Asymptotic tracking in DC-to-DC nonlinear power converters

E. Fossas-Colet; J.M. Olm-Miras

doi:10.3934/dcdsb.2002.2.295

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2002, Volume 2, Issue 2: 295-307. Doi: 10.3934/dcdsb.2002.2.295

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Asymptotic tracking in DC-to-DC nonlinear power converters

E. Fossas-Colet^1, and
J.M. Olm-Miras^1,

1.
Institut de'Organizació i Control de Sistemes Industrials, Universitat Politècnicade Catalunya, Avda. Diagonal 647, Pl. 11, 08028 Barcelona

Received: March 31, 2001

Revised: December 31, 2001

Published: April 2002

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Abstract

The aim of this paper is to solve a tracking problem in a particular second order control system that requires indirect control. A complete knowledge of the plant parameters is assumed. The calculation of the indirect tracking depends on the solution of an inverse problem given by an ordinary differential equation. In spite of the instability of the generic solution of the differential equation, the existence of a bounded, periodic solution for the tracking of a periodic signal is proved. Finally, the periodic solution is approximated by the harmonic balance method, and the original tracking problem is solved.

Keywords:

Systems governed by ordinary differential equations,
periodic solutions,
stability.

Mathematics Subject Classification: 34C25, 93C15.

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