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Stability analysis of the continuous-conduction-mode buck converter via Filippov's method

Lookup NU author(s): Dr Damian Giaouris, Professor Soumitro Banerjee, Dr Bashar Zahawi, Professor Volker Pickert

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Abstract

To study the stability of a nominal cyclic steady state in power electronic converters, it is necessary to obtain a linearization around the periodic orbit. In many past studies, this was achieved by explicitly deriving the Poincaré map that describes the evolution of the state from one clock instant to the next and then locally linearizing the map at the fixed point. However, in many converters, the map cannot be derived in closed form, and therefore this approach cannot directly be applied. Alternatively, the orbital stability can be worked out by studying the evolution of perturbations about a nominal periodic orbit, and some studies along this line have also been reported. In this paper, we show that Filippov's method - which has commonly been applied to mechanical switching systems - can be used fruitfully in power electronic circuits to achieve the same end by describing the behavior of the system during the switchings. By combining this and the Floquet theory, it is possible to describe the stability of power electronic converters. We demonstrate the method using the example of a voltage-mode-controlled buck converter operating in continuous conduction mode. We find that the stability of a converter is strongly dependent upon the so-called saltation matrix - the state transition matrix relating the state just after the switching to that just before. We show that the Filippov approach, especially the structure of the saltation matrix, offers some additional insights on issues related to the stability of the orbit, like the recent observation that coupling with spurious signals coming from the environment causes intermittent subharmonic windows. Based on this approach, we also propose a new controller that can significantly extend the parameter range for nominal period-1 operation. © 2008 IEEE.


Publication metadata

Author(s): Giaouris D, Banerjee S, Zahawi B, Pickert V

Publication type: Article

Publication status: Published

Journal: IEEE Transactions on Circuits and Systems I: Regular Papers

Year: 2008

Volume: 55

Issue: 4

Pages: 1084-1096

Print publication date: 01/05/2008

ISSN (print): 1549-8328

ISSN (electronic): 1558-0806

Publisher: IEEE

URL: http://dx.doi.org/10.1109/TCSI.2008.916443

DOI: 10.1109/TCSI.2008.916443


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