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A bode sensitivity integral for linear time-periodic systems
2005 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 50, no 12, 2034-2039 p.Article in journal (Refereed) Published
Abstract [en]

Bode's sensitivity integral is a well-known formula that quantifies some of the limitations in feedback control for linear time-invariant systems. In this note, we show that there is a similar formula for linear time-periodic systems. The harmonic transfer function is used to prove the result. We use the notion of roll-off 2, which means that the first time-varying Markov parameter is equal to zero. It then follows that the harmonic transfer function is an analytic operator and a trace class operator. These facts are used to prove the result.

Place, publisher, year, edition, pages
2005. Vol. 50, no 12, 2034-2039 p.
Keyword [en]
Bode sensitivity integral, linear time-periodic systems, performance limitations, frequency-response, feedback-systems, varying systems, tradeoffs, analog
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-15260DOI: 10.1109/TAC.2005.860247ISI: 000234062800010Scopus ID: 2-s2.0-30344454665OAI: oai:DiVA.org:kth-15260DiVA: diva2:333301
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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