基于Kharitonov引理的PWM推挽DC-DC转换器时间域分析新方法
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本文探讨了一种新颖的时间域分析方法，针对扰动脉冲宽度调制（PWM）推挽直流-直流转换器，发表在2012年的《控制理论与应用》期刊上。作者 Yogesh V. Hote 来自印度理工学院拉克纳分校电气工程系，该研究专注于解决传统PWM推挽变换器在非线性扰动下的动态行为。
论文的核心内容是基于Kharitonov定理的一个有趣推论，这个定理在系统稳定性分析中具有重要地位。Kharitonov定理原本用于判断线性系统的稳定性，但在本文中被巧妙地应用于PWM推挽变换器的时域分析，即使在存在非线性扰动的情况下，也能够保持线性模型的有效性。这意味着即使转换器的实际工作条件可能包含非线性因素，通过这种方法，工程师可以依然对系统的瞬态响应和稳态行为进行精确评估。
该分析方法的优势在于其简单、计算效率高且易于在精密应用领域，如航空航天工程中实施。通过 MATLAB 仿真验证了提出的分析方法的有效性，这对于电力电子工程师来说具有很高的实用价值，因为他们可以借此工具更深入地理解和控制这类转换器在实际运行中的性能。
论文的关键词包括：Kharitonov定理、扰动PWM（推挽直流-直流转换器）、瞬态响应、稳态响应以及稳定性。通过这篇论文，研究者为设计和优化电力电子设备提供了重要的理论支持，特别是在追求高精度和快速响应的现代工业环境中。这项工作对于提升PWM推挽直流-直流转换器的设计和控制技术具有重要意义。
J Control Theory
Appl
2012
10
(4)
465
-4
69
DOI
1O
.1007/s11768-012-0064-4
A new
approach
to time domain analysis
of
perturbed
P
叭响1:
push-pull DC-DC converter
Yogesh
V.
HOTE
Department
of
Electrical
Engineering
,
Indian
Institute
of
TI
巳
chnology
，
Roorkee
,
Uttarakh
缸尬，
India
Abstract:
In
this
paper, an analytical technique
is
presented
for
tim
巳
domain
an
a1
ysis
(transient
and
st
巳
ady-stat
巳
response) of perturbed
PWM
push-pull
DC-DC
conv
巳
rter
using interesting corollary
on
Kharitonov's
theorem.
The
main
advantage of
the
proposed analysis
is
that
even
though
the
transfer function
model
of a
PVI
币1"
push-pull
DC-DC
converter
is
perturb
时，
the
complete analysis
has
been
done
on
a linear transfer function
model
of a
PWM
push-pull
DC-DC
converter.
The
proposed analysis
is
verified
using
MATLAB
simulation. This analysis
will
be
very
much
useful
to
power electronics
engineers
, since
the
technique
is
very
simple
and
computationally efficient
and
easily applicable
in
precise applications
such
as
aerospace applications
Keywords:
Kh
aritonov's theorem; Perturbed
PVI
币1(
push-pull
DC-DC
conv
巳
rt
巳
r;
Transient response; Steady state
response; Stability; Aerospace applications.
1 Introduction
The study
of
a control system in time domain essen-
tially involves the evaluation
of
transient and
st
巳
ady-state
responses
of
the system. The nature
of
transient response
of
a linear control system is dependent on the system poles
only and not on the type
of
the input, whereas steady-state
respons
巳
depends
on both the system and the type
of
the
mput
口
2].
When the system is linear, the above analysis
can be done easily. But
, for uncertain or perturbed systems,
th
巳
complete
analysis in transient and steady state mode is a
challenging task. DC-DC converters are widely
us
巳
d
in reg-
ulated switch mode power supplies
, computer hardware, dc
motor drive applications and most importantly
in
aerospace
applications
[3]. In practice, there exist uncertainties in the
components
ofthe
DC-DC converter, i.e., values
ofthe
com-
ponents vary within certain bounds.
It
is because
of
the fact
that electrolytic capacitors
, which are used in the output
filters
of
DC-DC
converters, have tolerances from
-20%
to 100% around their nominal values. The capacitance
of
the capacitor and load resistance depends upon temperature,
which
may
change with time because
of
aging effec
t.
From
th
巳巳
xisting
literature, it is found that previous authors have
sucessesfully done robust stability testing
of
perturbed DC-
DC converter using
Kharitonov's theorem
[4-
6].
Recently
, simple technique has been proposed for robust
stability analysis
of
P\
币1{
push-pull state feedback control
of
DC-DC converter using Hermite-Biehler theorem [7-8].
But
, the results presented in [6,
8]
gives only the sufficient
condition
of
stability
of
state feedback controlled perturbed
PWM push-pull DC-DC converter. It is found that for de-
pendent uncertain polynomial
, Kharitonov's theorem gives
conservative results. The altemative approaches were pre-
sented for stability analysis
of
DC-DC converters in [9-11].
In [12]
, necessary and sufficient conditions
of
robust sta-
bility are established for
PWM
push-pull DC-DC converter
Received
14
March
2010;
revised
31
Octob
巳
r
201
1.
using Krishnamurthi's corollary on Routh criterion
as
re-
ported in [13].
It
is observed that power electronics engineering not only
needs stability but also needs complete information
of
the
system in both transient and steady-state conditions such
as
overshoot, peak overshoot, settling time, rise time, and
steady state error and dynamic error coefficients. Thus
, the
idea behind this paper is to investigate the dynamic behav-
ior
of
PWM
push-pull DC-DC converters, which will help
to design a system with the desired performance. To the best
of
my knowledge, we have not found any research paper,
which has achieved transient and steady analysis
of
per-
turbed DC-DC converter in a simple analytical manner.
In [14], Anderson
et
al. have shown that for stability
of
a third-order perturbed system, there is need for checking
only single polynomial instead
of
four
polynoll
垃
als.
Based
on this corollary
, in this paper, we have deterrnined time re-
sponse parameters
of
perturbed state feedback
PWM
push-
pull DC-DC converter [6] considering only single trans-
fer function (single closed-Ioop characteristic equation) and
thereby complete analysis in time domain have
be
巳
n
done.
In this analysis
, worst-case time domain
p
缸
ameters
，
i.e.,
rise time, peak time, settling time, peak overshoot, steady-
state response and dynamic error coefficients have been de-
terrnined for only single transfer function
of
a perturbed
P\
币1{
push-pull DC-DC converter model. In conventional
approach
, this analysis has to
be
carried out on all four
transfer function model
of
a
PWM
push-pull DC-DC con-
verter. The results are verified using simulation in
MAT-
LAB environmen
t.
This paper is organized as follows: Sec-
tion 2 includes
Kharitonov's theorem; Section 3 includes
brief review on time domain analysis; Section 4 includes
introduction
to
PWM
push-pull DC-DC converter; Section
5 includes time domain analysis
ofPWM
push-pull DC-DC
converter; Section 6 includes conclusion and finally refer-
ences are glven.
@
South
China
University
of
Technology
and
Academy
of
Math
巳
matics
and
Systems
Science
,
CAS
and
Springer-Verlag
Berlin
Heidelberg
2012
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