Study of Bifurcation and Chaos in DC-DC Boost Converter using Discrete-Time Map
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Transcript of Study of Bifurcation and Chaos in DC-DC Boost Converter using Discrete-Time Map
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Study of Bifurcation and Chaos in DC-DC Boost
Converter using Discrete-Time Map
Sajid Iqbal Ph.D student
Harbin Institute of Technology
![Page 2: Study of Bifurcation and Chaos in DC-DC Boost Converter using Discrete-Time Map](https://reader033.fdocuments.us/reader033/viewer/2022051617/55aabde81a28ab54138b47f6/html5/thumbnails/2.jpg)
• Zheng Jie
![Page 3: Study of Bifurcation and Chaos in DC-DC Boost Converter using Discrete-Time Map](https://reader033.fdocuments.us/reader033/viewer/2022051617/55aabde81a28ab54138b47f6/html5/thumbnails/3.jpg)
Contents
• Chaos and bifurcation
• DC-DC boost converter
• Discrete-time map
• Tools for finding chaotic dynamics
o Time series
o Bifurcation diagram
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‘Deterministic Chaos’ is an unstable aperiodic behavior in deterministic dynamical system, which shows sensitive dependence on initial conditions.
Edward Lorenz coined the term ‘Butterfly Effect’.
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‘Bifurcation’ is a sudden qualitative change in the behavior of a dynamical system caused by the variation of its parameters.
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In a boost chopper, the output voltage is always more or equal to the input voltage.
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DC-DC converters have many sources of nonlinearity like
Semiconductors devices: diodes, transistors
Passive components: capacitors, inductors and
Feedback control circuits
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A ‘time series plot’ is a display of data points that shows how values have changed over uniform time intervals
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A ‘bifurcation diagram’ is a visual summary chart of the behaviors exhibited by a dynamical system, when some parameters are varied.
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For developing a discrete-time system, the dynamical variables of the continuous-time system are sampled once every period.
The goal is to create a mapping, difference equation or iterative map as
Where ‘Xn’ is the state vector at the nth switching instant and k represents the feedback factor.
1 n(x ,k)nx f
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The discrete-time model of Tse is revisited. As an first-order iterative map
‘vn’ is the voltage and ‘dn’ is the duty cycle during the nth period.
1 n( ,d )n nv f v
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The iterates settle down to a fixed value
Period-1 orbit
1n nv v
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The iterated solutions reappear every second value
Period-2 orbit
2n nv v
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Time series plots of boost converter (cont.)
Aperiodic behavior
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Bifurcation diagram for boost converter.
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