Dinámica de un mapa estroboscópico discontinuo. Una aplicación al convertidor DC-DC BuckBoost
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Date
2021
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Pontificia Universidad Javeriana Cali
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In this work we show the ocurrence of big bnag bifurcation in the two-dimensional stroboscopic map asociated at a canonical form of PWL systems given by [13, 14] whit diferent matrix. the work consists of 3 chapters.
In the rst chapter we give a rigorous study of one and two dimensio nal discrete maps, canonical forms to two dimensional PWL systems and stroboscopic maps.
At the second chapter we show the necesary results about the ocurrence of big bang bifurcation in a one-dimensional discrete map and two-dimensional stroboscopic maps whit the same matrix, too get some elements of [2] to characterize the exponential matrix in the stroboscopic map and we study the main propieties of the stroboscopic map asociated a PWL system whit two diferent matrix to show the occurrence of the big bang bifurcation in this map.
Finaly in the third chapter we study the DC-DC Buck-Boost converter model given by [23], from a short description of its operation to the deduction of its model. After deduce the model we show the topologically equivalent system given by the canonical form studied in the Chapter 2 and we show the occurrence of the big bang bifurcation in this canonical form using the original parametres values and we show other phenomens like coexisting periodic orbits in the stroboscopic map asociated at the original adimensional system of the Buck-Boost converter