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Control and Analysis of Pulse-Modulated SystemsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: KTH , 2008. , xiii, 25 p.
##### Series

Trita-MAT. OS, ISSN 1401-2294 ; 08/OS/04
##### Keyword [en]

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: urn:nbn:se:kth:diva-4713ISBN: 978-91-7178-959-4OAI: oai:DiVA.org:kth-4713DiVA: diva2:13578
##### Public defence

2008-05-23, D3, D, Lindstedsvägen 5, KTH, Stockholm, 10:00
##### Opponent

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##### Supervisors

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#####

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##### Note

QC 20100628Available from: 2008-04-29 Created: 2008-04-29 Last updated: 2010-06-30Bibliographically approved
##### List of papers

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.

1. Stability analysis of a class of PWM systems$(function(){PrimeFaces.cw("OverlayPanel","overlay327138",{id:"formSmash:j_idt503:0:j_idt507",widgetVar:"overlay327138",target:"formSmash:j_idt503:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Dynamic phasor analysis of pulse-modulated systems$(function(){PrimeFaces.cw("OverlayPanel","overlay327185",{id:"formSmash:j_idt503:1:j_idt507",widgetVar:"overlay327185",target:"formSmash:j_idt503:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Harmonic analysis of pulse-width modulated systems$(function(){PrimeFaces.cw("OverlayPanel","overlay327149",{id:"formSmash:j_idt503:2:j_idt507",widgetVar:"overlay327149",target:"formSmash:j_idt503:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Sampled data control of DC-DC converters$(function(){PrimeFaces.cw("OverlayPanel","overlay327258",{id:"formSmash:j_idt503:3:j_idt507",widgetVar:"overlay327258",target:"formSmash:j_idt503:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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