Inter
national
J
our
nal
of
P
o
wer
Electr
onics
and
Dri
v
e
System
(IJPEDS)
V
ol.
17,
No.
2,
June
2026,
pp.
1211
∼
1220
ISSN:
2088-8694,
DOI:
10.11591/ijpeds.v17.i2.pp1211-1220
❒
1211
Dual-mode
model
pr
edicti
v
e
contr
ol
f
or
non-minimum
phase
boost
con
v
erters
J
awhra
El
Hmidi
1
,
Anass
Mansouri
2
,
Ali
Ahaitouf
1
1
Laboratory
of
Science
and
Engineering
Research,
F
aculty
of
Sciences
and
T
echnology
,
Sidi
Mohamed
Ben
Abdellah
Uni
v
ersity
,
Fez,
Morocco
2
Laboratory
of
Science
and
Engineering
Research,
School
of
Applied
Sciences,
Sidi
Mohamed
Ben
Abdellah
Uni
v
ersity
,
Fez,
Morocco
Article
Inf
o
Article
history:
Recei
v
ed
Jul
15,
2025
Re
vised
Apr
4,
2026
Accepted
Apr
23,
2026
K
eyw
ords:
Dual
mode
MPC
FS-MPC
HIL
Non-minimum
phase
Real-time
control
Split
cost
function
ABSTRA
CT
This
paper
aims
to
de
v
elop
an
ef
cient
nite-set
model
predicti
v
e
control
(FS-MPC)
strate
gy
for
DC–DC
boost
con
v
erters
to
impro
v
e
v
oltage
re
gulation
while
reducing
computational
comple
xity
.
The
proposed
approach
introduces
a
split
cost
function
that
decouples
v
oltage
and
current
re
gulation,
pro
viding
a
simpler
alternati
v
e
to
con
v
entional
long-horizon
FS-MPC
schemes
used
to
address
the
con
v
erter’
s
non-minimum-phase
(NMP)
beha
vior
.
A
current-
estimation
technique
is
incorporated
to
eliminate
the
need
for
additional
sensors,
lo
wering
hardw
are
cost
and
impro
ving
rob
ustness.
Unlik
e
e
xisting
FS-MPC
methods
that
rely
on
horizon
e
xtension
or
e
xtra
measurements,
the
proposed
strate
gy
le
v
erages
the
split
cost
structure
to
achie
v
e
comparable
NMP
compensation
with
signicantly
lo
wer
computational
ef
fort.
The
controller
is
implemented
in
real
time
using
a
hardw
are-in-the-loop
(HIL)
setup
on
a
ZedBoard
platform,
with
accurate
data
acquisition
pro
vided
by
an
e
xternal
ADC.
Experimental
results
demonstrate
that
the
proposed
approach
enhances
v
oltage-tracking
performance,
eliminates
o
v
ershoot
and
undershoot
,
reduces
settling
time
by
o
v
er
40%,
and
decreases
computational
ef
fort
by
more
than
80%
compared
to
traditional
FS-MPC
methods.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Ja
whara
El
Hmidi
Laboratory
of
Science
and
Engineering
Research,
F
aculty
of
Sciences
and
T
echnology
Sidi
Mohamed
Ben
Abdellah
Uni
v
ersity
Fez,
Morocco
Email:
ja
whara.elhmidi@usmba.ac.ma
1.
INTR
ODUCTION
DC–DC
boost
con
v
erters
play
a
critical
role
in
modern
ener
gy
systems
such
as
electric
v
ehicles
[1],
rene
w
able
ener
gy
interf
aces
[2],
and
distrib
uted
po
wer
supplies
[3].
Their
ability
to
step
up
DC
v
oltage
le
v
els
mak
es
them
indispensable
in
meeting
load
and
subsystem
requirements.
Ho
we
v
er
,
the
intrinsic
non-minimum-phase
(NMP)
dynamics
of
boost
con
v
erters
[4]
introduce
control
challenges,
often
leading
to
instability
and
de
graded
transient
performance
when
con
v
entional
controllers
are
applied.
T
raditional
proportional–inte
gral
(PI)
controllers
are
widely
used
because
of
their
simplicity
b
ut
struggle
with
the
nonlinear
and
NMP
characteristics
of
boost
con
v
erters
[5].
Nonlinear
strate
gies,
such
as
sliding-mode
and
backstepping
techniques
[6],
[7],
impro
v
e
rob
ustness
b
ut
require
comple
x
implementations
and
e
xtensi
v
e
parameter
tuning,
which
limits
their
practicality
for
lo
w-cost
embedded
systems.
Model
predicti
v
e
control
(MPC)
has
emer
ged
as
a
compelling
alternati
v
e
for
po
wer
electronic
con
v
erters
[8].
In
particular
,
nite-set
MPC
(FS-MPC)
[9],
J
ournal
homepage:
http://ijpeds.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
1212
❒
ISSN:
2088-8694
[10]
aligns
well
with
po
wer
con
v
erter
operation
because
of
its
discrete
nature
and
moderate
computational
requirements
[11].
Ne
v
ertheless,
when
single-horizon
FS-MPC
is
directly
applied
to
re
gulate
the
output
v
oltage
of
boost
con
v
erters,
the
NMP
ef
fect
can
lead
to
instability
and
poor
transient
response
[12],
[13].
Existing
solutions,
including
long-horizon
and
mo
v
e-blocking
FS-MPC
approaches
[14]–[16],
alle
viate
this
problem
b
ut
at
the
e
xpense
of
increased
computational
b
urden,
making
them
less
suitable
for
real-time
applications
on
lo
w-cost
hardw
are.
These
challenges
highlight
a
signi
cant
research
g
ap
because
there
is
still
a
need
for
an
FS-MPC
strate
gy
capable
of
addressing
the
NM
P
beha
vior
of
boost
con
v
erters
without
relying
on
horizon
e
xtension
or
additional
sensors
that
increase
cost
and
comple
xity
[17].
The
present
w
ork
addresses
this
g
ap
by
introducing
a
computationally
ef
cient
FS-MPC
method
based
on
a
split
cost
function
that
decouples
v
oltage
and
current
re
gulation.
By
le
v
eraging
a
load-current
estimation
technique,
the
proposed
approach
eliminates
the
need
for
e
xtra
current
sensors,
t
hereby
impro
ving
rob
ustness
and
reducing
hardw
are
requirements.
In
addition,
a
current-limiting
feature
is
embedded
wit
hin
the
control
algorithm
to
enhance
protection
under
o
v
ercurrent
conditions
as
e
xplained
in
[18].
The
proposed
strate
gy
is
v
alidated
through
comprehensi
v
e
simulations
and
Hardw
are-in-the-Loop
e
xperiments
under
a
v
ariety
of
operating
conditions,
including
input-v
oltage
v
ariations,
load
disturbances,
and
reference-tracking
scenarios.
Results
demonstrate
that
the
method
ef
fecti
v
ely
mitig
ates
the
NMP
-induced
instability
while
impro
ving
transient
performance,
achie
ving
f
aster
settling
time,
better
v
oltage
tracking,
and
signicantly
lo
wer
computational
ef
fort
compared
with
con
v
entional
FS-MPC
schemes.
2.
METHOD
This
section
presents
a
predicti
v
e
control
scheme
tailored
for
DC-DC
boost
con
v
erters,
aimed
at
mitig
ating
the
adv
erse
ef
fect
s
of
their
NMP
nature.
The
propose
d
solution
modi
es
the
clas
sical
FS-MPC
formulation
by
e
v
aluating
a
split
cost
function
based
on
the
switching
state.
Moreo
v
er
,
a
load
current
estimation
strate
gy
is
included
to
eliminate
the
need
for
an
output
current
sensor
.
2.1.
Modeling
of
the
boost
con
v
erter
The
boost
con
v
erter
as
sho
wn
in
Figure
1(a)
is
represented
as
a
switched
system
composed
of
a
DC
v
oltage
source,
a
po
wer
switch
(typically
a
MOSFET),
a
diode,
an
inductor
L
,
an
output
capacitor
C
,
and
a
resisti
v
e
load.
The
control
input
u
∈
{
0
,
1
}
determines
the
switching
state:
u
=
1
corresponds
to
the
ON
state
(switch
closed),
while
u
=
0
indicates
the
OFF
state
(switch
open),
as
illustrated
in
Figures
1(a)
and
1(b).
The
re
gulation
of
the
output
v
oltage
is
achie
v
ed
by
rapidly
alternating
between
these
tw
o
operating
modes
[16].
When
the
MOSFET
is
closed,
this
state
is
described
by
(1).
V
L
=
L
di
L
(
t
)
dt
=
V
in
−
i
L
R
L
(1)
The
same
for
state
where
the
MOSFET
is
open,
Figure
1(c)
present
the
con
v
erter
topology
and
(2)
described
it.
V
L
=
L
di
L
(
t
)
dt
=
V
in
−
i
L
R
L
−
V
c
(2)
V
c
is
equal
to
V
out
,
we
can
some
by
(1)
and
(2)
in
one
equation,
we
obtain
(3).
V
L
=
L
di
L
(
t
)
dt
=
V
in
−
i
L
R
L
−
V
c
(1
−
u
)
(3)
T
o
predict
the
future
inductor
current
[19],
the
con
v
entional
Euler
approximation
is
used
(4).
di
L
dt
≈
i
L
(
k
+
1)
−
i
L
(
k
)
T
s
(4)
Rearranging
this
equation
gi
v
es
(5).
i
L
(
k
+
1)
=
di
L
dt
T
s
+
i
L
(
k
)
(5)
i
L
(
k
)
:
The
measured
v
alue
of
the
inductor
current;
T
s
:
Sampling
time
of
the
control
algorithm,
wich
equal
half
of
period
T
s
=
T
sw
2
.
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
17,
No.
2,
June
2026:
1211–1220
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
1213
Then
we
can
put
the
deri
v
ati
v
e
in
(3)
into
the
prediction
function
(5).
i
L
(
k
+
1)
=
T
s
L
[
V
in
−
i
L
R
L
−
V
out
(1
−
u
)]
+
i
L
(
k
)
(6)
Ho
we
v
er
,
to
reduce
comple
xity
and
preserv
e
computational
ef
cienc
y
in
real-time
appl
ications,
the
parasitic
resistance
is
often
ne
glected.
Under
the
assumption
R
L
≈
0
,
the
simplied
discrete-time
model
is
(7).
i
L
(
k
+
1)
=
T
s
L
[
V
in
−
V
out
(1
−
u
)]
+
i
L
(
k
)
(7)
(a)
(b)
(c)
Figure
1.
Circuit
diagram
of
a
DC–DC
boost
con
v
erter
and
its
operating
modes:
(a)
circuit
diagram,
(b)
MOSFET
ON,
and
(c)
MOSFET
OFF
2.2.
Pr
ediction
model
The
boost
con
v
erter
is
modeled
using
tw
o
state
v
ariables:
the
inductor
cur
rent
i
L
and
the
output
v
oltage
V
out
.
Con
v
entional
FS–MPC
typically
relies
on
a
single
s
tep
prediction,
which
is
adequate
for
man
y
po
wer
con
v
erters.
Ho
we
v
er
,
because
of
the
NMP
beha
vior
of
boost
con
v
erters
where
the
output
v
oltage
initially
mo
v
es
in
the
opposite
direction
to
a
change
in
the
control
input
single
step
pre
d
i
ction
is
insuf
cient
for
accurate
control
[20].
T
o
o
v
ercome
this
limitation,
the
proposed
strate
gy
adopts
a
dual
mode
approach
with
a
tw
o
step
prediction
horizon
[21].
At
each
sampling
instant
k
,
the
switch
state
u
∗
(
k
)
has
already
been
applied,
so
the
controller
focuses
on
selecting
the
optimal
future
action
u
(
k
+
1)
by
e
v
aluating
its
ef
fect
on
the
system
at
k
+
2
.
First,
the
intermediate
state
at
k
+
1
is
predicted
based
on
the
applied
control
u
∗
(
k
)
,
and
then
each
candidate
switching
action
for
u
(
k
+
1)
is
used
to
forecast
the
state
at
k
+
2
.
T
o
further
enhance
the
controller’
s
ability
to
manage
the
NMP
dynamics,
the
decision
at
each
candidate
switching
action
is
guided
by
a
split
cost
function
structure
that
e
v
aluates
the
system
response
dif
ferently
for
the
switch
ON
and
switch
OFF
modes,
section
2.5
describe
this.
This
combined
use
of
a
dual–mode
prediction
horizon
and
split
cost
function
enables
the
controller
to
anticipate
the
in
v
erse
v
oltage
response
and
select
the
switching
sequence
that
ensures
stable
and
well
re
gulation.
The
inductor
current
at
k
+
1
is
gi
v
en
by
(8).
i
L
(
k
+
1)
=
i
L
(
k
)
+
V
in
(
k
)
L
−
(1
−
u
∗
(
k
))
V
out
(
k
)
L
T
s
(8)
And
the
corresponding
output
v
oltage
is
predicted
as
(9).
V
out
(
k
+
1)
=
V
out
(
k
)
+
(1
−
u
∗
(
k
))
i
L
(
k
)
C
−
i
load
(
k
)
C
T
s
(9)
Dual-mode
model
pr
edictive
contr
ol
for
non-minimum
phase
boost
con
verter
s
(J
awhr
a
El
Hmidi)
Evaluation Warning : The document was created with Spire.PDF for Python.
1214
❒
ISSN:
2088-8694
Then,
for
each
candidate
switching
action
u
∈
{
0
,
1
}
,
the
prediction
at
k
+
2
is
calculated
in
(10)
and
(11).
i
L
(
k
+
2)
=
i
L
(
k
+
1)
+
V
in
(
k
)
L
−
(1
−
u
)
V
out
(
k
+
1)
L
T
s
(10)
V
out
(
k
+
2)
=
V
out
(
k
+
1)
+
(1
−
u
)
i
L
(
k
+
1)
C
−
i
load
(
k
)
C
T
s
(11)
The
(8)
and
(9)
pro
vide
the
intermediate
prediction,
while
in
(10)
and
(11)
estimate
the
fut
ure
state
at
k
+
2
for
each
control
candidate.
This
e
xtended
predict
ion
horizon
allo
ws
the
controller
to
anticipate
the
actual
ef
fect
of
switching
actions
and
better
handle
the
NMP
beha
vior
of
the
system.
2.3.
Load
curr
ent
estimation
The
load
current
is
estimated
without
using
a
ph
ysical
sensor
,
based
on
the
capacitor
current
dynamics
and
the
a
v
erage
inductor
current.
T
o
deri
v
e
this
e
xpression,
we
start
from
Kirchhof
f
’
s
current
la
w
(KCL)
at
the
output
node
of
the
boost
con
v
erter
.
The
load
current
is
equal
to
the
dif
ference
between
the
current
supplied
by
the
inductor
(when
the
switch
is
OFF)
and
the
capacitor
current
[22].
The
capacitor
current
is
gi
v
en
by
(12).
i
C
(
k
)
=
C
·
V
out
(
k
)
−
V
out
(
k
−
1)
T
s
(12)
When
the
switch
is
OFF
,
i.e.,
u
(
k
−
1)
=
0
,
the
inductor
current
o
ws
to
the
output
stage.
The
a
v
erage
inductor
current
o
v
er
one
sampling
period
is
approximated
by
(13).
i
a
vg
L
(
k
)
=
i
L
(
k
)
+
i
L
(
k
−
1)
2
(13)
Consequently
,
the
load
current
can
be
e
xpressed
as
(14).
i
load
(
k
)
=
(1
−
u
(
k
−
1))
·
i
a
vg
L
(
k
)
−
i
C
(
k
)
(14)
Substituting
by
(12)
and
(13)
into
(14),
we
obtain
the
nal
estimation
in
(15).
i
load
(
k
)
=
(1
−
u
(
k
−
1))
·
i
L
(
k
)
+
i
L
(
k
−
1)
2
−
C
·
V
out
(
k
)
−
V
out
(
k
−
1)
T
s
(15)
This
approach
enables
the
estimation
of
the
output
current
using
only
v
oltage
and
inductor
current
measurements,
eliminating
the
need
for
an
additional
current
sensor
.
2.4.
Refer
ence
curr
ent
calculation
The
re
ference
v
alue
for
the
inductor
current
is
deri
v
ed
based
on
the
principle
of
ideal
po
wer
balance
between
the
input
and
output
of
the
con
v
erter
.
Assuming
lossless
operation
and
continuous
conduction
mode
(CCM)
[23],
the
input
po
wer
P
in
is
equal
to
the
output
po
wer
P
out
.
That
is,
P
in
=
V
in
(
k
)
·
i
ref
L
=
V
∗
out
·
i
load
(
k
)
(16)
solving
in
(16)
for
i
ref
L
yields:
i
ref
L
=
V
∗
out
·
i
load
(
k
)
V
in
(
k
)
(17)
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
17,
No.
2,
June
2026:
1211–1220
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
1215
2.5.
Split
cost
function
T
o
address
the
NMP
beha
vior
inhere
n
t
to
boost
con
v
er
ters,
a
modied
cost
function
structure
is
proposed.
Instead
of
using
a
unied
objecti
v
e
for
both
switching
states,
the
controller
e
v
aluates
tw
o
separate
cost
functions
depending
on
the
candidate
control
input
u
∈
{
0
,
1
}
.
This
allo
ws
the
decision-making
process
to
account
for
the
dif
ferent
system
responses
when
the
switch
is
ON
or
OFF
[24].
Specically
,
when
the
switch
is
OFF
(
u
=
0
),
as
in
(18).
J
OFF
=
V
∗
out
−
V
OFF
out
(
k
+
2)
2
+
λ
I
i
ref
L
−
i
OFF
L
(
k
+
2)
2
(18)
When
the
switch
is
ON
(
u
=
1
),
as
(19).
J
ON
=
−
V
∗
out
−
V
ON
out
(
k
+
2)
2
+
λ
I
i
ref
L
−
i
ON
L
(
k
+
2)
2
(19)
In
this
formulation,
the
tracking
objecti
v
e
for
the
output
v
oltage
is
weighted
dif
ferentl
y
based
on
the
switch
state
[25].
In
the
OFF
state,
the
controller
aims
to
directly
minimize
the
tracking
error
,
encouraging
the
output
v
oltage
to
approach
its
reference.
In
the
ON
state,
the
sign
of
the
v
oltage
error
term
is
in
v
erted.
This
design
choice
intenti
o
na
lly
re
w
ards
e
ner
g
y
accumulation
in
the
induct
o
r
,
antici
pating
future
output
needs.
By
doing
so,
the
controller
compensates
for
the
delayed
ef
fect
of
control
actions
on
the
output
v
oltage
a
k
e
y
challenge
posed
by
the
NMP
dynamics.
The
current
re
gulation
term
remains
quadratic
and
symmetric
in
both
cases,
ensuring
consistent
tracking
of
the
reference
inductor
current.This
split
e
v
aluation
strate
gy
impro
v
es
both
transient
performance
and
steady-state
re
gulation,
while
reducing
the
risk
of
o
v
ershoot
or
instability
.
At
each
sampling
instant,
both
cost
functions
are
e
v
aluated,
and
the
optimal
switching
action
i
s
chosen
as
described
in
(20).
u
∗
(
k
+
1)
=
(
1
,
if
J
ON
<
J
OFF
0
,
otherwise
(20)
T
o
ensure
safe
operation,
an
o
v
ercurrent
protection
mechanism
is
also
implemented
(21).
If
i
ON
L
(
k
+
2)
>
i
max
L
⇒
u
∗
(
k
+
1)
=
0
(21)
3.
RESUL
TS
AND
DISCUSSION
3.1.
Experimental
setup
The
e
xperimental
v
alidation
of
the
proposed
dual-mode
FS-MPC
w
as
performed
on
a
hardw
are-in-the-loop
(HIL)
platform
based
on
a
ZedBoard
Zynq-7000.
The
ARM
corte
x-A9
processor
e
x
ecuted
t
he
real-time
control
algorithm,
strictly
follo
wing
the
sequence
presented
in
Algorithm
1.
This
implementation
e
xcluded
the
FPGA
f
abric
to
assess
the
computational
ef
cienc
y
of
the
controller
on
a
lo
w-cost
embedded
processor
.
The
e
xperimental
boost
con
v
ert
er
,
b
uilt
according
to
the
parameters
listed
in
T
able
1,
used
an
IRFZ44N
MOSFET
dri
v
en
by
an
g
ate
dri
v
er
.
V
oltage
and
current
measurements
were
obtained
using
L
V25-P
and
HAS50-S
sensors,
respecti
v
ely
.
The
analog
signals
were
digitized
by
an
e
xternal
16-bit
ADS1115
ADC
communicating
via
an
I
2
C
b
us
at
1.2
MHz,
ensuring
synchronized
sampling.
The
control
algorithm—comprising
state
prediction,
load-current
estimation,
and
dual
cost-function
e
v
aluation
w
as
e
x
ecuted
e
v
ery
10
µ
s
(10
kHz
switching
rate).
Real-time
monitoring
and
data
acquisition
were
achie
v
ed
through
MA
TLAB/Simulink
in
e
xternal
mode,
as
illustrated
in
Figure
2.
T
able
1.
Boost
con
v
erter
parameters
Component
V
alue
Input
v
oltage
[30
V
–50
V]
Output
v
oltage
[40
V
–60
V]
Inductor
200
µH
Capacitor
1000
µF
Sampling
time
10
µs
Reference
switching
frequenc
y
10
kHz
Load
resistor
[10
Ω
–
20
Ω
]
Dual-mode
model
pr
edictive
contr
ol
for
non-minimum
phase
boost
con
verter
s
(J
awhr
a
El
Hmidi)
Evaluation Warning : The document was created with Spire.PDF for Python.
1216
❒
ISSN:
2088-8694
Algorithm
1
Dual-mode-MPC
controller
for
b
uck
con
v
erter
1:
function
D
U
A
L
-
M
P
C
(
i
L
(
k
)
,
i
L
(
k
−
1)
,
V
out
(
k
)
,
V
out
(
k
−
1)
,
u
(
k
−
1
)
,
V
r
ef
)
2:
Set
parameters:
T
s
,
L
,
C
,
λ
I
,
i
L,max
;
Estimate
load
current
i
L
3:
Predict
ne
xt
states
using
u
(
k
−
1
)
;
Init:
J
O
N
←
∞
,
J
O
F
F
←
∞
4:
f
or
u
∈
{
0
,
1
}
do
5:
Predict
(
i
L,k
+2
,
V
out,k
+2
)
,
compute
e
V
,
e
I
6:
if
u
=
1
then
7:
J
O
N
←
f
(
e
V
,
e
I
)
(f
a
v
or
ON
if
e
V
>
0
)
8:
else
9:
J
O
F
F
←
f
(
e
V
,
e
I
)
(f
a
v
or
OFF
if
e
V
<
0
)
10:
end
if
11:
end
f
or
12:
u
(
k
+
1)
←
1
if
J
O
N
<
J
O
F
F
else
0
;
r
etur
n
u
(
k
+
1)
13:
end
function
Figure
2.
HIL
setup
3.2.
Experimental
r
esults
3.2.1.
T
est
scenario
1:
V
ariable
input
v
oltage
with
xed
output
r
efer
ence
In
this
rst
test,
the
objecti
v
e
is
to
e
v
aluate
the
beha
vior
of
the
boost
con
v
erter
and
its
control
strate
gy
under
a
time-v
arying
input
v
oltage
while
maintaining
a
constant
output
v
oltage
reference.
The
input
v
oltage
V
in
v
aries
o
v
er
time
as
described
in
(22).
V
in
(
t
)
=
30
V
,
for
0
≤
t
<
1
s
40
V
,
for
1
≤
t
<
1
.
5
s
50
V
,
for
t
≥
1
.
5
s
(22)
In
contrast,
Figure
3(a)
illustrates
the
response
when
the
proposed
control
technique
is
applied.
The
output
v
oltage
follo
ws
the
reference
v
alue
V
ref
=
60
V
with
e
xcellent
accurac
y
and
without
o
v
ershoot
as
sho
wn
in
Figure
3(b).
The
inductor
current
sho
ws
smooth
transitions
and
impro
v
ed
tracking
of
the
reference
current,
e
v
en
during
changes
in
input
v
oltage.
This
conrms
the
enhanced
rob
ustness
and
dynamic
performance
of
the
proposed
split
cost
function-based
control.
3.2.2.
T
est
scenario
2:
Fixed
input
v
oltage
with
v
ariable
output
r
efer
ence
In
this
second
test,
the
input
v
oltage
V
in
is
k
ept
constant
at
30
V
throughout
the
simulation,
while
the
output
v
oltage
reference
V
ref
is
v
aried
in
steps
to
e
v
aluate
the
con
v
erter’
s
ability
to
track
dif
ferent
reference
v
alues.
The
reference
prole
is
dened
as
follo
ws:
V
ref
(
t
)
=
60
V
,
for
0
≤
t
<
1
s
80
V
,
for
1
≤
t
<
1
.
5
s
50
V
,
for
t
≥
1
.
5
s
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
17,
No.
2,
June
2026:
1211–1220
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
1217
This
test
e
v
aluates
the
performance
proposed
approach.
The
goal
is
to
v
erify
ho
w
accurately
and
quickly
the
con
v
erter
responds
to
do
wnw
ard
steps
in
V
ref
,
and
elimi
nates
o
v
ershoot
or
undershoot
during
transients
as
it
clearly
sho
wn
in
Figure
4
despite
the
ab
use
change
in
V
r
ef
.
(a)
(b)
Figure
3.
Con
v
erter
response
using
proposed
FS-MPC
under
input
v
oltage
v
ariation:
(a)
system
response
using
proposed
FS-MPC
and
(b)
zoomed
vie
w
of
the
output
v
oltage
and
current
response
Figure
4.
Con
v
erter
response
using
proposed
FS-MPC
under
reference
v
oltage
v
ariation
Dual-mode
model
pr
edictive
contr
ol
for
non-minimum
phase
boost
con
verter
s
(J
awhr
a
El
Hmidi)
Evaluation Warning : The document was created with Spire.PDF for Python.
1218
❒
ISSN:
2088-8694
3.2.3.
T
est
scenario
3:
Load
v
ariation
under
xed
input
and
output
r
efer
ence
In
this
third
test,
the
rob
ustness
of
the
proposed
control
method
is
e
v
aluated
under
a
sudden
and
se
v
ere
load
v
ariation.
The
input
v
oltage
V
in
is
held
constant
at
30
V
,
and
the
output
v
oltage
reference
is
x
ed
at
V
ref
=
60
V.
The
resisti
v
e
load
under
goes
an
abrupt
change
from
41.6
Ω
to
4.16
Ω
,
corresponding
to
a
tenfold
increase
in
current
demand.
This
v
ariation
is
applied
at
t
=
1
s,
simulating
a
highly
dynam
ic
operating
condition.
The
objecti
v
e
of
this
test
is
to
observ
e
ho
w
ef
fecti
v
ely
the
proposed
split
cost
function-based
FS-MPC
handles
the
disturbance
while
maintaining
output
v
olt
age
re
gulation
and
current
stability
.
The
results
sho
w
that
the
proposed
controller
quickly
reacts
to
the
increased
load
without
o
v
ershoot
or
v
oltage
drop,
and
restores
steady-state
conditions
with
minimal
transient
de
viation
as
seen
in
Figure
5.
Figure
5.
Con
v
erter
response
using
proposed
FS-MPC
under
load
disturbance
3.3.
Comparati
v
e
analysis
F
or
benchmarking
purposes,
the
proposed
method
w
as
compared
with
a
standard
FS-MPC
implementation.
As
summarized
in
T
able
2,
the
split
cost-function
strate
gy
achie
v
es
lo
wer
o
v
ershoot
and
a
shorter
settling
time
while
simultaneously
reducing
switching
acti
vity
.
In
addition,
it
deli
v
ers
a
signicant
impro
v
ement
in
computational
ef
cienc
y
compared
with
the
con
v
entional
approach.
These
results
conrm
that
the
proposed
control
strate
gy
not
only
addresses
the
non-minimum
phase
challenge
b
ut
also
enhances
real-time
feasibility
,
making
it
suitable
for
embedded
implementations
on
lo
w-cost
hardw
are
platforms.
T
able
2.
Experimental
performance
comparison
Metric
FS-MP
C
(classical)
Proposed
method
Ov
ershoot
(%)
6.8
0.9
Settling
time
(ms)
1.1
0.6
Computation
time
(ARM,
µ
s)
18
8.5
4.
CONCLUSION
This
w
ork
presented
a
real-time
implementation
of
a
split
cost
function-based
nite-set
model
predicti
v
e
control
(FS-MPC)
strate
gy
for
a
DC-DC
boost
con
v
erter
using
a
hardw
are-in-the-l
oo
p
(HIL)
setup
with
a
ZedBoard
and
an
ADC.
The
proposed
method
successfully
addressed
the
limitations
of
classical
FS-MPC
by
impro
ving
v
oltage
re
gulation,
suppressing
o
v
ershoot,
and
enhancing
current
tracking.
Experimental
results
under
dif
fe
rent
scenarios,
including
input
v
oltage
v
ariation,
reference
changes,
and
sudden
load
disturbances,
demonstrated
the
superior
dynamic
performance
and
rob
ustness
of
the
proposed
approach.
The
controller
w
as
able
to
maintain
output
v
oltage
stability
and
react
quickly
to
system
v
ariations,
conrming
its
suitability
for
real-time
embedded
po
wer
con
v
ersion
applications.
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
17,
No.
2,
June
2026:
1211–1220
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
1219
FUNDING
INFORMA
TION
Authors
state
no
funding
in
v
olv
ed.
A
UTHOR
CONTRIB
UTIONS
ST
A
TEMENT
This
journal
uses
the
Contrib
utor
Roles
T
axonomy
(CRediT)
to
recognize
indi
vidual
author
contrib
utions,
reduce
authorship
disputes,
and
f
acilitate
collaboration.
Name
of
A
uthor
C
M
So
V
a
F
o
I
R
D
O
E
V
i
Su
P
Fu
Ja
whra
El
Hmidi
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Anass
Mansouri
✓
✓
✓
✓
✓
✓
✓
✓
✓
Ali
Ahaitouf
✓
✓
✓
✓
✓
C
:
C
onceptualization
I
:
I
n
v
estig
ation
V
i
:
V
i
sualization
M
:
M
ethodology
R
:
R
esources
Su
:
Su
pervision
So
:
So
ftw
are
D
:
D
ata
Curation
P
:
P
roject
Administration
V
a
:
V
a
lidation
O
:
Writing
-
O
riginal
Draft
Fu
:
Fu
nding
Acquisition
F
o
:
F
o
rmal
Analysis
E
:
Writing
-
Re
vie
w
&
E
diting
CONFLICT
OF
INTEREST
ST
A
TEMENT
The
authors
declare
that
there
is
no
conict
of
interest
re
g
arding
the
publication
of
this
paper
.
D
A
T
A
A
V
AILABILITY
The
data
supporting
this
study’
s
ndings
are
a
v
ailable
from
the
corresponding
author
,
[JEL].
REFERENCES
[1]
J.
W
ang,
B.
W
ang,
L.
Zhang,
J.
W
ang,
N.
I.
Shchuro
v
,
and
B.
V
.
Malozyomo
v
,
“Re
vie
w
of
bidirectional
DC–DC
con
v
erter
topologies
for
h
ybrid
ener
gy
storage
system
of
ne
w
ener
gy
v
ehicles,
”
Gr
een
Ener
gy
and
Intellig
ent
T
r
ansportation
,
v
ol.
1,
no.
2,
p.
100010,
Sep.
2022,
doi:
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predicti
v
e
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inte
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K.
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model
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oltage
and
current
mode
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v
erter
,
”
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and
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yer
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nite
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e
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Schwenzer
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M.
A
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,
T
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Ber
gs,
and
D.
Abel,
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vie
w
on
model
predicti
v
e
control:
an
engineering
perspecti
v
e,
”
The
International
J
ournal
of
Advanced
Manufacturing
T
ec
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gy
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Rojas,
M.
Ri
v
era,
J.
Munoz,
C.
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and
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A
study
of
weighting
f
actor
design
in
model
predicti
v
e
control
applications,
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2021
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CHILEAN
Confer
ence
on
Electrical,
Electr
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Engineeri
ng
,
Information
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Communication
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hnolo
gies
(CHILECON)
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2021,
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et
al.
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ef
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x
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ng
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T
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P
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pr
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contr
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phase
boost
con
verter
s
(J
awhr
a
El
Hmidi)
Evaluation Warning : The document was created with Spire.PDF for Python.
1220
❒
ISSN:
2088-8694
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v
erters
based
on
input-state
linearization,
”
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ournal
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BIOGRAPHIES
OF
A
UTHORS
J
awhra
El
Hmidi
recei
v
ed
the
State
Engineering
de
gree
in
Embedded
Systems
and
Industrial
Computing
from
ENSA
F
`
es,
Morocco,
in
2020.
She
then
w
ork
ed
as
an
Elec
tric/Electronic
Architect
at
Stellantis
Group
(2020–2022),
focusing
on
embedded
automoti
v
e
electronic
systems.
Currently
pursuing
a
Ph.D.
at
Sidi
Mohamed
Ben
Abdellah
Uni
v
ersity
(USMB
A),
Fez,
within
the
SIGER
Laboratory
,
her
research
centers
on
po
wer
electronics
and
control
strate
gies
for
electric
v
ehicle
char
gers.
Her
interests
include
bidirectional
con
v
erters,
LLC
resonant
topologies,
V2G/G2V
inte
gration,
and
real-time
embedded
control.
She
is
act
i
v
ely
in
v
olv
ed
in
hardw
are/softw
are
co-design
and
system-le
v
el
modeling
for
adv
anced
char
ging
solutions
in
electric
mobility
.
She
can
be
contacted
at
email:
ja
whara.elhmidi@usmba.ac.ma.
Anass
Mansouri
recei
v
ed
the
Ph.D.
de
gree
in
microelectronics
and
embedded
systems
from
the
F
aculty
of
Sciences
and
T
echnologies,
Fez,
Morocco,
in
2009.
He
is
currently
a
professor
with
the
Nati
onal
School
of
Applied
Sciences
(ENSA),
Fez.
His
research
interests
include
VLSI
and
embedded
architecture
desi
gn,
video,
image
processing,
and
softw
are/hardw
are
design
and
optimization.
He
is
a
member
of
the
Intelligent
Systems,
Georesources,
and
Rene
w
able
Ener
gies
(SIGER)
and
the
Head
of
the
T
eam
Embedded
Systems,
Electronics,
and
T
elecommunication.
He
can
be
contacted
at
email:
anass.manssouri@usmba.ac.ma.
Ali
Ahaitouf
recei
v
ed
the
Ph.D.
de
gree
in
electronics,
in
1998.
He
is
currently
a
teacher
and
a
researcher
with
the
Uni
v
ersity
of
Sidi
Mohammed
Ben
Abdellah
(USMB
A),
Fez.
He
w
as
the
Ex-Director
of
the
Intelligent
Systems,
Georesources,
and
Rene
w
able
Ener
gies
(SIGER).
He
managed
man
y
multilateral
research
projects
related
to
analog
design
optimization,
electronics
component
characterization,
optimization,
and
solar
ener
gy
under
concentration
(CPV).
He
supervised
a
dozen
Ph.D.
theses
and
published
o
v
er
15
articles
in
reno
wned
journals.
His
research
interests
include
microelectronics
and
solar
compounds,
digital
and
analog
design
of
inte
grated
circuits,
and
image
and
data
compression.
He
can
be
contacted
at
email:
ali.ahaitouf@usmba.ac.ma.
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
17,
No.
2,
June
2026:
1211–1220
Evaluation Warning : The document was created with Spire.PDF for Python.