84 research outputs found
Analysis and Control of Period Doubling Bifurcation in Buck Converters Using Harmonic Balance
Period doubling bifurcation in buck convertersis studied by using the harmonic balance method.A simple dynamic model of a buck converter in continuous conduction modeunder voltage mode or current mode controlis derived.This model consists of the feedback connection of a linear system and a nonlinear one.An exact harmonic balance analysis is usedto obtain a necessary and sufficient condition fora period doubling bifurcation to occur.If such a bifurcation occurs,the analysis also provides information on its exact location.Using the condition for bifurcation,a feedforward control is designed thateliminates a period doubling bifurcation.This results in a wider range of allowed source voltage,and also in improved output voltage regulation
Bifurcation Boundary Conditions for Switching DC-DC Converters Under Constant On-Time Control
Sampled-data analysis and harmonic balance analysis are applied to analyze
switching DC-DC converters under constant on-time control. Design-oriented
boundary conditions for the period-doubling bifurcation and the saddle-node
bifurcation are derived. The required ramp slope to avoid the bifurcations and
the assigned pole locations associated with the ramp are also derived. The
derived boundary conditions are more general and accurate than those recently
obtained. Those recently obtained boundary conditions become special cases
under the general modeling approach presented in this paper. Different analyses
give different perspectives on the system dynamics and complement each other.
Under the sampled-data analysis, the boundary conditions are expressed in terms
of signal slopes and the ramp slope. Under the harmonic balance analysis, the
boundary conditions are expressed in terms of signal harmonics. The derived
boundary conditions are useful for a designer to design a converter to avoid
the occurrence of the period-doubling bifurcation and the saddle-node
bifurcation.Comment: Submitted to International Journal of Circuit Theory and Applications
on August 10, 2011; Manuscript ID: CTA-11-016
Unified model of voltage/current mode control to predict saddle-node bifurcation
A unified model of voltage mode control (VMC) and current mode control (CMC)
is proposed to predict the saddle-node bifurcation (SNB). Exact SNB boundary
conditions are derived, and can be further simplified in various forms for
design purpose. Many approaches, including steady-state, sampled-data, average,
harmonic balance, and loop gain analyses are applied to predict SNB. Each
approach has its own merits and complement the other approaches.Comment: Submitted to International Journal of Circuit Theory and Applications
on December 23, 2010; Manuscript ID: CTA-10-025
Sampled-Data and Harmonic Balance Analyses of Average Current-Mode Controlled Buck Converter
Dynamics and stability of average current-mode control of buck converters are
analyzed by sampled-data and harmonic balance analyses. An exact sampled-data
model is derived. A new continuous-time model "lifted" from the sampled-data
model is also derived, and has frequency response matched with experimental
data reported previously. Orbital stability is studied and it is found
unrelated to the ripple size of the current-loop compensator output. An
unstable window of the current-loop compensator pole is found by simulations,
and it can be accurately predicted by sampled-data and harmonic balance
analyses. A new S plot accurately predicting the subharmonic oscillation is
proposed. The S plot assists pole assignment and shows the required ramp slope
to avoid instability.Comment: Submitted to International Journal of Circuit Theory and Applications
on August 9, 2011; Manuscript ID: CTA-11-016
Closed-Form Critical Conditions of Subharmonic Oscillations for Buck Converters
A general critical condition of subharmonic oscillation in terms of the loop
gain is derived. Many closed-form critical conditions for various control
schemes in terms of converter parameters are also derived. Some previously
known critical conditions become special cases in the generalized framework.
Given an arbitrary control scheme, a systematic procedure is proposed to derive
the critical condition for that control scheme. Different control schemes share
similar forms of critical conditions. For example, both V2 control and voltage
mode control have the same form of critical condition. A peculiar phenomenon in
average current mode control where subharmonic oscillation occurs in a window
value of pole can be explained by the derived critical condition. A ripple
amplitude index to predict subharmonic oscillation proposed in the past
research has limited application and is shown invalid for a converter with a
large pole.Comment: Submitted to an IEEE Journal on Dec. 23, 2011, and resubmitted to
IEEE Transactions on Circuits and Systems-I on Feb. 14, 2012. My current six
papers in arXiv have a common reviewe
Closed-Form Critical Conditions of Saddle-Node Bifurcations for Buck Converters
A general and exact critical condition of saddle-node bifurcation is derived
in closed form for the buck converter. The critical condition is helpful for
the converter designers to predict or prevent some jump instabilities or
coexistence of multiple solutions associated with the saddle-node bifurcation.
Some previously known critical conditions become special cases in this
generalized framework. Given an arbitrary control scheme, a systematic
procedure is proposed to derive the critical condition for that control scheme.Comment: Submitted to IEEE Transactions on Automatic Control on Jan. 9, 2012.
Seven of my arXiv manuscripts have a common reviewe
Using Nyquist or Nyquist-Like Plot to Predict Three Typical Instabilities in DC-DC Converters
By transforming an exact stability condition, a new Nyquist-like plot is
proposed to predict occurrences of three typical instabilities in DC-DC
converters. The three instabilities are saddle-node bifurcation (coexistence of
multiple solutions), period-doubling bifurcation (subharmonic oscillation), and
Neimark bifurcation (quasi-periodic oscillation). In a single plot, it
accurately predicts whether an instability occurs and what type the instability
is. The plot is equivalent to the Nyquist plot, and it is a useful design tool
to avoid these instabilities. Nine examples are used to illustrate the accuracy
of this new plot to predict instabilities in the buck or boost converter with
fixed or variable switching frequency.Comment: Submitted to an IEEE journal in 201
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