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Frequency-domain analysis of linear time-periodic systems
2005 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 50, no 12, 1971-1983 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature.

Place, publisher, year, edition, pages
2005. Vol. 50, no 12, 1971-1983 p.
Keyword [en]
convergence analysis, frequency-response operators, linear time-periodic systems, series expansions, sampled-data systems, response operators, h(infinity), infinity, h(2), controllers, norm, h-2
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-15259DOI: 10.1109/TAC.2005.860294ISI: 000234062800004Scopus ID: 2-s2.0-30344466922OAI: oai:DiVA.org:kth-15259DiVA: diva2:333300
Note

QC 20111110

Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Model Reduction for Linear Time-Varying Systems
Open this publication in new window or tab >>Model Reduction for Linear Time-Varying Systems
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Lund: Lund University, 2004. 174 p.
Series
Institutionen för reglerteknik, Lunds universitet, ISSN 0280-5316 ; 1071
Keyword
Model reduction, Linear systems, Time-varying systems, Error bounds, Frequency-domain analysis, Convergence analysis, Performance limitations
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-74698 (URN)
Public defence
2004-12-03, M:B, Maskinhuset, Lunds tekniska högskola, Lund, 10:15 (English)
Opponent
Supervisors
Note
QC 20120206Available from: 2012-02-06 Created: 2012-02-03 Last updated: 2012-02-06Bibliographically approved

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Sandberg, Henrik

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