Bifurcation behavior of the buck converter

Chakrabarty, Krishnendu; Poddar, Gautam; Banerjee, Soumitro

doi:10.1109/63.491637

Cited by 154 publications

(82 citation statements)

References 9 publications

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“…The orbit is periodic if the state at time point 9 coincides with that at time point 1. It has been shown that as a parameter (say, the input voltage) is varied, the orbit may lose stablity and highperiodic or chaotic orbits may occur [6], [7], [10]. Our concern here is to determine the stability of this orbit.…”

Section: Buck Converter and Its Mathematical Modelmentioning

confidence: 99%

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Stability Analysis of the Continuous-Conduction-Mode Buck Converter Via Filippov's Method

Giaouris

Banerjee

Zahawi

et al. 2008

IEEE Trans. Circuits Syst. I

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201

148

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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.

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Section: Buck Converter and Its Mathematical Modelmentioning

confidence: 99%

“…Similarly, (6) has to be solved to analyze the stability. The behavior of the perturbations around the fixed point is given by (7), again for .…”

Section: ) Trajectory Sensitivity Approachmentioning

confidence: 99%

Stability Analysis of the Continuous-Conduction-Mode Buck Converter Via Filippov's Method

Giaouris

Banerjee

Zahawi

et al. 2008

IEEE Trans. Circuits Syst. I

Self Cite

201

148

View full text Add to dashboard Cite

show abstract

“…In order to design a buck converter, the following input-output parameters are needed: Input voltage (V in ), output voltage (V 0 ), power rating (P 0 ), switching frequency (f s ), output voltage ripple (ΔV 0 ), and inductor current ripple (ΔI). Then, the low pass filter parameters (L and C) can be calculated using the formulas in [19]. Depending on the operation mode, either CCM or DCM, the value of the inductance is determined.…”

Section: Bifurcation and Chaos Applied To Buck Convertermentioning

confidence: 99%

An Experimental Simulation of a Design Three-Port DC-DC Converter

Sharif¹,

Harb²,

Hu³

et al. 2014

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Traditional DC-DC converter topologies interface two power terminals: a source and a load. The construction of diverse and flexible power management and distribution (PMAD) systems with such topologies is governed by a tight compromise between converter count, efficiency, and control complexity. The broader impact of the current research activity is the development of enhanced power converter systems suitable for a wide range of applications. Potential users of this technology include the designers of portable and stand-alone systems such as laptops, hand-held electronics, and communication repeater stations. High power topology options support the evolution of clean power technologies such as hybrid-electric vehicles (HEV's) and solar vehicles. DC-DC converter is considered as an advanced environmental issue since it is a greenhouse emission eliminator. By utilizing the advancement of these renewable energy sources, we minimize the use of fossil fuel. Thus, we will have a cleaner and pollution free environment. In this paper, a threeport DC-DC converter is designed and discussed. The converter was built and tested at the energy research laboratory at Taibah University, Al Madinah, KSA.

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“…Their nonlinear behavior has been extensively studied in various publications (Banerjee et al, 2001;di Bernardo et al, 1998;Fossas and Olivar, 1996). The literature shows that two different types of nonlinearities can occur, slow scale (El Aroudi et al, 1999) and fast scale (Banerjee and Chakrabarty, 1998;Chakrabarty et al, 1996) bifurcations. These bifurcations had been separately investigated as the outer voltage loop which had generally been believed to cause the slow-scale bifurcation is much slower than the inner current loop which causes the fast-scale bifurcation and the two loops were believed not to interact with each other.…”

Section: Introductionmentioning

confidence: 99%

Fast-Slow Scale Bifurcation in Higher Order Open Loop Current-Mode Controlled DC-DC Converters

Daho

Giaouris

Banerjee³

et al. 2009

IFAC Proceedings Volumes

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Higher order converters, without an external voltage control loop, have been known not to exhibit a fast-slow scale bifurcation interaction, as the slow-scale bifurcation has generally been believed to be caused by parameter changes in the outer loop. In this paper, it is shown that a current-mode controlled Ćuk converter can exhibit an interaction between fast-scale and slow-scale bifurcations even in the absence of this closed outer voltage control loop. The phenomenon is probed using an approach based on the system's monodromy matrix that does not only predict this instability but also provides a systematic method for the development of new control strategies to avoid the onset of this bifurcation. Analytical and numerical results prove that the new controller greatly extends the stable region of operation of the converter.

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Bifurcation behavior of the buck converter

Cited by 154 publications

References 9 publications

Stability Analysis of the Continuous-Conduction-Mode Buck Converter Via Filippov's Method

Stability Analysis of the Continuous-Conduction-Mode Buck Converter Via Filippov's Method

An Experimental Simulation of a Design Three-Port DC-DC Converter

Fast-Slow Scale Bifurcation in Higher Order Open Loop Current-Mode Controlled DC-DC Converters

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