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Harmonic analysis of pulse-width modulated systems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2009 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 4, 851-862 p.Article in journal (Refereed) Published
Abstract [en]

The paper considers the so-called dynamic phasor model as a basis for harmonic analysis of a class switching systems. The analysis covers both periodically switched systems and non-periodic systems where the switching is controlled by feedback. The dynamic phasor model is a powerful tool for exploring cyclic properties of dynamic systems. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems.

Place, publisher, year, edition, pages
2009. Vol. 45, no 4, 851-862 p.
Keyword [en]
Pulse-width modulation, Harmonic analysis, Dynamic phasors, Periodic systems, Switched-mode circuits, TIME-PERIODIC-SYSTEMS, STABILITY ANALYSIS, CONVERTERS
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-13748DOI: 10.1016/j.automatica.2008.10.029ISI: 000265155700001Scopus ID: 2-s2.0-61849182595OAI: oai:DiVA.org:kth-13748DiVA: diva2:327149
Note
QC 20100628Available from: 2010-06-28 Created: 2010-06-28 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Control and Analysis of Pulse-Modulated Systems
Open this publication in new window or tab >>Control and Analysis of Pulse-Modulated Systems
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The thesis consists of an introduction and four appended papers. In the introduction we give an overview of pulse-modulated systems and provide a few examples of such systems. Furthermore, we introduce the so-called dynamic phasor model which is used as a basis for analysis in two of the appended papers. We also introduce the harmonic transfer function and finally we provide a summary of the appended papers.

The first paper considers stability analysis of a class of pulse-width modulated systems based on a discrete time model. The systems considered typically have periodic solutions. Stability of a periodic solution is equivalent to stability of a fixed point of a discrete time model of the system dynamics.

Conditions for global and local exponential stability of the discrete time model are derived using quadratic and piecewise quadratic Lyapunov functions. A griding procedure is used to develop a systematic method to search for the Lyapunov functions.

The second paper considers the dynamic phasor model as a tool for stability analysis of a general class of pulse-modulated systems. The analysis covers both linear time periodic systems and systems where the pulse modulation is controlled by feedback. The dynamic phasor model provides an $\textbf{L}_2$-equivalent description of the system dynamics in terms of an infinite dimensional dynamic system. The infinite dimensional phasor system is approximated via a skew truncation. The truncated system is used to derive a systematic method to compute time periodic quadratic Lyapunov functions.

The third paper considers the dynamic phasor model as a tool for harmonic analysis of a class of pulse-width modulated systems. The analysis covers both linear time periodic systems and non-periodic systems where the switching is controlled by feedback. As in the second paper of the thesis, we represent the switching system using the L_2-equivalent infinite dimensional system provided by the phasor model. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems. The infinite dimensional phasor system is approximated via a square truncation. We assume that the response of the truncated system to a periodic disturbance is also periodic and we consider the corresponding harmonic balance equations. An approximate solution of these equations is stated in terms of a harmonic transfer function which is analogous to the harmonic transfer function of a linear time periodic system. The aforementioned assumption is proved to hold for small disturbances by proving the existence of a solution to a fixed point equation. The proof implies that for small disturbances, the approximation is good.

Finally, the fourth paper considers control synthesis for switched mode DC-DC converters. The synthesis is based on a sampled data model of the system dynamics. The sampled data model gives an exact description of the converter state at the switching instances, but also includes a lifted signal which represents the inter-sampling behavior. Within the sampled data framework we consider H-infinity control design to achieve robustness to disturbances and load variations. The suggested controller is applied to two benchmark examples; a step-down and a step-up converter. Performance is verified in both simulations and in experiments.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. xiii, 25 p.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 08/OS/04
Keyword
Pulse-width modulation, Periodic systems, Stability analysis, Harmonic analysis, Lyapunov methods, Dynamic phasors, Harmonic transfer function, Switched mode power converters, Sampled data modeling, H-infinity synthesis
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-4713 (URN)978-91-7178-959-4 (ISBN)
Public defence
2008-05-23, D3, D, Lindstedsvägen 5, KTH, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20100628Available from: 2008-04-29 Created: 2008-04-29 Last updated: 2010-06-30Bibliographically approved

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