Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
8,
No.
6,
December
2018,
pp.
4282
–
4289
ISSN:
2088-8708,
DOI:
10.11591/ijece.v8i6.pp4282-4291
4282
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
A
No
v
el
Nonlinear
Contr
ol
of
Boost
Con
v
erter
using
CCM
Phase
Plane
Ek
o
Setiawan
1
and
Ichijo
Hodaka
2
1
Interdisciplinary
Graduate
School
of
Agriculture
and
Engineering,
Uni
v
ersity
of
Miyazaki,
Japan
2
Department
of
En
vironmental
Robotics,
Uni
v
ersity
of
Miyazaki,
Japan
Article
Inf
o
Article
history:
Recei
v
ed
Jan
20,
2018
Re
vised
Jul
18,
2018
Accepted
Aug
7,
2018
K
eyw
ord:
Nonlinear
control
Boost
con
v
erter
Continuous
Conduction
Mode
Phase
plane
ABSTRA
CT
Boost
con
v
erter
is
one
of
fundamental
DC-DC
con
v
erters
and
used
to
deli
v
er
electric
po
wer
with
boosted
v
oltage
in
man
y
electrical
systems.
Se
v
eral
control
strate
gies
ha
v
e
been
applied
to
control
a
boost
con
v
erter
deli
v
ering
a
constant
output
v
oltage.
Gener
-
ally
,
boost
con
v
erter
w
orks
in
tw
o
modes;
one
is
called
a
Continuous
Conduction
Mode
(CCM).
Man
y
researches
use
CCM
model
in
the
controller
design,
b
ut
the
y
ne
v
er
en-
sure
that
the
controller
al
w
ays
w
orks
in
CCM.
This
paper
proposes
no
v
el
nonlinear
controller
of
boost
con
v
e
rter
designed
using
the
modification
of
flo
w
in
phase
plane.
The
proposed
controller
guarantees
that
the
boost
con
v
erter
w
orks
only
in
CCM
re
gion.
The
simulation
result
confirms
that
our
proposed
controller
brings
the
state
v
ariables
from
an
y
initial
point
to
a
desired
operating
point
successfully
.
Copyright
c
2018
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Ichijo
Hodaka
Department
of
En
vironmental
of
Robotics,
Uni
v
ersity
of
Miyazaki,
Japan
1-1,
Gakuen
Kibanadai-nishi,
Miyazaki,
889-2192,
Japan
Phone:
+81
985
587
352
Email:
hijhodaka[at]cc.miyazaki-u.ac.jp
1.
INTR
ODUCTION
Ov
er
the
last
fe
w
decades,
DC-DC
con
v
erters
ha
v
e
been
the
subject
of
great
interest
due
to
its
e
xtensi
v
e
increment
of
utilization
in
dif
ferent
applications.
Right
no
w
,
the
y
are
popularized
in
standard
and
redone
items
that
po
wer
an
e
xtensi
v
e
v
ariety
of
applications,
for
e
xample,
photo
v
oltaic
(PV)
po
wer
systems
[1,
2],
wind
turbines
(WT)
[3,
4
]
,
brushless
DC
(BLDC)
motor
[5,
6]
etc.
Among
these
con
v
erters,
the
boost
con
v
erter
is
a
fundamental
controller
which
is
used
in
man
y
systems
due
to
its
simplicity
.
In
order
to
achie
v
e
the
operating
point,
boost
con
v
erter
usually
w
orks
with
the
controller
techniques
.
There
are
tw
o
controllers
for
the
DC-DC
con
v
erter
as
pulse-width
modulation
(PWM)
and
phase-shift
modu-
lation
(PSM).
The
PWM
has
been
widely
utilized
to
control
of
DC-DC
con
v
erter
in
se
v
eral
applications.
In
the
case
of
less
number
of
components
usage
and
high-reliability
demand,
the
PWM
control
sho
ws
the
better
performance
than
PSM
[7].
Proportional-inte
gral-deri
v
ati
v
e
(PID)
and
sliding-mode
control
(SMC)
are
used
widely
in
a
DC-DC
con
v
erter
.
The
PID
control
of
fers
the
good
stability
system,
b
ut
it
only
operates
on
limited
operating
point.
The
SMC
pro
vides
lar
ger
operating
point
than
PID.
The
SMC
w
orks
well
at
most
operating
point.
Ho
we
v
er
,
the
fundamental
barrier
for
SMC
e
x
ecution
is
a
marv
el
called
’chattering’.
Based
on
conduction
mode,
t
he
DC-DC
con
v
erter
is
analyzed
in
tw
o
modes
as
continuous-conducti
on
mode
(CCM)
and
discontinuous-conduction
m
o
de
(DCM).
The
CCM
is
the
most
often
used
in
DC-DC
con
v
erter
analysis
to
design
a
controller
.
Although
it
is
often
chosen,
none
of
the
pre
vious
literature
e
xamines
that
their
proposed
controller
w
orks
only
on
CCM
re
gion.
Since
t
he
design
is
based
on
CCM,
the
controller
and
system
should
w
ork
only
in
that
re
gion
or
the
anal
ysis
and
design
may
mislead
the
controller
.
Moreo
v
er
,
the
controller
of
boost
con
v
erter
should
be
able
to
handle
an
y
operating
points
with
correct
design.
The
rapid
de
v
elopment
of
the
v
ery
lar
ge
scale
inte
grated
circuit
technology
brings
digitally
controlled
DC-DC
con
v
erter
as
hot
topic
[8].
Digital
processors
also
ha
v
e
the
adv
antage
of
being
less
susceptible
to
aging
and
en
vironmental
or
parameter
v
ariations.
In
addition,
the
processor
can
monitor
the
system,
perform
self-
J
ournal
Homepage:
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.com/journals/inde
x.php/IJECE
I
ns
t
it
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A
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ine
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w
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i
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o
u
r
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a
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o
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
I
SSN:
2088-8708
4283
Figure
1.
Boost
con
v
erter
Figure
2.
Discrete-time
of
state
diagnostics
and
tests,
and
communicate
status
to
a
display
or
a
host
computer
[9].
Implementation
of
digital
controller
requires
system
analysis
in
discrete-time
domain.
This
paper
proposes
nonlinear
controller
which
be
able
to
handle
an
y
initial
point
and
k
eep
the
system
w
orks
in
CCM.
This
paper
focuses
on
one
type
DC-DC
con
v
erter
which
is
boost
con
v
erter
b
ut
the
idea
has
possibility
to
be
applied
on
other
con
v
erter
.
The
proposed
controller
design
is
based
on
flo
w
modification
of
phase
plane.
The
analysis
is
conducted
in
discrete
time-domain
which
is
required
by
a
digital
controller
due
to
the
popularity
of
digital
controller
.
Section
2
e
xplains
analysis
of
boost
con
v
erter
in
di
screte
time-domain.
Digital
implementation
of
controller
requires
indirectly
the
discrete
time-domain
analysis.
Section
3
sho
ws
the
control
system
specificat
ion
in
CCM
of
boost
con
v
erter
.
Section
4
proposes
the
nonlinear
control
which
its
design
based
on
phase
plane
e
xamination
of
an
y
ini
tial
condition.
Section
6
simulates
the
system
on
se
v
eral
initial
points.
Finally
,
Section
7
tells
the
important
point
of
this
paper
.
2.
D
YN
AMIC
MODEL
OF
BOOST
CONVER
TER
The
boost
con
v
erter
consist
of
inductor
L
,
capacitor
C
,
MOSFET
M
and
diode
D
as
sho
wn
in
F
igure
1.
The
circuit
equation
of
boost
con
v
erter
is
deri
v
ed
as
follo
ws.
V
=
L
_
i
(
t
)
+
v
M
(
t
)
;
v
M
(
t
)
=
v
D
(
t
)
+
v
(
t
)
i
(
t
)
=
i
M
(
t
)
+
i
D
(
t
)
;
i
D
(
t
)
=
C
_
v
(
t
)
+
v
(
t
)
=R
(1)
The
diode
v
oltage
and
MOSFET
v
oltage
are
denoted
as
v
D
and
v
M
respecti
v
ely
.
A
resisti
v
e
load
R
is
connected
to
the
boost
con
v
erter
.
A
v
oltage
source
V
supplies
a
constant
v
oltage
for
boost
con
v
erter
.
The
con
v
erter
is
controlled
by
duty-ratio
d
of
PWM.
In
CCM,
there
are
tw
o
modes
which
w
ork
alternately
.
In
the
first
mode
or
mode-1,
the
MOSFET
M
is
conducted
and
the
diode
D
is
di
sconnected.
W
e
assume
that
the
MOSFET
v
oltage
is
constant
V
M
during
mode-1
and
there
is
no
current
on
diode
(
i
D
(
t
)
=
0
).
The
second
mode
or
mode-2
occurs
when
the
MOSFET
is
of
f
and
diode
is
conducted.
W
e
assume
that
the
diode
v
oltage
is
constant
V
D
and
there
is
no
current
on
MOSFET
(
i
M
(
t
)
=
0
)
during
mode-2.
The
equation
of
boost
con
v
erter
becomes
as
follo
ws.
mode-1
L
_
i
(
t
)
=
V
V
M
C
_
v
(
t
)
=
v
(
t
)
=R
(2)
mode-2
L
_
i
(
t
)
=
V
V
D
v
(
t
)
C
_
v
(
t
)
=
i
(
t
)
v
(
t
)
=R
:
(3)
In
this
section,
we
introduce
a
non-dimensional
v
ariable
x
1
and
x
2
which
is
described
as
follo
ws.
(
x
1
=
v
(
t
)
V
+
V
D
V
x
2
=
i
(
t
)
V
q
L
C
(4)
The
deri
v
ati
v
e
of
non-dimensional
state
on
each
mode
can
be
calculated
by
substituting
_
i
(
t
)
and
_
v
(
t
)
of
equation
(2)
and
(3)
as
follo
ws.
mode-1
(
_
x
1
=
_
v
(
t
)
V
=
1
V
(
V
x
1
+
V
V
D
)
R
C
=
1
R
C
x
1
1
R
C
1
V
D
V
_
x
2
=
_
i
(
t
)
V
q
L
C
=
1
V
q
L
C
V
V
M
L
=
1
p
LC
1
V
M
V
(5)
mode-2
8
<
:
_
x
1
=
_
v
(
t
)
V
=
1
V
i
(
t
)
C
v
(
t
)
R
C
=
1
p
LC
x
2
1
R
C
x
1
1
R
C
1
V
D
V
_
x
2
=
_
i
(
t
)
V
q
L
C
=
1
V
q
L
C
V
V
D
v
(
t
)
L
=
1
p
LC
x
1
(6)
A
No
vel
Nonlinear
Contr
ol
of
Boost
Con
verter
using
CCM
Phase
Plane
(Ek
o
Setiawan)
Evaluation Warning : The document was created with Spire.PDF for Python.
4284
ISSN:
2088-8708
The
state
space
equation
of
non-dimensional
v
ariable
can
be
written
as
follo
ws.
_
x
=
1
R
C
0
0
0
|
{z
}
A
1
x
+
"
1
R
C
(1
V
D
V
)
1
p
LC
1
V
M
V
#
|
{z
}
b
1
(7)
_
x
=
"
1
R
C
1
p
LC
1
p
LC
0
#
|
{z
}
A
2
x
+
1
R
C
(1
V
D
V
)
0
|
{z
}
b
2
(8)
As
sho
wn
in
Figure
2,
mode-1
w
orks
from
the
be
ginning
t
0
until
t
=
t
0
+
T
d
.
Based
on
general
solution
of
state
space
equation,
the
last
state
of
mode-1
can
be
written
as
follo
ws.
x
(
t
0
+
T
d
)
=
e
A
1
(
t
0
+
T
d
t
0
)
x
(
t
0
)
+
Z
t
0
+
T
d
t
0
e
A
1
(
t
0
+
T
d
p
)
b
1
dp
where
8
<
:
q
=
p
t
0
T
p
=
q
T
+
t
0
dp
dq
=
T
=
e
A
1
T
d
x
(
t
0
)
+
Z
d
0
e
A
1
T
(
d
q
)
b
1
T
dq
(9)
In
CCM,
the
boost
con
v
erter
has
tw
o
state-space
equations
(7)
and
(8).
The
last
state
of
mode-1
is
equal
to
the
initial
state
of
mode-2.
On
the
ne
xt
mode,
the
last
state
of
mode-2
will
be
as
the
initial
state
of
the
ne
xt
period
mode-1.
These
phenomenons
occurs
repeatedly
.
Based
on
these
f
acts,
the
solution
of
boost
con
v
erter
per
period
(
T
)
can
be
obtained
by
substituting
the
last
state
of
mode-1
(
x
(
t
0
+
T
d
)
)
into
the
general
solution
of
mode-2
as
follo
ws.
x
(
t
0
+
T
)
=
e
A
2
T
(1
d
)
x
(
t
0
+
T
d
)
+
Z
1
d
e
A
2
(
t
0
+
T
(
q
T
+
t
0
))
b
2
T
dq
=
e
A
2
T
(1
d
)
e
A
1
T
d
x
(
t
0
)
+
e
A
2
T
(1
d
)
Z
d
0
e
A
1
T
(
d
q
)
b
1
T
dq
+
Z
1
d
e
A
2
T
(1
q
)
b
2
T
dq
(10)
Let
us
assume
that
the
sensor
measures
e
v
ery
end
of
switching
period
(
T
).
This
measurement
is
sho
wn
as
dot-point
in
Figure
2.
W
e
will
introduce
ne
w
v
ariable
to
distinguish
with
the
continuous-time
v
ariable
x
.
Then,
the
discrete
representation
of
solution
(10)
is
defined
as
follo
ws:
(
k
+
1)
=
x
(
t
0
+
(
k
+
1)
T
)
=
e
~
A
2
(1
d
)
e
~
A
1
d
x
(
t
0
+
k
T
)
|
{z
}
(
k
)
+
e
~
A
2
(1
d
)
Z
d
0
e
~
A
1
(
d
q
)
~
b
1
dq
+
Z
1
d
e
~
A
2
(1
q
)
~
b
2
dq
(11)
where
~
A
1
=
"
1
0
0
0
,
~
A
2
=
"
1
"
2
"
2
0
,
~
b
1
=
"
1
"
2
,
~
b
2
=
"
1
0
,
"
1
=
T
R
C
,
"
2
=
T
p
LC
,
=
(1
V
M
V
)
,
and
=
(1
V
D
V
)
(12)
Assuming
the
period
T
is
small
then
the
element
of
~
A
1
,
~
A
2
,
~
b
1
,
and
~
b
2
become
small
too.
The
e
xpo-
nential
part
in
(11)
can
be
calculated
using
the
definition
of
e
xponential
as
follo
ws.
e
M
=
I
+
M
+
1
2!
M
2
+
:::
e
~
A
1
d
=
I
+
~
A
1
d
+
~
A
1
2
d
2
2
+
:::
|
{z
}
ne
glected
'
I
+
~
A
1
d
e
~
A
2
(1
d
)
e
~
A
1
d
'
I
+
~
A
1
d
+
~
A
2
(1
d
)
e
~
A
2
(1
d
)
Z
d
0
e
~
A
1
(
d
q
)
~
b
1
dq
'
(
I
+
~
A
2
(1
d
))
Z
d
0
(
I
+
~
A
1
(
d
q
))
~
b
1
dq
=
~
b
1
d
Z
1
d
e
~
A
2
(1
q
)
~
b
2
dq
'
Z
1
d
(
I
+
~
A
2
(1
q
))
~
b
2
dq
=
~
b
2
(1
d
)
(13)
IJECE
V
ol.
8,
No.
6,
December
2018:
4282
–
4289
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
I
SSN:
2088-8708
4285
Thus,
the
discrete-time
solution
of
state
(11)
is
simplified
as
follo
ws
(
k
+
1)
=
(
I
+
~
A
1
d
+
~
A
2
(1
d
))
|
{z
}
^
A
(
k
)
+
~
b
1
d
+
~
b
2
(1
d
)
|
{z
}
^
b
(14)
The
equation
(14)
is
used
to
simulate
the
boost
con
v
erter
on
the
ne
xt
sections.
3.
CONTR
OL
PR
OBLEM
A
boost
con
v
erter
in
continuous-conduction
mode
(CCM)
has
the
limitation
such
as:
1.
the
output
v
oltage
v
(
t
)
must
be
greater
than
the
input
v
oltage
V
subtracted
by
the
diode
v
oltage
V
D
.
This
is
the
principle
of
boost.
In
the
non-dimensional
state,
1
ne
v
er
be
ne
g
ati
v
e,
2.
the
inductor
current
i
(
t
)
must
be
greater
than
zero
as
the
definition
of
CCM.
It
means
that
the
state
2
must
not
ne
g
ati
v
e,
and
3.
the
tw
o
pre
vious
conditions
are
satisfied
for
an
y
initial
states.
Breaking
the
limitation
means
the
model
is
not
proper
an
ymore
in
the
controller
design.
K
eeping
the
wrong
model
may
mislead
the
analysis
of
controller
design.
The
three
limitations
will
be
used
as
control
specification
in
this
paper
.
T
able
1.
The
parameter
of
Boost
Con
v
erter
P
arameter
Symbol
V
alue
Input
v
oltage
V
10
V
Inductor
L
300
H
Capacitor
C
100
F
MOSFET
v
oltage
V
M
162
mV
Diode
v
oltage
V
D
0.5
V
Load
R
10
Switching
period
T
20
s
Reference
v
oltage
V
r
ef
16
V
Let
us
s
imulate
the
beha
vior
of
boost
con
v
erter
using
parameters
of
boost
from
[12]
as
sho
wn
in
T
able
1.
The
param
eters
are
also
used
in
the
ne
xt
sections.
W
e
e
xamines
the
beha
vior
of
boost
con
v
erter
without
the
controller
called
as
open-loop
response.
The
boost
con
v
erter
is
gi
v
en
a
constant
equilibrium
duty
ratio
notated
as
D
eq
.
The
mathematics
softw
are
(e.g.
W
olfram
Mathematica)
finds
the
v
alue
of
equilibrium
duty-ratio
(
D
eq
)
by
solving
the
duty-ratio
when
equation
(14)
is
equal
to
[
1
;
2
]
T
as
follo
ws.
D
eq
=
r
ef
+
r
ef
(15)
where
r
ef
=
(
V
r
ef
V
+
V
D
)
=V
.
In
order
to
e
xamine
the
beha
vior
of
boost
for
an
y
initial
condition,
let
us
utilize
phase
pl
ane.
The
phase
plane
of
open-loop
response
is
sho
wn
in
Figure
3.
The
dashed
line
i
n
Figure
3
sho
ws
the
set
of
equilibrium
condition.
Let
us
focus
on
the
phase
trajectory
of
tw
o
initial
conditions
which
are
notated
as
A
and
B.
It
sho
ws
that
the
system
can
achie
v
e
equilibrium
point
well
for
both
initial
conditions.
F
or
the
initial
condition
B,
the
system
enters
the
ne
g
ati
v
e
re
gion
of
1
and
2
which
breaks
the
limitation
of
CCM
boost
con
v
erter
.
In
order
to
a
v
oid
this
situation,
a
proper
controller
is
required.
4.
PID
CONTR
OLLER
Among
the
se
v
eral
controllers
of
boost
con
v
erter
,
PID
controller
is
the
mature
controller
which
well-
e
xplained
in
se
v
eral
papers
such
as
[7,
8,
11,
13,
14].
This
section
discusses
the
implementation
of
PID
controller
and
its
characteristic
on
boost
con
v
erter
.
The
PID
controller
i
n
discrete-time
domain
is
e
xpressed
as
follo
ws
[11].
u
(
k
)
=
K
P
2
4
e
(
k
)
+
T
T
I
k
X
j
=0
e
(
j
)
+
T
D
T
f
e
(
k
)
e
(
k
1)
g
3
5
(16)
A
No
vel
Nonlinear
Contr
ol
of
Boost
Con
verter
using
CCM
Phase
Plane
(Ek
o
Setiawan)
Evaluation Warning : The document was created with Spire.PDF for Python.
4286
ISSN:
2088-8708
Figure
3.
Phase
plane
of
open-loop
response
The
recursi
v
e
e
xpression
of
PID
control
in
discrete-time
is
formed
by
dif
ference
between
simultaneous
input
(
u
(
k
)
=
u
(
k
)
u
(
k
1)
).
The
pre
vious
PID
control
can
be
e
xpressed
as
follo
ws
[11,
12]:
u
(
k
)
=
u
(
k
1)
+
u
(
k
)
=
d
(
k
1)
+
(
K
P
+
K
I
+
K
D
)
e
(
k
)
(
K
P
+
2
K
D
)
e
(
k
1)
+
K
D
e
(
k
2)
(17)
where
K
I
=
K
P
T
T
I
,
K
D
=
K
P
T
D
T
,
e
(
k
)
=
V
r
ef
v
(
k
)
,
e
(
k
1)
=
V
r
ef
v
(
k
1)
,
and
e
(
k
2)
=
V
r
ef
v
(
k
2)
.
PID
controller
or
called
com
p
e
nsator
in
some
references
is
usually
designed
by
small-signal
model
of
DC-DC
con
v
erter
[10].
The
small-signal
model
is
deri
v
ed
by
adding
small
pert
urbation
on
inductor
current
i
(
t
)
,
capacitor
v
oltage
v
(
t
)
and
duty-ratio
d
.
Since
the
PID
controller
is
designed
by
linearizat
ion
around
the
equilibrium
point,
implementation
of
PID
controller
needs
equilibrium
duty-ratio
D
eq
as
described
in
follo
wing
equation
[13].
d
(
k
)
=
D
eq
+
u
(
k
)
(18)
Let
us
e
xamine
the
beha
vior
of
PID
controller
in
the
phase
plane.
The
parameter
of
PID
needs
to
be
tuned
before
used.
Based
on
[14],
the
Zie
gler
-Nichols
(ZN)
has
the
best
performance
comparing
with
the
others.
The
simulation
sho
ws
that
the
boost
system
achie
v
es
ultimate
g
ain
(
K
U
)
and
ultimate
period
(
T
U
)
on
0.06
and
1,8
ms
respecti
v
ely
.
According
to
the
ZN
table
on
[14],
the
P-g
ain
(
K
P
),
D-g
ain
(
K
D
),
and
I-g
ain
(
K
I
)
are
0.036,
8
10
4
and
0.405
respecti
v
ely
.
Let
us
dra
w
the
phase
trajectory
of
PID
controller
on
se
v
eral
initial
condition
v
(0)
s
and
i
(0)
s.
The
phase
trajectory
of
PID
controller
is
observ
ed
by
applying
(14),
(17)
,
(18)
and
(15)
on
the
se
v
eral
initial
points.
Figure
4
sho
ws
the
phase
trajectory
of
PID
controller
for
se
v
eral
initial
conditions.
Based
on
Figure
4,
the
flo
w
of
state
tends
to
go
to
ne
g
ati
v
e
area
of
2
at
first.
Most
of
tested
initial
state
enters
the
ne
g
ati
v
e
area
of
1
and
2
which
breaks
the
limitation
of
Boost
con
v
erter
in
CCM
.
This
f
act
sho
ws
that
the
PID
does
not
guarantee
the
boost
con
v
erter
w
orks
al
w
ays
in
CCM.
It
means
that
the
controller
design
using
CCM
is
not
suitable
with
the
implementation.
5.
PR
OPOSED
CONTR
OLLER
This
paper
proposes
the
nonlinear
feedback
control
which
is
des
igned
based
on
manipulation
of
flo
w
i
n
phase
plane.
The
flo
w
is
consisted
from
tw
o
v
ectors
which
are
(
1
(
k
)
1
(
k
1)
)
and
(
2
(
k
)
2
(
k
1)
)
as
sho
wn
in
Figure
5.
The
flo
w
is
forced
to
has
a
specific
direction.
In
that
condition,
the
follo
wing
equality
w
orks.
(
1
(
k
)
1
(
k
1))
cos
+
(
2
(
k
)
2
(
k
1))
sin
=
0
(19)
The
proposed
controller
is
designed
by
solvi
n
g
the
duty
ratio
d
in
the
equation
(19).
Then,
a
proportional
controller
is
added
to
push
the
controller
to
the
reference
r
ef
=
(
v
r
ef
V
+
V
D
)
=V
.
Finally
,
the
o
v
erall
proposed
controller
is
described
as
follo
ws.
d
pr
oposed
(
k
)
=
k
(
r
ef
1
(
k
))
+
"
2
1
(
k
)
sin
(
"
1
+
"
1
1
(
k
)
"
2
2
(
k
))
cos
"
2
[
2
(
k
)
cos
+
(
+
1
(
k
))
sin
]
(20)
The
proposed
controller
consists
of
tw
o
parts.
The
firs
t
part
is
proportional
term
and
the
second
part
is
modification
of
flo
w
.
The
parameter
k
and
needs
to
be
tuned,
which
represent
speed
of
achie
v
ement
reference
IJECE
V
ol.
8,
No.
6,
December
2018:
4282
–
4289
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
I
SSN:
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4287
(a)
v
(0)
=
11
V
;
i
(0)
=
1
A
(b)
v
(0)
=
11
V
;
i
(0)
=
4
A
(c)
v
(0)
=
20
V
;
i
(0)
=
1
A
(d)
v
(0)
=
20
V
;
i
(0)
=
4
A
Figure
4.
Phase
trajectory
of
PID
controller
Figure
5.
Modification
of
flo
w
Figure
6.
Phase
plane
of
proposed
controller
(
V
r
ef
=
16
V)
and
flo
w
direction
respecti
v
ely
.
The
best
v
alue
of
k
and
are
0.06
and
(-0.35
)
respecti
v
ely
.
The
phase
plane
of
proposed
controller
is
sho
wn
in
Figure
6.
The
phase
plane
sho
ws
that
the
controller
can
handle
an
y
initial
point
on
CCM
boost
con
v
erter
.
An
y
initial
points
are
pushed
into
the
equilibrium
line
(dashed
line
in
Figure
3)
without
passing
the
ne
g
ati
v
e
area
of
1
and
2
.
6.
SIMULA
TION
This
section
simulates
the
proposed
controller
response
on
time
domain.
The
proposed
controller
(20)
is
compared
with
PID
controller
(18)
which
described
in
Section
4.
The
simulation
is
conducted
in
se
v
eral
initial
points.
The
comparison
between
proposed
and
PID
controller
are
sho
wn
in
Figure
7.
The
PID
controller
response
is
sho
wn
in
dashed-line
while
the
proposed
controller
is
e
xpressed
in
solid
blue
line.
The
proposed
controller
sho
w
smother
response
than
PID
controller
.
In
the
PID
controller
,
the
output
v
oltage
goes
to
less
than
input
v
oltage
10
V
.
This
condition
is
not
proper
for
boost
con
v
erter
characteristic
which
must
greater
than
the
input
v
oltage.
Moreo
v
er
,
the
phase
plane
of
proposed
controller
on
v
arious
reference
point
is
sho
wn
in
Figure
8.
Figure
8
gi
v
es
clear
information
that
the
proposed
controller
has
capability
to
handle
an
y
references
point
without
entering
the
ne
g
ati
v
e
area
of
states.
A
No
vel
Nonlinear
Contr
ol
of
Boost
Con
verter
using
CCM
Phase
Plane
(Ek
o
Setiawan)
Evaluation Warning : The document was created with Spire.PDF for Python.
4288
ISSN:
2088-8708
(b)
v
(0)
=
11
V
;
i
(0)
=
1
A
(c)
v
(0)
=
11
V
;
i
(0)
=
4
A
(d)
v
(0)
=
20
V
;
i
(0)
=
1
A
(e)
v
(0)
=
20
V
;
i
(0)
=
4
A
Figure
7.
Comparison
between
proposed
and
PID
on
se
v
eral
initial
points
(a)
v
r
ef
=
9
:
5
V
(b)
v
r
ef
=
13
:
0
V
(c)
v
r
ef
=
16
:
5
V
(d)
v
r
ef
=
20
:
0
V
(e)
v
r
ef
=
23
:
5
V
(f)
v
r
ef
=
27
:
0
V
Figure
8.
Proposed
phase
plane
of
the
v
arious
reference
point
7.
CONCLUSION
This
paper
has
pointed
out
that
the
PID
control
does
not
guarantee
that
boost
con
v
erter
al
w
ays
w
orks
within
CCM.
This
paper
has
formulated
a
discrete
approximation
of
CCM
boost
con
v
erter
,
and
proposed
a
IJECE
V
ol.
8,
No.
6,
December
2018:
4282
–
4289
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
I
SSN:
2088-8708
4289
no
v
el
nonlinear
controller
that
guarantees
that
boost
con
v
erter
al
w
ays
w
orks
properly
within
CCM
for
an
y
initial
condition.
Moreo
v
er
,
the
proposed
controller
has
adv
antage
more
than
PID
that
it
can
handles
an
y
reference
point
without
tuning
the
parameters
ag
ain.
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Stallon,
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K
umar
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umar
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ficient
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erter
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arasitic
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erter
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erter
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