The switched-inductor structure can be inserted into a traditional Buck-Boost converter to get a high voltage conversion ratio. Nonlinear phenomena may occur in this new converter, which might well lead the system to be unstable. In this paper, a discrete iterated mapping model is established when the new Buck-Boost converter is working at continuous conduction current-controlled mode. On the basis of the discrete model, the bifurcation diagrams and Poincare sections are drawn and then used to analyze the effects of the circuit parameters on the performances. It can be seen clearly that various kinds of nonlinear phenomena are easy to occur in this new converter, including period-doubling bifurcation, border collision bifurcation, tangent bifurcation, and intermittent chaos. Value range of the circuit parameters that may cause bifurcations and chaos are also discussed. Finally, the time-domain waveforms, phase portraits, and power spectrum are obtained by using Matlab/Simulink, which validates the theoretical analysis results.

In recent years, much attention was paid to the switched-inductor structure because of its several unique characteristics. One of the most remarkable feature of the switched-inductor structure is that it can be combined with the traditional DC-DC converters to provide new converters with a steep voltage conversion ratio [

The nonlinear phenomena in the new Buck-Boost converter may be rather complex than that in the traditional converters, which will deteriorate the performance of the converter to some extent. The bifurcation and the chaos in traditional DC-DC converters were studied extensively [

For this reason, the nonlinear phenomena in a current-mode controlled Buck-Boost converter with switched-inductor structure are studied in this paper. The discrete iterated mapping model under continuous conduction mode (CCM) is established. The bifurcation diagrams and Poincare sections are drawn based on the discrete-time model, which intuitively reflect the influence of the circuit parameters on the system performance. It can be shown clearly that many kinds of nonlinear phenomena existing in this new converter, such as period-doubling bifurcation, border collision bifurcation, tangent bifurcation, and intermittent chaos. At last, the time-domain waveform, phase portraits, and power spectrum under various load resistance are obtained by Matlab/Simulink, which validates the conclusions that came from the theoretical analysis. The research result provides an important reference for engineering design and performance analysis.

The schematic of the new current-mode controlled Buck-Boost converter with switched-inductor structure is shown in Figure

Current-mode controlled buck-boost converter with switched-inductor structure.

Switching topologies of the converter. (a) Switch is on; (b) switch is off.

As shown in Figure

Let

where

Similarly, the differential equation can be written as follows during

where

Noting that there is a conversion between

Also, we can get

Considering that

where

According to the control theory, solutions of (

where

In general, the discrete time model can be established by means of stroboscopic map, S-switching map, or A-switching map. The stroboscopic map was widely used to analyze the nonlinear phenomena in the switching converters [

Let

where

Also, when the converter is working during “off” period, the solution of

where

and

Based on the operating principle of the converter, the switching condition of the system can be defined as

According to (

If

If

where

Let

The voltage drop on

Thus, a voltage-second balance on

giving

where

Similarly, for a classical Buck-Boost converter, we can easily get that

Comparing (

For the power converters, many kinds of methods like phase portraits, bifurcation diagrams, and time-domain waveform can be used to analyze the nonlinear phenomenon in the system. In this work, the bifurcation diagrams and Poincare sections are drawn based on the discrete iterated mapping model. Time-domain waveform, phase portraits, and power spectrum are obtained by building simulation module in Matlab/Simulink, which validates the theoretical analysis results.

It can be seen clearly from Figure

Let reference current

Bifurcation diagram with different circuit parameters. (a)

The bifurcation diagram with load resistance

The bifurcation diagram with input voltage

Poincare sections can be an effective method to analyze the dynamic characteristics of nonlinear systems. According to nonlinear dynamics theory, the performance of the system can be judged by observing the number of the cutoff points on the Poincare sections. One point or a few discrete points indicates that the converter is working in periodical state, while the cutoff point with a fractal structure reveals a chaotic behavior.

To prove that when the reference current

The Poincare sections under different value of reference current. (a)

It can be seen clearly from Figures

The bifurcation diagram in Figure

The time-domain waveform and phase portrait when

The time-domain waveform and phase portrait when

The time-domain waveform and phase portrait when

The time-domain waveform and phase portrait when

The time-domain waveform and phase portrait when

From Figures

The time-domain waveform and phase portrait when the load resistance is equal to 55 Ω are shown in Figure

According to the time-domain waveforms and phase portraits from Figure

The power spectrum is also an effective way to analyze the stability of the circuit. When the circuit operates in the cycle

The power spectrum under different value of load resistance. (a)

Inserting the switched-inductor structure into traditional Buck-Boost converter can increase its voltage conversion ratio significantly. However, it will lead to a conversion of the inductors from series connection to parallel connection, which makes it easier for the system to be affected by the circuit parameters. In this paper, the nonlinear behaviors of the Buck-Boost converter with switched-inductor structure have been studied systematically. The discrete iterated mapping model under CCM is established. The effects of circuit parameters on system performance are analyzed using bifurcation diagrams and Poincare sections. Then, the corresponding time-domain waveforms, phase portraits, and power spectrum are obtained by Matlab/Simulink. The research results show that various kinds of nonlinear phenomena are easy to come in this new converter, including period-doubling bifurcation, border collision bifurcation, tangent bifurcation, and intermittent chaos. The results between the theoretical analysis and the simulation are in general agreement with each other. According to the analysis above, the Buck-Boost converter with switched-inductor structure belongs to strongly nonlinear system, and its performance can be easily affected when the circuit parameters are varied. Therefore, the parameters should be chosen appropriately according to the research results. The analysis methods and research findings will possess an important reference value to engineering design and performance analysis.

This work is supported by the National Natural Science Foundation of China (no. 51107016), the National Key Basic Research Program of China (973 Program) under Grant (2013CB035605), and the Postdoctoral science-research developmental foundation of Heilongjiang province (no. LHB-Q12086).