the available tools for linear time-varying systems, such as balanced truncation. The method is illustrated on inverter locomotives. (Less)
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author
supervisor
organization
publishing date
type
Thesis
publication status
published
subject
keywords
linear time-varying, model reduction, balanced truncation, error bounds, power converters, periodic modeling, harmonics, inverter locomotive
pages
102 pages
publisher
Department of Automatic Control, Lund Institute of Technology (LTH)
language
English
LU publication?
yes
id
bc30540e-ec94-4f25-9ec1-4d510faf47e0 (old id 1044347)
date added to LUP
2008-03-05 13:32:27
date last changed
2016-09-19 08:44:59
@misc{bc30540e-ec94-4f25-9ec1-4d510faf47e0,
  abstract     = {Linear time-invariant models are widely used in the control community. They often serve as approximations of nonlinear systems. For control purposes linear approximations are often good enough since feedback control systems are inherently robust to model errors. In this thesis some of the possibilities for linear time-varying modeling are studied. In the thesis it is shown that the balanced truncation procedure can be applied to reduce the order of linear time-varying systems. Many of the attractive properties of balanced truncation for time-invariant systems can be generalized into the time-varying framework. For example, it is shown that a truncated input-output stable system will be input-output stable, and computable simple worst-case error bounds are derived. The method is illustrated with model reduction of a nonlinear diesel exhaust catalyst model. It is also shown that linear time-periodic models can be used for analysis of systems with power converters. Power converters produce harmonics in the power grids and give frequency coupling that cannot be modeled with standard time-invariant linear models. With time-periodic models we can visualize the coupling and also use all the available tools for linear time-varying systems, such as balanced truncation. The method is illustrated on inverter locomotives.},
  author       = {Sandberg, Henrik},
  keyword      = {linear time-varying,model reduction,balanced truncation,error bounds,power converters,periodic modeling,harmonics,inverter locomotive},
  language     = {eng},
  note         = {Licentiate Thesis},
  pages        = {102},
  publisher    = {Department of Automatic Control, Lund Institute of Technology (LTH)},
  title        = {Linear Time-Varying Systems: Modeling and Reduction},
  year         = {2002},
}