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BIFURCATION ANALYSIS ON NONSMOOTH TORUS DESTRUCTION SCENARIO OF DELAYED-PWM SWITCHED BUCK CONVERTER

Department of Electrical and Electronics Engineering & Computer Science, Universidad Nacional de Colombia — Sede Manizales, Manizales, Caldas, Colombia

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F. ANGULO

Department of Electrical and Electronics Engineering & Computer Science, Universidad Nacional de Colombia — Sede Manizales, Manizales, Caldas, Colombia

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, and

G. OLIVAR

Department of Electrical and Electronics Engineering & Computer Science, Universidad Nacional de Colombia — Sede Manizales, Manizales, Caldas, Colombia

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https://doi.org/10.1142/S0218127409024013Cited by:7 (Source: Crossref)

Abstract

In this paper, we propose a qualitative and quantitative dynamical study about the evolution of nonsmooth torus in a Digital Delayed Pulse-Width Modulator (PWM) switched buck converter. We explain the birth and destruction of the torus by successive discontinuity induced bifurcations (DIBs). The Digital-PWM control is based on Zero Average Dynamics (ZAD) strategy and a one-period delay is included in the control law. The control parameter (k_s) of the ZAD strategy can be varied in a large range, ideally (-∞, ∞). On these borders, the dynamical behavior is the same and thus an annulus-like parameter space is considered. Under variation of k_s, the system gets closer to a codimension-two bifurcation point, where two simultaneous border-collision bifurcations (BC) meet. The system leaves the high-order periodic behavior and a high-order band torus appears. Wrinkles and nonsmoothness due to more and more successive border-collisions bifurcations cause the torus destruction in high-order band chaos with tent-map-like structures and Mandelbrot-like sets. Finally, the chaotic bands merge in one-band chaos. The switched converter is modeled as a piecewise linear system where an analytical expression of the Poincaré map is available. Characteristics as duality, symmetry and recurrent behavior are determined using additional numerical methods for the Poincaré map decomposition in periodic sequences.

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