I
A
E
S
I
n
t
e
r
n
at
io
n
al
Jou
r
n
al
of
A
r
t
if
ic
ia
l
I
n
t
e
ll
ig
e
n
c
e
(
I
J
-
A
I
)
V
ol
. 13, No. 4, D
e
c
e
m
be
r
2024, pp.
4003
~
4018
I
S
S
N
:
2252
-
8938
,
D
O
I
:
10.11591/
ij
a
i.
v13.i4.pp
4003
-
4018
4003
Jou
r
n
al
h
om
e
page
:
ht
tp
:
//
ij
ai
.
ia
e
s
c
or
e
.c
om
O
p
t
i
m
i
z
i
n
g t
h
e
p
osi
t
i
on
of
p
h
ot
ovol
t
ai
c
sol
ar
t
r
ac
k
e
r
p
an
e
l
s
w
i
t
h
ar
t
i
f
i
c
i
al
i
n
t
e
l
l
i
ge
n
c
e
u
si
n
g
M
A
T
L
A
B
S
i
m
u
l
i
n
k
R
ic
ar
d
o L
in
e
ls
on
, F
ah
m
y R
in
an
d
a S
ap
u
t
r
i
D
e
pa
r
t
m
e
nt
of
E
ngi
ne
e
r
i
ng P
hys
i
c
s
,
F
a
c
ul
t
y of
E
ngi
ne
e
r
i
ng
a
nd
I
n
f
or
m
a
t
i
c
s
,
U
ni
ve
r
s
i
t
a
s
M
ul
t
i
m
e
di
a
N
u
s
a
nt
a
r
a
, T
a
nge
r
a
ng, I
ndone
s
i
a
A
r
t
ic
le
I
n
f
o
A
B
S
T
R
A
C
T
A
r
ti
c
le
h
is
to
r
y
:
R
e
c
e
iv
e
d
J
a
n
10
,
2024
R
e
vi
s
e
d
M
a
r
5
,
2024
A
c
c
e
pt
e
d
M
a
r
21
,
2024
This
research
aims
to
apply
an
artificial
intelligen
ce
(AI)
system
to
cont
rol
the
position
of
photovoltaic
(PV)
panels
to
maximize
the
use
of
solar
energ
y
using
the
solar
tracker.
The
implementation
of
AI
algorithms
to
achieve
o
ptimal
panel
orientation,
co
nsidering
factors
such
as
sunlight
intensity
a
nd
sun
position
is
also
discussed.
The
simulation
results
using
matrix
lab
oratory
(
MATLAB
)
Simulink
can
be
observ
ed
on
the
scope
,
display
ing
the
p
osition
control
graph
of
the
solar
panel
from
sunrise
to
sunset.
By
emp
loying
proportional
integral
derivative
(PID)
control,
the
error
is
likely
to
be
mi
nimal,
ensuring
that
the
panel
will
continu
e
to
follow
the
sun
until
it
sets
at
the
maximum
point
of
4:00
PM.
After
that,
the
panel
can
be
adjusted
back
or
reset
to
t
he
initial
position
at
6:00
AM
for
the
following
day.
In
a
f
ull
-
day
simulation,
the
solar
panel
will
follow
the
sun'
s
movement
from
su
nset
to
sunrise.
At
the
basic
level,
sunrise
occurs
in
the
first
hour
at
positi
on
1.0,
which
is
6:00
AM
in
the
minimum
poi
nt
at
the
bottom
left
corn
er
of
the
curve,
and
sunset
occurs
in
the
afternoon
at
position
5.25,
which
is
4:00
PM
at
the
maximum point in the
top right cor
ner of the
curve.
K
e
y
w
o
r
ds
:
A
r
ti
f
ic
ia
l
in
te
ll
ig
e
nc
e
M
A
T
L
A
B
S
im
ul
in
k
P
hot
ovol
ta
ic
P
r
opor
ti
ona
l
in
te
gr
a
l
de
r
iv
a
ti
ve
c
ont
r
ol
S
ol
a
r
m
ot
or
t
r
a
c
ke
r
This is an
open
acce
ss artic
le unde
r the
CC BY
-
SA
license.
C
or
r
e
s
pon
di
n
g A
u
th
or
:
F
a
hm
y R
in
a
nda
S
a
put
r
i
D
e
pa
r
tm
e
nt
of
E
ngi
ne
e
r
in
g P
hys
ic
s
, U
ni
ve
r
s
it
a
s
M
ul
ti
m
e
di
a
N
us
a
nt
a
r
a
St
.
S
c
ie
nt
ia
B
oul
e
va
r
d
,
G
a
di
ng S
e
r
pong,
C
ur
ug
S
a
nge
r
e
ng,
K
a
b
upa
te
n
T
a
nge
r
a
ng,
B
a
nt
e
n
15810,
I
ndone
s
ia
E
m
a
il
:
f
a
hm
y.r
in
a
nda
@
um
n.a
c
.i
d
1.
I
N
T
R
O
D
U
C
T
I
O
N
T
o
a
c
hi
e
ve
th
e
goa
ls
of
na
ti
ona
l
s
e
lf
-
r
e
li
a
nc
e
a
nd
e
ne
r
gy
r
e
s
il
ie
nc
e
,
a
s
s
ti
pul
a
te
d
in
th
e
pr
im
a
r
y
r
e
gul
a
ti
on
gove
r
ni
ng
e
ne
r
gy
is
s
ue
s
in
I
ndone
s
ia
,
na
m
e
ly
G
ove
r
nm
e
nt
R
e
gul
a
ti
on
N
um
be
r
79
of
2014
c
onc
e
r
ni
ng
th
e
na
ti
ona
l
e
n
e
r
gy
pol
ic
y
,
th
e
I
ndone
s
i
a
n
gove
r
nm
e
nt
pr
om
ot
e
s
th
e
ut
il
iz
a
ti
on
of
r
e
ne
w
a
bl
e
e
ne
r
gy
a
nd
r
e
s
tr
a
in
s
th
e
us
e
of
f
os
s
il
e
ne
r
gy
s
our
c
e
s
.
T
h
e
pol
ic
y
s
e
ts
a
ta
r
ge
t
f
or
th
e
m
ix
of
r
e
ne
w
a
bl
e
e
ne
r
gy
f
r
om
2020 to 2050
[
1]
.
A
ddi
ti
ona
ll
y, r
e
gul
a
ti
ons
r
e
ga
r
di
ng t
he
us
e
of
r
e
ne
w
a
bl
e
e
ne
r
gy i
n I
ndone
s
ia
a
r
e
out
li
ne
d i
n
P
r
e
s
id
e
nt
ia
l
R
e
gul
a
ti
on
N
um
be
r
112
of
2022
c
onc
e
r
ni
ng
th
e
a
c
c
e
le
r
a
ti
on
of
r
e
ne
w
a
bl
e
e
ne
r
gy
de
v
e
lo
pm
e
nt
f
or
e
le
c
tr
ic
it
y
s
uppl
y
[
2]
.
R
e
ne
w
a
bl
e
e
ne
r
gy
i
s
in
de
e
d
be
c
om
in
g
a
pr
im
a
r
y
f
oc
us
in
e
f
f
or
ts
to
r
e
duc
e
th
e
im
pa
c
t
of
c
li
m
a
te
c
ha
nge
a
nd
de
pe
nde
nc
e
on
f
os
s
il
f
ue
ls
[
3]
-
[
5]
.
M
a
ny
a
r
ti
f
ic
ia
l
in
te
ll
ig
e
nc
e
(
A
I
)
te
c
hnol
ogi
e
s
a
r
e
e
m
pl
oye
d
in
m
ode
li
ng
a
nd
a
n
a
ly
z
in
g
r
e
ne
w
a
bl
e
e
ne
r
gy
s
ys
te
m
s
to
e
nha
n
c
e
e
f
f
ic
ie
nc
y,
r
e
li
a
bi
li
ty
,
a
nd
pe
r
f
or
m
a
nc
e
[
6]
, [
7]
.
G
lo
ba
l
e
f
f
or
ts
to
f
in
d
s
us
ta
in
a
bl
e
e
ne
r
gy
s
ol
ut
io
ns
ha
ve
s
pa
r
ke
d
in
c
r
e
a
s
e
d
in
te
r
e
s
t
in
s
ol
a
r
e
ne
r
gy
te
c
hnol
ogi
e
s
in
th
e
l
a
s
t
f
e
w
d
e
c
a
de
s
[
8]
,
[
9]
.
A
s
one
of
th
e
m
o
s
t
pr
om
is
in
g
r
e
ne
w
a
bl
e
r
e
s
our
c
e
s
,
s
ol
a
r
e
ne
r
gy
ha
s
s
ig
ni
f
ic
a
nt
pot
e
nt
ia
l
to
m
a
ke
a
s
ubs
ta
nt
ia
l
c
ont
r
ib
ut
io
n
to
t
he
w
or
ld
'
s
e
n
e
r
gy
ne
e
d
s
[
3]
,
[
10]
,
[
11]
.
I
n
th
is
c
ont
e
xt
,
phot
ovol
ta
ic
(
P
V
)
pa
ne
ls
,
s
e
r
vi
ng
a
s
th
e
c
or
e
of
th
e
s
ol
a
r
e
ne
r
gy
c
onve
r
s
io
n
s
ys
te
m
in
to
e
le
c
tr
ic
it
y,
a
r
e
r
e
c
e
iv
in
g
s
pe
c
ia
l
a
tt
e
nt
io
n
[
12]
,
[
13]
.
F
ig
ur
e
1
is
th
e
s
ol
a
r
e
ne
r
gy
ge
ne
r
a
ti
on
by
r
e
gi
on
m
e
a
s
ur
e
d
in
te
r
a
w
a
tt
-
hour
s
(
T
W
h)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
, V
ol
. 13, No. 4, D
e
c
e
m
be
r
2024:
4003
-
4018
4004
F
ig
ur
e
1.
G
lo
ba
l
s
ol
a
r
e
ne
r
gy ge
ne
r
a
ti
on
[
14]
H
ow
e
ve
r
, c
ha
ll
e
ng
e
s
a
s
s
oc
ia
te
d
w
it
h t
he
va
r
ia
bi
li
ty
of
s
unl
ig
ht
in
te
ns
it
y a
nd t
h
e
c
ha
ngi
ng
pos
it
io
n of
th
e
s
un
th
r
oughout
th
e
da
y
a
f
f
e
c
t
th
e
e
ne
r
gy
out
put
g
e
ne
r
a
te
d
by
P
V
pa
ne
ls
[
15]
.
T
h
e
r
e
f
or
e
,
opt
im
iz
in
g
th
e
or
ie
nt
a
ti
on
of
pa
ne
ls
to
w
a
r
ds
s
unl
ig
ht
be
c
om
e
s
c
r
uc
ia
l
to
e
nha
nc
e
th
e
e
f
f
ic
ie
nc
y
of
th
e
P
V
s
y
s
te
m
[
16]
.
T
he
gl
oba
l
de
ve
lo
pm
e
nt
of
A
I
w
it
h
va
r
io
us
a
ppl
ic
a
ti
ons
i
s
il
lu
s
tr
a
t
e
d
in
F
ig
ur
e
2.
W
he
r
e
a
nnu
a
l
pa
te
nt
s
obt
a
in
e
d
gl
oba
ll
y e
xc
e
e
de
d 30,000 pa
t
e
nt
s
f
or
t
he
pe
r
io
d f
r
om
2018 to 2
020.
F
ig
ur
e
2. T
he
gl
oba
l
de
ve
lo
pm
e
nt
of
AI
[
17]
I
nt
e
gr
a
ti
ng
A
I
w
it
h
th
e
c
ont
r
ol
of
P
V
pa
ne
l
pos
it
io
ns
pr
e
s
e
n
ts
a
n
in
nov
a
ti
ve
s
ol
ut
io
n
to
va
r
io
us
c
ha
ll
e
nge
s
. A
I
a
ll
ow
s
t
he
s
ys
te
m
t
o l
e
a
r
n f
r
om
pa
s
t
e
xpe
r
ie
nc
e
s
a
nd i
m
pr
ove
i
ts
pe
r
f
or
m
a
nc
e
ove
r
t
im
e
. I
t
c
a
n
a
da
pt
to
c
ha
ngi
ng
e
nvi
r
onm
e
nt
a
l
c
ondi
ti
ons
,
e
ns
ur
in
g
opt
im
a
l
pos
it
io
ni
ng
of
th
e
pa
ne
ls
.
T
hi
s
dyna
m
ic
opt
im
iz
a
ti
on ma
xi
m
iz
e
s
t
he
ut
il
iz
a
ti
on of
s
ol
a
r
e
ne
r
gy, e
nha
nc
i
ng ove
r
a
ll
e
f
f
ic
ie
nc
y.
T
o
unde
r
s
ta
nd
a
nd
im
pl
e
m
e
nt
th
is
s
ol
ut
io
n,
th
is
a
r
t
ic
le
e
xpl
or
e
s
c
onc
r
e
te
a
ppl
ic
a
ti
ons
of
A
I
i
n
c
ont
r
ol
li
ng
th
e
pos
it
io
n
of
P
V
pa
ne
ls
us
in
g
th
e
m
a
tr
ix
l
a
bor
a
to
r
y
(
M
A
T
L
A
B
)
S
im
ul
in
k
s
im
ul
a
ti
on
e
nvi
r
onm
e
nt
.
T
he
a
dva
nt
a
ge
s
of
M
A
T
L
A
B
S
im
ul
in
k
in
in
te
gr
a
ti
ng
phys
ic
a
l
m
ode
ls
a
nd
A
I
a
lg
or
it
hm
s
m
a
ke
it
a
n
id
e
a
l
pl
a
tf
or
m
f
or
de
ve
lo
pi
ng
in
te
ll
ig
e
nt
c
ont
r
ol
s
ol
ut
io
ns
f
or
th
e
pos
it
io
ni
ng
of
P
V
pa
ne
ls
.
T
hr
ough
th
e
Y
ea
r
so
l
a
r
en
er
g
y
g
en
er
a
t
i
o
n
(
T
Wh
)
Y
ea
r
N
u
m
b
er
o
f
p
a
t
en
t
s
g
en
er
a
t
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
O
pt
imi
z
in
g t
he
pos
it
io
n of
photov
ol
ta
ic
s
ol
ar
t
r
a
c
k
e
r
pane
ls
w
it
h ar
ti
fi
c
ia
l
…
(
R
ic
ar
do L
in
e
ls
on
)
4005
unde
r
s
ta
ndi
ng
a
nd
im
pl
e
m
e
nt
a
ti
on
of
th
is
s
ol
ut
io
n,
it
is
e
xp
e
c
te
d
th
a
t
th
is
r
e
s
e
a
r
c
h
c
a
n
c
ont
r
ib
ut
e
to
th
e
di
s
c
ove
r
y
of
in
nova
ti
ve
s
ol
ut
io
ns
th
a
t
not
onl
y
e
nha
nc
e
s
ol
a
r
e
ne
r
gy
e
f
f
ic
ie
nc
y
but
a
ls
o
pa
ve
th
e
w
a
y
f
or
th
e
de
ve
lo
pm
e
nt
of
m
or
e
e
nvi
r
onm
e
nt
a
ll
y f
r
i
e
ndl
y a
nd s
us
ta
in
a
bl
e
e
ne
r
gy t
e
c
hnol
ogi
e
s
.
S
e
ve
r
a
l
r
e
la
te
d
s
tu
di
e
s
c
onduc
te
d
by
pr
e
vi
ous
r
e
s
e
a
r
c
he
r
s
pr
ovi
de
a
s
ynt
he
s
is
of
ke
y
s
tu
di
e
s
in
th
is
f
ie
ld
,
hi
ghl
ig
ht
in
g
m
e
th
odol
ogi
e
s
,
f
in
di
ngs
,
a
nd
r
e
s
e
a
r
c
h
c
ont
r
ib
ut
io
ns
.
S
hi
nde
e
t
al
.
[
18]
in
ve
s
ti
ga
te
d
th
e
in
te
gr
a
ti
on
of
pr
opor
ti
ona
l
in
te
gr
a
l
de
r
iv
a
ti
ve
(
P
I
D
)
c
ont
r
ol
le
r
s
a
da
pt
in
g
to
m
a
xi
m
um
pow
e
r
poi
nt
tr
a
c
ki
ng
(
M
P
P
T
)
f
or
a
s
ol
a
r
a
r
r
a
y.
A
li
e
t
al
.
[
19]
f
in
de
d t
ha
t
th
e
B
a
t
A
lg
or
it
hm
(
P
I
D
-
B
A
)
pe
r
f
or
m
s
t
he
be
s
t
in
t
e
r
m
s
of
s
e
tt
li
ng
ti
m
e
a
nd
ove
r
s
hoot
f
or
th
e
s
un
tr
a
c
ki
ng
s
y
s
te
m
o
n
phot
ovol
ta
ic
pa
ne
ls
.
on
dua
l
-
a
xi
s
tr
a
c
ki
ng
opt
im
iz
a
ti
on
f
or
s
ol
a
r
c
e
ll
s
us
in
g
th
e
im
pe
r
ia
li
s
t
c
om
pe
ti
ti
ve
a
lg
or
it
hm
(
I
C
A
)
.
L
iv
e
e
t
al
.
[
20
]
c
onduc
te
d
a
s
im
ul
a
ti
on
s
tu
dy
of
f
uz
z
y
a
ut
o
-
tu
ni
ng
P
I
D
c
ont
r
ol
le
r
s
us
in
g
M
A
T
L
A
B
.
M
a
s
r
ur
e
t
al
.
[
21]
e
xpl
or
e
d
th
e
opt
im
a
l
ti
lt
a
ngl
e
to
m
a
xi
m
iz
e
P
V
yi
e
ld
s
.
M
os
a
la
m
[
22]
e
va
lu
a
te
d
th
e
ope
r
a
ti
on
of
a
n
in
te
gr
a
te
d
P
V
s
ys
te
m
w
it
h
bui
ld
in
gs
.
O
uf
e
tt
oul
e
t
al
.
[
23]
a
na
ly
z
e
d
th
e
p
e
r
f
or
m
a
nc
e
of
P
V
m
odul
e
pos
it
io
ns
in
a
s
ol
a
r
P
V
a
r
r
a
y
unde
r
pa
r
ti
a
l
s
ha
di
ng
c
ondi
ti
ons
.
Q
a
is
e
t
a
l.
[
24]
s
ta
te
d
th
a
t
th
e
r
e
s
e
a
r
c
h
ut
il
iz
e
s
th
e
T
hr
e
e
-
D
io
de
M
ode
l
(
T
D
M
)
f
or
phot
ovol
ta
ic
m
odul
e
s
,
w
he
r
e
it
s
opt
im
a
li
ty
is
de
te
r
m
in
e
d
by
th
e
opt
im
iz
a
ti
on
a
lg
or
it
hm
us
e
d,
s
uc
h
a
s
th
e
C
ir
c
le
S
e
a
r
c
h
A
lg
or
it
hm
(
C
S
A
)
,
w
hi
c
h
pr
ovi
de
s
hi
ghl
y
a
c
c
ur
a
te
r
e
s
ul
ts
a
nd
lo
w
e
r
a
bs
ol
ut
e
c
ur
r
e
nt
e
r
r
or
c
om
pa
r
e
d
to
ot
he
r
a
lg
or
it
hm
s
.
F
a
hm
id
a
e
t
a
l.
[
25
]
s
im
ul
a
te
d
th
e
m
a
xi
m
um
pow
e
r
poi
nt
pos
it
io
n
o
f
P
V
us
in
g
M
A
T
L
A
B
s
im
s
c
a
pe
.
I
khw
a
n
e
t
al
.
[
26]
a
ppl
ie
d
m
ode
l
pr
e
di
c
ti
ve
c
ont
r
o
l
to
dua
l
-
a
xi
s
s
ol
a
r
t
r
a
c
ke
r
s
us
in
g
M
A
T
L
A
B
S
im
ul
in
k
s
im
ul
a
ti
ons
.
G
a
ne
s
a
n
e
t
al
.
[
27]
f
oc
us
e
d
on
m
ode
li
n
g
a
nd
s
im
ul
a
ti
ng
th
e
in
c
r
e
m
e
nt
a
l
c
onduc
ta
nc
e
a
lg
or
it
hm
f
or
s
ol
a
r
M
P
P
T
.
T
he
di
s
ti
nc
ti
on
of
th
is
r
e
s
e
a
r
c
h
f
r
om
s
im
il
a
r
s
tu
di
e
s
li
e
s
in
c
r
e
a
ti
ng
a
uni
que
a
ppr
oa
c
h
to
opt
im
iz
in
g
th
e
pos
it
io
n
of
P
V
pa
ne
l
s
a
nd
c
ons
id
e
r
in
g
th
e
r
e
a
l
-
ti
m
e
va
r
ia
bi
li
ty
of
s
un
pos
it
io
n
c
ha
nge
s
.
T
hi
s
s
tu
dy
ut
il
iz
e
s
di
f
f
e
r
e
nt
va
r
ia
bl
e
s
in
th
e
P
I
D
c
on
tr
ol
le
r
,
pa
ne
l,
a
nd
m
ot
or
pa
r
a
m
e
te
r
s
th
a
t
w
il
l
im
pa
c
t
M
A
T
L
A
B
S
im
ul
in
k s
im
ul
a
ti
ons
.
T
hi
s
r
e
s
e
a
r
c
h
ha
s
s
e
ve
r
a
l
obj
e
c
ti
ve
s
th
a
t
de
ta
il
it
s
f
oc
us
a
nd
c
ont
r
ib
ut
io
ns
to
th
e
unde
r
s
ta
ndi
ng
a
nd
de
ve
lo
pm
e
nt
of
s
ol
a
r
e
ne
r
gy
te
c
hnol
ogy.
F
ir
s
tl
y,
th
e
r
e
s
e
a
r
c
h
a
im
s
to
c
om
pr
e
he
nd
th
e
c
onc
e
pt
of
P
V
s
,
a
c
r
uc
ia
l
pr
oc
e
s
s
i
n c
onve
r
ti
ng he
a
t
e
ne
r
gy i
nt
o e
le
c
tr
ic
it
y. W
it
h a
pr
of
o
und unde
r
s
ta
ndi
ng of
t
hi
s
pr
oc
e
s
s
, t
he
r
e
s
e
a
r
c
h
is
e
xpe
c
te
d t
o pr
ovi
de
be
tt
e
r
i
ns
ig
ht
s
i
nt
o t
he
e
ne
r
gy c
onve
r
s
io
n
m
e
c
ha
ni
s
m
i
n P
V
pa
ne
ls
.
N
e
xt
,
th
e
r
e
s
e
a
r
c
h
t
a
r
ge
ts
a
n
unde
r
s
ta
ndi
ng
of
th
e
m
ove
m
e
nt
o
f
th
e
s
un
s
ol
a
r
tr
a
c
ke
r
s
ys
t
e
m
,
a
vi
ta
l
e
le
m
e
nt
in
e
ne
r
gy
e
f
f
ic
ie
nc
y
f
or
s
ol
a
r
pa
ne
ls
.
T
hi
s
goa
l
in
c
lu
d
e
s
a
n
a
na
ly
s
i
s
of
how
th
e
m
ove
m
e
nt
of
s
ol
a
r
pa
ne
ls
c
a
n
be
opt
im
iz
e
d
to
e
nha
nc
e
th
e
e
f
f
ic
ie
nc
y
of
s
ol
a
r
e
ne
r
gy
c
ol
le
c
ti
on
th
r
oughout
th
e
da
y.
A
not
he
r
k
e
y
obj
e
c
ti
ve
is
to
unde
r
s
t
a
nd
a
nd
opt
im
iz
e
th
e
m
ove
m
e
nt
of
s
ol
a
r
pa
ne
ls
a
s
qui
c
kl
y
a
s
pos
s
ib
le
to
w
a
r
ds
th
e
opt
im
a
l
s
un
pos
it
io
n.
A
d
e
e
p
unde
r
s
ta
ndi
ng
of
th
e
dyna
m
ic
s
of
th
is
m
o
ve
m
e
nt
f
or
m
s
th
e
ba
s
i
s
f
or
de
s
ig
ni
ng
a
s
ys
t
e
m
th
a
t
is
r
e
s
pons
iv
e
a
nd a
da
pt
iv
e
t
o c
ha
ng
e
s
i
n t
he
s
un'
s
pos
it
io
n.
I
n
a
ddi
ti
on
to
th
e
t
e
c
hni
c
a
l
a
s
pe
c
ts
,
th
is
r
e
s
e
a
r
c
h
ha
s
a
s
ig
ni
f
ic
a
nt
im
pa
c
t
on
th
e
de
ve
lo
pm
e
nt
of
A
I
to
opt
im
iz
e
th
e
pos
it
io
n
of
P
V
pa
ne
l
s
.
B
y
le
ve
r
a
gi
ng
A
I
,
th
is
r
e
s
e
a
r
c
h
ope
ns
th
e
pot
e
nt
ia
l
to
im
pr
ove
th
e
e
f
f
ic
ie
nc
y
of
s
ol
a
r
e
ne
r
gy
ut
il
iz
a
ti
on
a
nd
r
e
duc
e
de
pe
nde
nc
e
on
c
onve
nt
io
na
l
e
ne
r
gy
s
our
c
e
s
.
T
he
be
n
e
f
it
s
of
th
is
r
e
s
e
a
r
c
h
in
c
lu
de
r
e
duc
in
g
ope
r
a
ti
ona
l
c
os
t
s
of
pow
e
r
pl
a
nt
s
th
r
ough
th
e
opt
im
iz
a
ti
on
of
r
e
ne
w
a
bl
e
e
ne
r
gy
us
e
, a
s
w
e
ll
a
s
m
a
ki
ng
a
pos
it
iv
e
c
ont
r
ib
ut
io
n
to
th
e
ove
r
a
ll
de
ve
lo
pm
e
nt
of
r
e
ne
w
a
bl
e
e
ne
r
gy
te
c
hnol
ogy.
T
hu
s
,
th
is
r
e
s
e
a
r
c
h
not
onl
y
a
im
s
to
d
e
e
pe
n
th
e
unde
r
s
ta
ndi
ng
of
P
V
te
c
hnol
ogy
but
a
ls
o
s
e
e
k
s
to
pr
ovi
de
pr
a
c
ti
c
a
l
s
ol
ut
io
ns
t
o e
nha
nc
e
e
f
f
ic
ie
nc
y a
nd s
u
s
ta
in
a
bi
li
ty
i
n s
ol
a
r
e
ne
r
g
y ut
il
iz
a
ti
on.
2.
M
E
T
H
O
D
T
he
r
e
s
e
a
r
c
h
m
e
th
odol
ogy
a
ppl
ie
d
in
th
is
pr
oj
e
c
t
c
ons
is
ts
of
s
e
ve
r
a
l
s
ta
ge
s
out
li
ni
ng
th
e
s
te
ps
of
s
ys
te
m
de
ve
lo
pm
e
nt
a
nd
da
ta
a
na
ly
s
is
.
F
ir
s
tl
y,
th
e
s
ys
te
m
d
e
s
ig
n
in
vol
ve
s
c
r
e
a
ti
ng
a
c
ir
c
ui
t
f
or
th
e
P
I
D
c
ont
r
ol
le
r
,
pa
ne
l,
a
nd
m
ot
or
.
N
e
xt
,
va
r
ia
bl
e
de
te
r
m
in
a
ti
on
in
vo
l
ve
s
us
in
g
va
r
ia
bl
e
va
lu
e
s
in
th
e
P
I
D
c
ont
r
ol
le
r
,
pa
ne
l,
a
nd
m
ot
o
r
s
im
ul
a
ti
ons
to
e
ns
ur
e
th
e
pr
e
c
i
s
io
n
a
nd
a
c
c
ur
a
c
y
of
th
e
r
e
s
ul
ts
. T
he
f
ol
lo
w
in
g
a
r
e
pa
r
a
m
e
te
r
va
r
ia
bl
e
s
f
or
th
e
P
V
pa
ne
l
a
nd
m
ot
or
s
e
t
to
de
te
r
m
in
e
th
e
opt
i
m
a
l
li
m
it
s
of
P
I
D
c
ont
r
ol
f
or
th
e
P
V
pos
it
io
n
c
onc
e
r
ni
ng t
he
s
un'
s
or
ie
nt
a
ti
on.
P
V
P
a
ne
l:
−
D
a
m
pi
ng
c
oe
f
f
ic
ie
nt
(
K
d)
:
th
e
va
lu
e
K
d=
5
r
e
f
e
r
s
to
th
e
da
m
pi
n
g
c
oe
f
f
ic
ie
nt
in
m
ot
io
n
c
ont
r
ol
,
a
f
f
e
c
ti
ng
how
qui
c
kl
y t
he
s
ol
a
r
pa
ne
l
m
ove
m
e
nt
w
il
l
r
e
a
c
h t
he
d
e
s
ir
e
d p
os
it
io
n w
it
hout
s
ig
ni
f
ic
a
nt
ove
r
s
hoot
.
−
I
nve
r
s
e
of
m
om
e
nt
of
i
ne
r
ti
a
(
1/
J
)
:
th
e
va
lu
e
1/
J
=
8.6
in
di
c
a
t
e
s
t
he
i
nve
r
s
e
of
t
he
m
om
e
nt
of
i
ne
r
ti
a
of
t
he
s
ol
a
r
pa
ne
l,
i
nf
lu
e
nc
in
g t
he
pa
ne
l'
s
r
e
s
pons
e
t
o c
h
a
nge
s
i
n m
ot
i
on.
M
ot
or
:
−
M
ot
or
ga
in
(
K
g)
:
th
e
va
lu
e
K
g=
2
,
000
r
e
f
le
c
ts
how
e
f
f
e
c
ti
ve
ly
th
e
m
ot
or
c
a
n
tr
a
ns
f
e
r
e
le
c
tr
ic
a
l
e
ne
r
gy
in
to
m
e
c
ha
ni
c
a
l
m
ot
io
n.
−
F
r
ic
ti
on
c
oe
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
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e
ll
, V
ol
. 13, No. 4, D
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c
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m
be
r
2024:
4003
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4018
4006
−
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or
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s
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pons
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s
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c
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r
te
d i
nt
o m
e
c
ha
ni
c
a
l
e
ne
r
gy by the
m
ot
or
.
T
he
ne
xt
s
te
p
in
vol
ve
s
th
e
d
e
ve
lo
pm
e
nt
of
a
n
A
I
m
od
e
l
w
it
h
t
he
de
s
ig
n
of
a
n
a
da
pt
iv
e
a
lg
or
it
hm
.
T
hi
s
a
lg
or
it
hm
c
ons
id
e
r
s
e
nvi
r
onm
e
nt
a
l
va
r
ia
bl
e
s
to
opt
im
iz
e
th
e
pa
ne
l'
s
pos
it
io
n
r
e
la
ti
ve
to
th
e
or
ie
nt
a
ti
on
of
th
e
s
un.
A
f
te
r
w
a
r
d,
th
e
in
te
gr
a
ti
on
of
A
I
w
it
h
th
e
P
V
p
a
ne
l
c
ont
r
ol
s
ys
te
m
is
c
a
r
r
ie
d
out
u
s
in
g
M
A
T
L
A
B
S
im
ul
in
k, e
ns
ur
in
g t
he
a
li
gnm
e
nt
a
nd pe
r
f
or
m
a
nc
e
of
t
he
s
ys
te
m
.
S
im
ul
a
ti
on
a
nd
te
s
ti
ng a
r
e
th
e
im
pl
e
m
e
nt
a
ti
on s
ta
ge
s
of
th
e
P
V
pa
ne
l
or
ie
nt
a
ti
on
s
ys
t
e
m
m
ode
l
in
to
th
e
s
im
ul
a
ti
on.
T
hi
s
is
done
to
te
s
t
th
e
s
ys
te
m
'
s
r
e
s
pons
e
to
e
nvi
r
onm
e
nt
a
l
c
ha
nge
s
a
nd
e
ns
ur
e
th
a
t
th
e
s
ys
te
m
c
a
n
a
da
pt
dyna
m
ic
a
ll
y. T
he
a
na
ly
s
i
s
of
r
e
s
ul
ts
i
s
th
e
f
in
a
l
s
te
p,
i
nvol
vi
ng
th
e
e
va
lu
a
ti
on
of
s
ys
t
e
m
e
f
f
ic
ie
nc
y
a
nd r
e
s
pons
e
i
n va
r
io
us
e
nvi
r
onm
e
nt
a
l
c
ondi
ti
ons
. F
ur
th
e
r
m
or
e
, t
he
pa
r
a
m
e
te
r
va
r
ia
bl
e
s
on t
he
P
V
pa
ne
l
a
nd
m
ot
or
a
r
e
s
e
t
to
de
te
r
m
in
e
th
e
op
ti
m
a
l
li
m
it
s
o
f
P
I
D
c
ont
r
ol
f
or
th
e
P
V
pos
it
io
n
c
o
nc
e
r
ni
ng
th
e
s
un'
s
or
ie
nt
a
ti
on.
F
or
th
e
P
V
pa
ne
l,
th
e
v
a
r
ia
bl
e
s
in
vol
ve
da
m
pi
ng
c
oe
f
f
ic
ie
nt
:
a
nd
in
ve
r
s
e
of
m
om
e
nt
of
in
e
r
ti
a
,
w
hi
le
f
or
th
e
m
ot
or
,
th
e
va
r
ia
bl
e
s
in
c
lu
de
m
ot
or
ga
in
,
f
r
ic
t
io
n
c
oe
f
f
ic
ie
nt
,
to
r
que
c
ons
ta
nt
,
in
ve
r
s
e
of
in
duc
ta
nc
e
,
a
nd
r
e
s
is
t
a
nc
e
.
T
he
va
lu
e
s
of
th
e
s
e
va
r
ia
bl
e
s
a
r
e
c
a
r
e
f
ul
ly
c
hos
e
n
to
a
c
hi
e
ve
a
n
opt
im
a
l
b
a
la
nc
e
be
twe
e
n s
y
s
te
m
r
e
s
pons
e
a
nd e
ne
r
gy e
f
f
ic
ie
nc
y.
3.
R
E
S
U
L
T
S
A
N
D
D
I
S
C
U
S
S
I
O
N
3.1.
E
n
e
r
gy c
on
ve
r
s
io
n
i
n
s
ol
ar
p
an
e
ls
S
ol
a
r
pow
e
r
ge
ne
r
a
ti
on w
it
h
a
PV
pa
ne
l
s
ys
te
m
i
s
t
he
pr
e
dom
in
a
nt
t
ype
of
s
ol
a
r
pow
e
r
ge
ne
r
a
ti
on
i
n
I
ndone
s
ia
.
I
ts
m
a
in
a
dv
a
nt
a
ge
li
e
s
in
a
m
or
e
e
f
f
ic
ie
nt
pr
oc
e
s
s
,
m
a
ki
ng
th
e
in
s
ta
ll
a
ti
on
c
o
s
ts
m
or
e
a
f
f
or
da
bl
e
.
T
hi
s
pow
e
r
ge
ne
r
a
ti
on
s
ys
te
m
c
onve
r
ts
s
ol
a
r
e
ne
r
gy dir
e
c
tl
y i
nt
o e
le
c
tr
ic
a
l
e
n
e
r
gy t
hr
ough the
PV
c
onc
e
pt
.
B
a
s
e
d on
t
he
F
ig
ur
e
3, a
s
ol
a
r
c
e
ll
i
s
a
n
e
le
c
tr
oni
c
c
om
pone
nt
m
a
de
of
s
e
m
ic
ondu
c
to
r
m
a
te
r
ia
l
th
a
t
is
s
e
ns
it
iv
e
to
li
ght
.
T
he
m
a
in
c
om
pone
nt
u
s
e
d
in
th
e
m
a
nuf
a
c
tu
r
e
of
s
ol
a
r
c
e
ll
s
is
a
phot
odi
ode
,
a
n
e
le
c
tr
oni
c
c
om
pone
nt
t
ha
t
is
r
e
s
pons
iv
e
t
o l
ig
ht
.
T
hi
s
s
e
ns
it
iv
it
y a
ll
ow
s
s
o
la
r
c
e
ll
s
t
o c
a
pt
ur
e
s
unl
ig
ht
a
nd
di
r
e
c
t
it
t
o t
h
e
ne
xt
s
ys
te
m
to
be
c
onve
r
te
d
in
to
e
le
c
tr
ic
a
l
e
n
e
r
gy.
T
he
ba
s
ic
pr
in
c
ip
le
of
th
e
P
V
or
P
V
e
f
f
e
c
t
c
onc
e
pt
is
to
di
r
e
c
tl
y c
onve
r
t
s
unl
ig
ht
i
nt
o e
le
c
tr
ic
it
y t
hr
ough the
us
e
of
s
ol
a
r
c
e
ll
s
.
F
ig
ur
e
3. S
c
he
m
a
ti
c
di
a
gr
a
m
of
P
V
s
ys
te
m
I
n
th
is
c
onc
e
pt
,
s
ol
a
r
c
e
ll
s
f
unc
ti
on
a
s
a
to
ol
to
c
a
pt
ur
e
li
ght
,
w
hi
c
h
c
ont
a
in
s
phot
ons
f
r
om
th
e
s
un.
P
hot
ons
a
r
e
th
e
ba
s
ic
uni
ts
of
s
ol
a
r
e
ne
r
gy
th
a
t
c
a
n
be
c
a
pt
ur
e
d by
s
ol
a
r
c
e
ll
s
a
nd
th
e
n
c
onve
r
te
d
in
to
e
le
c
tr
ic
a
l
pow
e
r
.
S
ol
a
r
c
e
ll
s
ope
r
a
te
on
th
e
pr
in
c
ip
le
oppos
it
e
to
li
ght
e
m
it
ti
ng
di
ode
s
(
L
E
D
s
)
,
w
hi
c
h
c
onve
r
t
e
le
c
tr
ic
a
l
e
ne
r
gy
in
to
li
ght
or
c
a
n
be
c
ons
id
e
r
e
d
s
im
il
a
r
to
phot
odi
ode
s
i
n
th
e
p
-
n
ju
nc
ti
on
r
e
la
ti
ons
hi
p.
W
he
n
phot
ons
w
it
h hi
ghe
r
e
ne
r
gy t
ha
n t
he
e
ne
r
gy ga
p a
r
r
iv
e
, t
he
s
e
m
ic
onduc
to
r
a
bs
or
bs
t
he
s
e
photons
t
o f
or
m
e
le
c
tr
on
-
hol
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
O
pt
imi
z
in
g t
he
pos
it
io
n of
photov
ol
ta
ic
s
ol
ar
t
r
a
c
k
e
r
pane
ls
w
it
h ar
ti
fi
c
ia
l
…
(
R
ic
ar
do L
in
e
ls
on
)
4007
pa
ir
s
a
s
c
ha
r
ge
c
a
r
r
ie
r
s
.
S
ubs
e
que
nt
ly
,
e
le
c
tr
ons
a
nd
hol
e
s
m
ove
s
e
que
nt
ia
ll
y
to
w
a
r
ds
th
e
p
a
nd
n
s
e
m
ic
onduc
to
r
la
ye
r
s
,
c
r
e
a
ti
ng
a
pot
e
nt
ia
l
di
f
f
e
r
e
nc
e
a
nd
phot
oc
ur
r
e
nt
,
w
hi
c
h
is
th
e
c
ur
r
e
nt
ge
ne
r
a
te
d
by
li
ght
.
W
he
n
phot
ons
c
ol
li
de
w
it
h
th
e
s
ol
a
r
c
e
ll
'
s
w
a
ll
,
a
pr
oc
e
s
s
of
g
e
ne
r
a
ti
ng
e
le
c
tr
ic
c
ur
r
e
nt
oc
c
ur
s
.
T
hi
s
pr
oc
e
s
s
be
gi
ns
w
he
n a
photon hi
ts
t
he
s
e
m
ic
onduc
to
r
w
a
ll
, c
a
us
in
g t
he
l
os
s
of
a
n e
le
c
tr
on i
n t
he
w
a
ll
c
onduc
to
r
a
to
m
.
T
he
a
to
m
th
a
t
lo
s
e
s
th
is
e
le
c
tr
on
is
c
a
ll
e
d
a
hol
e
.
E
le
c
tr
ons
h
a
ve
a
n
e
ga
ti
ve
c
h
a
r
ge
,
w
hi
le
phot
on
s
ha
ve
a
pos
it
iv
e
c
ha
r
ge
.
T
hi
s
di
f
f
e
r
e
nc
e
in
c
ha
r
ge
c
r
e
a
te
s
a
n
e
le
c
tr
ic
c
u
r
r
e
nt
.
I
n
a
s
ol
a
r
c
e
ll
,
vol
ta
ge
a
nd
c
ur
r
e
nt
a
r
is
e
w
he
n
two
c
onne
c
te
d
e
le
c
tr
ode
s
a
r
e
in
a
s
ol
id
a
nd
li
qui
d
s
ys
te
m
.
W
he
n
th
e
c
onne
c
te
d
e
le
c
tr
ode
r
e
c
e
iv
e
s
li
ght
f
r
om
t
he
s
un, t
he
vol
ta
ge
a
nd c
ur
r
e
nt
w
il
l
a
ut
om
a
ti
c
a
ll
y a
ppe
a
r
.
3.
2
.
T
h
e
i
m
p
ac
t
of
s
u
n
li
gh
t
i
n
t
e
n
s
it
y
T
he
l
e
ve
l
of
s
unl
ig
ht
r
a
di
a
ti
on r
e
c
e
iv
e
d di
r
e
c
tl
y by s
ol
a
r
c
e
ll
s
d
ir
e
c
tl
y a
f
f
e
c
ts
t
he
vol
ta
ge
a
nd c
ur
r
e
nt
ge
ne
r
a
te
d
f
r
om
th
e
P
V
c
onc
e
pt
.
U
nde
r
c
ondi
ti
ons
w
he
r
e
s
un
li
ght
r
a
di
a
ti
on
in
te
ns
it
y
r
e
m
a
in
s
c
ons
ta
nt
,
a
n
in
c
r
e
a
s
e
in
e
nvi
r
onm
e
nt
a
l
te
m
pe
r
a
tu
r
e
c
a
n
le
a
d
to
a
de
c
r
e
a
s
e
in
v
ol
ta
ge
on
s
ol
a
r
pa
ne
ls
.
C
onve
r
s
e
ly
,
th
e
e
le
c
tr
ic
c
ur
r
e
nt
ge
ne
r
a
te
d
by
s
ol
a
r
c
e
ll
s
w
il
l
in
c
r
e
a
s
e
.
C
h
a
nge
s
in
te
m
pe
r
a
tu
r
e
on
s
ol
a
r
c
e
ll
s
c
a
n
be
in
f
lu
e
nc
e
d
by
s
e
ve
r
a
l
f
a
c
to
r
s
,
in
c
lu
di
ng
a
ir
te
m
pe
r
a
tu
r
e
,
c
lo
ud
c
ondi
ti
ons
,
a
nd
w
i
nd
s
pe
e
d
a
r
ou
nd
th
e
lo
c
a
ti
on
of
s
ol
a
r
pa
n
e
l
pl
a
c
e
m
e
nt
.
I
t
is
im
por
ta
nt
to
unde
r
s
ta
nd
th
a
t
f
lu
c
tu
a
ti
ons
in
s
unl
ig
ht
in
te
ns
it
y
a
nd
c
ha
nge
s
in
e
nvi
r
onm
e
nt
a
l
te
m
pe
r
a
tu
r
e
c
a
n
ha
ve
a
s
ig
ni
f
ic
a
nt
im
pa
c
t
on
th
e
s
ys
te
m
'
s
r
e
s
pons
e
.
T
he
r
e
f
or
e
,
pa
r
a
m
e
te
r
a
dj
us
tm
e
nt
s
on
th
e
pa
ne
l
a
nd
m
ot
or
,
s
uc
h
a
s
d
a
m
pi
ng
c
oe
f
f
ic
ie
nt
a
nd
in
ve
r
s
e
of
m
om
e
nt
of
in
e
r
ti
a
,
s
houl
d
c
ons
id
e
r
va
r
ia
ti
ons
in
s
unl
ig
ht
in
te
ns
it
y
a
nd
te
m
pe
r
a
tu
r
e
c
ha
nge
s
th
a
t
m
a
y
oc
c
ur
.
B
y
in
c
or
por
a
ti
ng
th
e
s
e
f
a
c
to
r
s
in
to
th
e
a
na
ly
s
is
,
th
is
r
e
s
e
a
r
c
h c
a
n pr
ovi
de
de
e
pe
r
i
ns
ig
ht
s
i
nt
o t
he
pe
r
f
or
m
a
nc
e
of
t
he
P
V
s
ys
te
m
i
n dyna
m
ic
a
ll
y r
e
s
ponding t
o
e
nvi
r
onm
e
nt
a
l
va
r
ia
ti
ons
.
3.
3
.
I
m
p
r
ove
m
e
n
t
of
e
f
f
ic
ie
n
c
y
T
he
e
f
f
ic
ie
nc
y
of
s
ol
a
r
pa
ne
ls
c
a
n
be
e
nha
nc
e
d
th
r
ough
th
e
us
e
of
r
e
f
le
c
to
r
s
or
c
onc
e
nt
r
a
to
r
s
.
R
e
f
le
c
to
r
s
or
c
onc
e
nt
r
a
to
r
s
s
ha
pe
d
li
ke
m
ir
r
or
s
s
e
r
ve
a
s
r
e
f
le
c
to
r
s
a
nd
f
oc
us
s
unl
ig
ht
ont
o
th
e
s
ol
a
r
c
e
ll
pa
ne
ls
.
T
hi
s
r
e
f
le
c
ti
on
of
s
unl
ig
ht
in
c
r
e
a
s
e
s
th
e
c
onc
e
nt
r
a
ti
on
of
li
ght
on
th
e
s
ol
a
r
c
e
ll
pa
ne
ls
,
r
e
s
ul
ti
ng
in
a
s
ig
ni
f
ic
a
nt
in
c
r
e
a
s
e
in
th
e
ge
ne
r
a
t
e
d
e
le
c
tr
ic
a
l
e
n
e
r
gy.
S
tu
di
e
s
s
how
th
a
t
t
he
a
ddi
ti
on
of
r
e
f
le
c
to
r
s
or
c
onc
e
nt
r
a
to
r
s
c
a
n
in
c
r
e
a
s
e
th
e
pow
e
r
out
put
of
s
ol
a
r
c
e
ll
pa
ne
ls
by
up
to
a
ppr
ox
im
a
te
ly
46%
.
A
lt
hough
th
is
m
e
th
od
pr
ovi
de
s
im
pr
ove
d
pe
r
f
or
m
a
nc
e
,
it
s
houl
d
be
not
e
d
th
a
t
c
onc
e
nt
r
a
ti
ng
li
ght
in
te
ns
it
y
c
a
n
le
a
d
to
a
r
a
pi
d
in
c
r
e
a
s
e
in
th
e
te
m
pe
r
a
tu
r
e
of
t
he
s
ol
a
r
c
e
ll
pa
ne
ls
.
T
he
in
c
r
e
a
s
e
in
th
e
te
m
pe
r
a
tu
r
e
of
s
ol
a
r
c
e
ll
pa
ne
ls
c
a
n
ne
ga
ti
ve
ly
a
f
f
e
c
t
th
e
pow
e
r
out
put
.
I
n
f
a
c
t,
e
ve
r
y
1
˚
C
in
c
r
e
a
s
e
in
th
e
te
m
p
e
r
a
tu
r
e
of
s
ol
a
r
p
a
ne
ls
, e
s
pe
c
ia
ll
y
f
r
om
th
e
s
ta
nda
r
d
te
m
p
e
r
a
tu
r
e
of
25
˚
C
, c
a
n
c
a
us
e
a
de
c
r
e
a
s
e
of
a
bout
0.5%
i
n t
he
t
ot
a
l
pow
e
r
ge
ne
r
a
te
d. T
h
e
r
e
f
or
e
, opt
im
iz
in
g t
he
e
f
f
ic
ie
nc
y of
s
ol
a
r
c
e
l
l
pa
ne
ls
not
onl
y i
nvol
ve
s
i
nc
r
e
a
s
in
g l
ig
ht
i
nt
e
ns
it
y but a
ls
o c
ons
id
e
r
in
g e
f
f
e
c
ti
ve
t
e
m
pe
r
a
tu
r
e
c
ont
r
ol
.
H
ig
h a
ir
te
m
pe
r
a
tu
r
e
s
c
a
n
a
ls
o
b
e
a
pe
r
f
or
m
a
nc
e
-
r
e
duc
in
g
f
a
c
to
r
f
or
s
ol
a
r
pa
ne
ls
.
A
ddi
ti
ona
ll
y,
th
e
p
r
e
s
e
nc
e
of
s
ha
di
ng
obs
ta
c
le
s
c
a
n
r
e
duc
e
th
e
out
put
of
s
ol
a
r
pa
ne
ls
,
a
nd
bypa
s
s
di
ode
s
c
a
n
be
im
pl
e
m
e
nt
e
d
a
s
a
s
ol
ut
io
n
to
a
ddr
e
s
s
th
is
is
s
ue
.
B
y
c
on
s
id
e
r
in
g
th
e
in
f
lu
e
nc
e
of
va
r
ia
bl
e
s
s
u
c
h
a
s
l
ig
ht
in
te
ns
it
y,
te
m
pe
r
a
tu
r
e
,
a
nd
s
h
a
di
ng,
th
i
s
r
e
s
e
a
r
c
h
le
a
ds
to
a
m
or
e
hol
is
ti
c
unde
r
s
ta
ndi
ng
of
th
e
f
a
c
to
r
s
th
a
t
a
f
f
e
c
t
th
e
e
f
f
ic
ie
nc
y
a
nd
pe
r
f
or
m
a
nc
e
of
s
ol
a
r
pa
ne
ls
.
3.
4
.
S
ol
ar
t
r
ac
k
e
r
S
ol
a
r
pow
e
r
pl
a
nt
s
a
r
e
one
of
t
he
f
or
m
s
of
r
e
ne
w
a
bl
e
e
ne
r
gy po
w
e
r
pl
a
nt
s
t
ha
t
a
r
e
i
nc
r
e
a
s
in
gl
y b
e
in
g
im
pl
e
m
e
nt
e
d
in
I
ndone
s
ia
,
e
s
p
e
c
ia
ll
y
in
a
r
e
a
s
th
a
t
a
r
e
not
ye
t
c
o
ve
r
e
d
by
th
e
e
le
c
tr
ic
it
y
gr
id
.
T
hi
s
s
ys
te
m
r
e
li
e
s
on
s
unl
ig
ht
a
s
th
e
m
a
in
s
our
c
e
of
e
ne
r
gy
a
nd
c
onve
r
ts
it
in
to
e
le
c
tr
ic
it
y
th
r
ough
th
e
us
e
of
s
ol
a
r
pa
ne
ls
.
T
he
pow
e
r
c
a
pa
c
it
y
ge
ne
r
a
te
d
by
s
ol
a
r
pa
ne
ls
is
de
te
r
m
in
e
d
by
th
e
num
be
r
of
s
ol
a
r
c
e
ll
s
in
th
e
pa
ne
l,
a
s
w
e
ll
a
s
th
e
te
m
pe
r
a
tu
r
e
a
nd s
unl
ig
ht
r
a
di
a
ti
on t
ha
t
a
f
f
e
c
t
th
e
s
e
s
ol
a
r
pa
ne
ls
.
I
t
is
known tha
t
th
e
o
r
ie
nt
a
ti
on
of
s
unl
ig
ht
c
ha
nge
s
w
it
h
th
e
a
xi
s
of
th
e
e
a
r
th
'
s
r
ot
a
ti
ona
l
r
ot
a
ti
on.
T
he
in
te
ns
it
y of
s
unl
ig
ht
hi
tt
in
g
t
he
s
ur
f
a
c
e
of
t
he
s
e
m
ic
onduc
to
r
di
ode
l
a
ye
r
of
t
he
s
ol
a
r
pa
ne
l
c
a
us
e
s
e
le
c
tr
ons
i
n
th
e
di
ode
l
a
ye
r
t
o ge
ne
r
a
te
a
vol
ta
ge
a
nd c
ur
r
e
nt
di
f
f
e
r
e
nc
e
due
t
o t
he
P
V
e
f
f
e
c
t.
W
it
h
th
e
vol
ta
ge
a
nd c
ur
r
e
n
t
di
f
f
e
r
e
nc
e
, pot
e
nt
ia
l
e
le
c
tr
ic
a
l
e
ne
r
gy i
s
f
or
m
e
d, w
hi
c
h w
il
l
be
di
r
e
c
te
d t
o t
he
e
le
c
tr
ic
a
l
s
to
r
a
ge
s
our
c
e
.
T
w
o
s
tr
a
te
gi
e
s
c
a
n
be
a
ppl
ie
d
to
a
c
hi
e
ve
th
e
m
a
xi
m
um
pow
e
r
out
put
f
r
om
s
ol
a
r
pa
ne
ls
.
F
ir
s
t,
pow
e
r
out
put
c
ont
r
ol
c
a
n
be
done
by
a
dj
us
ti
ng
th
e
out
put
vol
ta
ge
us
in
g
a
pow
e
r
c
onve
r
te
r
known
a
s
M
P
P
T
.
T
he
s
c
he
m
a
ti
c
di
a
gr
a
m
of
s
ol
a
r
tr
a
c
ke
r
is
s
how
n
in
F
ig
ur
e
4
a
nd
th
e
s
im
ul
a
ti
on
is
s
how
n
in
F
ig
ur
e
5.
I
n
a
ddi
ti
on,
th
e
pow
e
r
out
put
of
s
ol
a
r
pa
n
e
ls
c
a
n
a
l
s
o
be
in
c
r
e
a
s
e
d
by
m
a
xi
m
i
z
in
g
th
e
s
unl
ig
ht
r
a
di
a
ti
on
r
e
a
c
hi
ng
th
e
s
ur
f
a
c
e
of
t
he
s
ol
a
r
pa
ne
l.
T
o
in
c
r
e
a
s
e
th
e
s
unl
ig
ht
r
a
di
a
ti
on
r
e
a
c
hi
ng
th
e
s
ol
a
r
pa
ne
l,
it
c
a
n
be
a
c
hi
e
ve
d
by
a
dj
us
ti
ng
th
e
pos
it
io
n
of
th
e
pa
ne
l
to
a
lwa
ys
be
pe
r
pe
ndi
c
ul
a
r
to
th
e
di
r
e
c
ti
on
of
th
e
s
un.
T
hi
s
is
be
c
a
us
e
th
e
pos
it
io
n
of
th
e
s
un
c
ha
nge
s
t
hr
oughout t
he
da
y f
r
om
e
a
s
t
to
w
e
s
t.
T
he
r
e
f
or
e
, s
ol
a
r
pa
ne
ls
ne
e
d t
o be
a
bl
e
t
o m
ove
i
n l
in
e
w
it
h t
he
m
ove
m
e
nt
of
t
he
s
un t
o opti
m
iz
e
r
a
di
a
ti
on a
t
a
ll
t
im
e
s
. T
hi
s
s
ys
te
m
i
s
known a
s
a
s
ol
a
r
t
r
a
c
ke
r
. T
he
f
or
c
e
s
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
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8938
I
nt
J
A
r
ti
f
I
nt
e
ll
, V
ol
. 13, No. 4, D
e
c
e
m
be
r
2024:
4003
-
4018
4008
a
P
V
pa
ne
l
a
r
e
g
e
ne
r
a
ll
y
r
e
la
te
d
to
s
ol
a
r
e
ne
r
gy
a
nd
li
ght
w
a
ve
s
.
C
ha
ng
e
s
in
f
r
e
que
nc
y
or
w
a
ve
le
ngt
h
c
a
n
a
f
f
e
c
t
th
e
a
m
ount
of
e
ne
r
gy r
e
c
e
iv
e
d by the
s
ol
a
r
pa
ne
l.
F
ig
ur
e
4. S
c
he
m
a
ti
c
di
a
gr
a
m
of
s
ol
a
r
t
r
a
c
ke
r
F
ig
ur
e
5. S
ol
a
r
t
r
a
c
ke
r
s
im
ul
a
ti
on
B
a
s
e
d
on
th
e
F
ig
ur
e
6,
w
he
n
th
e
c
ur
ve
of
th
e
P
V
m
ove
m
e
nt
in
put
s
ig
na
l
in
c
r
e
a
s
e
s
,
it
c
a
n
r
e
f
le
c
t
a
s
it
ua
ti
on
w
he
r
e
th
e
P
V
s
ys
te
m
r
e
c
e
iv
e
s
a
ddi
ti
ona
l
e
ne
r
gy
or
s
ig
na
ls
. T
hi
s
c
a
n
be
c
a
u
s
e
d
by
f
a
c
to
r
s
s
uc
h
a
s
a
n
in
c
r
e
a
s
e
in
s
unl
ig
ht
in
te
ns
it
y,
c
h
a
nge
s
in
th
e
a
ngl
e
of
il
lu
m
in
a
ti
on,
or
a
n
im
pr
ove
m
e
nt
in
th
e
e
f
f
ic
ie
nc
y
of
s
ol
a
r
pa
n
e
ls
. I
n t
hi
s
c
ont
e
xt
,
a
n i
nc
r
e
a
s
e
i
n t
he
s
ig
na
l
c
ur
ve
c
a
n
i
ndi
c
a
te
t
ha
t
th
e
P
V
s
y
s
te
m
i
s
r
e
c
e
iv
in
g m
or
e
po
w
e
r
or
e
ne
r
gy, pote
nt
ia
ll
y e
nha
nc
in
g i
ts
pe
r
f
or
m
a
nc
e
a
nd e
le
c
tr
ic
a
l
out
put
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
O
pt
imi
z
in
g t
he
pos
it
io
n of
photov
ol
ta
ic
s
ol
ar
t
r
a
c
k
e
r
pane
ls
w
it
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ti
fi
c
ia
l
…
(
R
ic
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in
e
ls
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)
4009
F
ig
ur
e
6. C
ur
ve
of
s
ol
a
r
t
r
a
c
ke
r
i
nput
s
ig
na
l
(
up)
O
n t
he
c
ont
r
a
r
y, i
n
F
ig
ur
e
7,
a
de
c
r
e
a
s
e
i
n t
he
P
V
i
nput
s
ig
na
l
c
ur
ve
c
a
n r
e
f
le
c
t
a
c
ondi
ti
on w
he
r
e
t
he
e
ne
r
gy
or
s
ig
na
l
r
e
c
e
iv
e
d
by
th
e
P
V
s
ys
te
m
i
s
de
c
r
e
a
s
in
g.
F
a
c
to
r
s
th
a
t
m
a
y
c
a
us
e
th
is
d
e
c
r
e
a
s
e
c
oul
d
in
c
lu
de
c
lo
ud
c
ove
r
,
r
e
duc
e
d s
unl
ig
ht
in
te
ns
it
y,
or
te
c
hni
c
a
l
is
s
ue
s
w
it
h
s
ol
a
r
pa
n
e
ls
.
T
he
de
c
r
e
a
s
e
in
th
e
s
ig
na
l
c
ur
ve
m
a
y
in
di
c
a
te
th
a
t
th
e
P
V
s
ys
te
m
is
ge
ne
r
a
ti
ng
le
s
s
e
n
e
r
gy
or
pow
e
r
,
w
hi
c
h
c
a
n
a
f
f
e
c
t
it
s
pe
r
f
or
m
a
nc
e
a
nd
e
le
c
tr
ic
a
l
out
put
.
F
ig
ur
e
7. C
ur
ve
of
s
ol
a
r
tr
a
c
ke
r
i
nput
s
ig
na
l
(
dow
n)
F
ig
ur
e
8
de
m
ons
tr
a
te
s
a
m
a
xi
m
um
w
or
m
a
ngul
a
r
ve
lo
c
it
y
of
2245
de
g/
s
,
in
di
c
a
ti
ng
th
e
s
y
s
te
m
'
s
c
a
pa
bi
li
ty
f
or
r
a
pi
d
a
dj
us
tm
e
nt
s
.
T
he
s
ol
a
r
tr
a
c
ke
r
a
ls
o
e
xh
ib
it
s
a
m
a
xi
m
um
m
ot
or
to
r
que
of
0.2
N
m
,
hi
ghl
ig
ht
in
g
it
s
m
e
c
ha
ni
c
a
l
s
tr
e
ngt
h.
A
ddi
ti
ona
ll
y,
th
e
m
a
xi
m
u
m
m
ot
or
pow
e
r
of
3.85
kW
s
ho
w
c
a
s
e
s
it
s
e
ne
r
gy
e
f
f
ic
ie
nc
y.
T
he
s
y
s
te
m
'
s
r
e
s
pons
e
to
c
h
a
nge
s
in
th
e
s
ig
na
l
c
ur
ve
il
lu
s
tr
a
te
s
it
s
a
bi
li
ty
to
r
e
a
c
t
s
w
if
tl
y
to
f
lu
c
tu
a
ti
ons
i
n t
he
ope
r
a
ti
ona
l
e
nvi
r
onm
e
nt
.
T
he
hi
gh
m
a
xi
m
um
a
ngul
a
r
ve
lo
c
it
y
of
th
e
w
or
m
a
t
2245
d
e
g/
s
in
di
c
a
te
s
th
e
s
ys
te
m
'
s
a
bi
li
ty
to
r
e
s
pond
qui
c
kl
y
a
nd
a
c
c
ur
a
te
ly
to
c
ha
nge
s
in
th
e
s
un'
s
pos
it
io
n
.
T
hi
s
is
c
r
uc
ia
l
f
or
m
a
xi
m
iz
in
g
th
e
e
f
f
ic
ie
nc
y
of
s
ol
a
r
e
ne
r
gy
c
ol
le
c
ti
on.
T
he
m
a
xi
m
um
m
ot
or
to
r
qu
e
o
f
0.2
N
m
in
di
c
a
te
s
th
e
m
ot
or
'
s
a
bi
li
ty
to
m
ove
th
e
s
ol
a
r
t
r
a
c
ke
r
s
ys
te
m
w
it
h s
uf
f
ic
ie
nt
pow
e
r
t
o ove
r
c
om
e
r
e
s
is
ta
n
c
e
a
nd pote
nt
ia
l
lo
a
ds
dur
in
g ope
r
a
ti
on.
T
he
hi
gh ma
xi
m
um
m
ot
or
pow
e
r
of
3.85 kW
s
ugge
s
ts
t
ha
t
th
e
m
ot
or
c
a
n s
uppl
y s
uf
f
ic
ie
nt
pow
e
r
f
or
e
f
f
ic
ie
nt
ope
r
a
ti
on
of
th
e
s
ol
a
r
tr
a
c
ke
r
s
ys
te
m
.
T
hi
s
le
ve
l
of
p
ow
e
r
e
ns
ur
e
s
th
e
m
ot
or
c
a
n
dr
iv
e
th
e
s
ys
te
m
e
f
f
e
c
ti
ve
ly
.
A
de
qua
te
m
ot
or
pow
e
r
is
c
r
uc
ia
l
f
or
a
c
h
ie
vi
ng
th
e
ne
c
e
s
s
a
r
y
s
pe
e
d
a
nd
to
r
que
.
C
ons
e
que
nt
ly
,
it
s
uppor
ts
t
he
s
ys
t
e
m
'
s
a
bi
li
ty
t
o t
r
a
c
k t
he
s
un a
c
c
ur
a
te
ly
a
nd r
e
li
a
bl
y.
Y
a
w
s
i
g
n
a
l
(
°
)
Y
a
w
s
i
g
n
a
l
(°)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
, V
ol
. 13, No. 4, D
e
c
e
m
be
r
2024:
4003
-
4018
4010
F
ig
ur
e
8. G
r
a
phs
of
w
or
m
a
ngul
a
r
ve
lo
c
it
y, m
ot
or
t
or
que
, a
nd
m
ot
or
pow
e
r
3.
5
.
S
ol
ar
p
an
e
l
c
on
t
r
ol
u
s
in
g
p
r
op
or
t
io
n
al
i
n
t
e
gr
al
d
e
r
iv
at
i
ve
T
he
s
un,
a
s
a
n
e
ne
r
gy
s
our
c
e
,
unde
r
goe
s
m
ove
m
e
nt
th
a
t
m
us
t
be
tr
a
c
ke
d
by
s
ol
a
r
pa
ne
ls
to
ge
ne
r
a
te
e
ne
r
gy opti
m
a
ll
y. S
ol
a
r
pa
ne
ls
ne
e
d
t
he
a
bi
li
ty
t
o t
r
a
c
k t
he
s
un'
s
m
ove
m
e
nt
, w
hi
c
h oc
c
ur
s
c
ont
in
uous
ly
due
t
o
th
e
e
a
r
th
'
s
r
ot
a
ti
on
on
it
s
a
xi
s
.
T
ypi
c
a
ll
y,
s
ol
a
r
pa
ne
ls
a
r
e
in
s
ta
ll
e
d
w
it
hout
a
dj
us
ti
ng
th
e
ir
pos
it
io
n
to
f
ol
lo
w
th
e
s
unl
ig
ht
, r
e
s
ul
ti
ng i
n s
ubopti
m
a
l
out
put
vol
ta
ge
.
T
o a
ddr
e
s
s
t
hi
s
i
s
s
ue
, d
e
vi
c
e
s
a
r
e
us
e
d t
o a
dj
us
t
th
e
t
il
t
of
s
ol
a
r
pa
ne
ls
, a
ll
ow
in
g t
he
m
t
o dyn
a
m
ic
a
ll
y
f
ol
lo
w
th
e
s
un'
s
po
s
it
io
n.
T
hi
s
c
ont
in
uous
a
dj
us
tm
e
nt
m
a
xi
m
iz
e
s
s
unl
ig
ht
e
xpos
ur
e
th
r
oughout
th
e
d
a
y.
A
s
a
r
e
s
ul
t,
th
e
out
put
vol
ta
ge
of
s
ol
a
r
pa
ne
l
s
i
s
s
ig
ni
f
ic
a
nt
ly
e
nha
n
c
e
d.
P
a
ne
ls
w
it
h
th
i
s
dyna
m
ic
s
c
he
dul
in
g
p
e
r
f
or
m
be
tt
e
r
c
om
pa
r
e
d t
o t
hos
e
w
it
hout
i
t.
A
c
ont
r
ol
le
r
is
ne
e
de
d
to
r
e
gul
a
te
th
e
m
ove
m
e
nt
of
s
ol
a
r
pa
ne
ls
,
a
nd
in
th
is
pa
pe
r
,
th
e
de
s
ig
n
of
a
c
ont
r
ol
le
r
us
in
g t
he
P
I
D
m
e
th
od
i
s
c
a
r
r
ie
d ou
t
to
c
ont
r
ol
th
e
po
s
it
io
n of
s
ol
a
r
pa
ne
ls
opt
im
a
ll
y
a
lo
ng t
he
s
un'
s
pa
th
.
M
ode
li
ng
a
nd
s
im
ul
a
ti
on
a
r
e
don
e
us
in
g
S
im
ul
in
k
in
M
A
T
L
A
B
,
a
n
in
te
r
a
c
ti
ve
e
nvi
r
onm
e
nt
f
or
num
e
r
ic
a
l
c
a
lc
ul
a
ti
ons
,
vi
s
ua
li
z
a
ti
on,
a
nd
pr
ogr
a
m
m
in
g.
T
he
us
e
of
M
A
T
L
A
B
e
na
bl
e
s
da
ta
a
na
ly
s
is
,
a
lg
or
it
hm
de
ve
lo
pm
e
nt
, a
nd t
he
c
r
e
a
ti
on of
m
ode
ls
a
nd
a
ppl
ic
a
ti
ons
.
P
I
D
c
ont
r
ol
,
a
s
one
of
th
e
c
ont
r
ol
m
e
th
ods
,
is
e
m
pl
oye
d
to
im
pr
ove
th
e
s
ys
te
m
'
s
r
e
s
pons
e
.
P
r
opor
ti
ona
l
c
ont
r
ol
a
m
pl
if
ie
s
th
e
e
r
r
or
s
ig
na
l,
s
pe
e
di
ng
up
t
he
s
ys
te
m
'
s
out
put
to
w
a
r
ds
th
e
s
e
tp
oi
nt
.
T
h
e
r
e
la
ti
ons
hi
p be
twe
e
n t
he
c
ont
r
ol
le
r
i
nput
u(
t)
a
nd t
he
e
r
r
o
r
s
ig
na
l
e
(
t)
i
n F
ig
ur
e
9 i
s
de
s
c
r
ib
e
d i
n (
1)
[
18]
.
u(
t)
=
K
p e
(
t)
(
1)
F
ig
ur
e
9. B
lo
c
k di
a
gr
a
m
of
pr
opor
ti
ona
l
c
ont
r
ol
T
he
in
put
s
ig
na
l
w
il
l
be
s
um
m
e
d
w
it
h
th
e
f
e
e
db
a
c
k
s
ig
na
l,
a
nd
th
e
e
r
r
or
ge
ne
r
a
te
d
f
r
om
th
is
s
um
m
a
ti
on ope
r
a
ti
on w
il
l
be
m
ul
t
ip
li
e
d by the
p
r
opor
ti
ona
l
c
on
s
ta
nt
(
K
p)
t
o pr
oduc
e
t
he
c
ont
r
ol
le
r
i
nput
u(
t
)
.
T
he
in
te
gr
a
l
c
ont
r
ol
f
unc
ti
on
(
K
i)
is
e
s
s
e
nt
ia
ll
y
d
e
s
ig
ne
d
to
e
li
m
in
a
te
of
f
s
e
t
e
r
r
or
s
th
a
t
of
te
n
a
r
is
e
f
r
om
pr
opor
ti
ona
l
c
ont
r
ol
.
T
he
r
e
la
ti
ons
hi
p
be
twe
e
n
th
e
in
te
gr
a
l
c
ont
r
ol
out
put
u(
t
)
a
nd
th
e
e
r
r
or
s
ig
na
l
e
(
t
)
ba
s
e
d
on F
ig
ur
e
10 i
s
de
s
c
r
ib
e
d i
n (
2)
[
18]
.
i
nput
W
o
rm
A
n
g
u
l
a
r
V
el
o
c
i
t
y
(d
eg
/
s
)
W
o
rm
M
o
t
o
r
T
o
rq
u
e
(Nm)
W
o
rm
M
o
t
o
r
P
o
w
er
(k
W
)
T
i
me
T
i
me
T
i
me
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
O
pt
imi
z
in
g t
he
pos
it
io
n of
photov
ol
ta
ic
s
ol
ar
t
r
a
c
k
e
r
pane
ls
w
it
h ar
ti
fi
c
ia
l
…
(
R
ic
ar
do L
in
e
ls
on
)
4011
u
(
t
)
=
Ki
∫
0
e
(
t
)
d
(
t
)
(
2)
F
ig
ur
e
10. B
lo
c
k di
a
gr
a
m
of
i
nt
e
gr
a
l
c
ont
r
ol
D
e
s
c
r
ip
ti
on:
u(
t)
:
P
I
D
c
ont
r
ol
le
r
out
put
s
ig
na
l
K
p:
pr
opor
ti
ona
l
c
ons
ta
nt
K
i:
i
nt
e
gr
a
l
c
ons
ta
nt
K
d:
de
r
iv
a
ti
ve
c
ons
ta
nt
e
(
t)
:
e
r
r
or
s
ig
na
l
d(
t)
:
di
s
tu
r
ba
nc
e
D
e
r
iv
a
ti
ve
c
ont
r
ol
i
s
of
te
n r
e
f
e
r
r
e
d t
o a
s
a
s
pe
e
d c
ont
r
ol
le
r
be
c
a
us
e
i
ts
out
put
i
s
di
r
e
c
tl
y pr
opor
ti
ona
l
to
th
e
r
a
te
of
c
ha
nge
of
th
e
e
r
r
or
s
ig
na
l.
T
h
e
bl
oc
k
di
a
gr
a
m
of
de
r
iv
a
ti
ve
c
ont
r
ol
is
s
how
n
in
F
ig
ur
e
11.
T
h
e
r
e
la
ti
ons
hi
p
be
twe
e
n
th
e
de
r
iv
a
ti
ve
c
ont
r
ol
out
put
u
(
t
)
a
nd
th
e
e
r
r
or
s
ig
na
l
e
(
t
)
is
de
s
c
r
ib
e
d
in
(
3)
[
18]
.
T
hi
s
c
ont
r
ol
m
e
th
od he
lp
s
i
m
pr
ove
t
he
s
ys
te
m
'
s
r
e
s
pons
e
t
o c
h
a
nge
s
i
n t
he
e
r
r
or
s
ig
na
l
.
u
(
t
)
=
Kd
d
(
e
)
t
(
3)
F
ig
ur
e
11. B
lo
c
k di
a
gr
a
m
of
de
r
iv
a
ti
ve
c
ont
r
ol
T
he
c
om
bi
na
ti
on
of
th
e
th
r
e
e
c
ont
r
ol
le
r
s
f
or
m
s
a
P
I
D
c
ont
r
ol
le
r
.
P
I
D
c
ont
r
ol
le
r
s
a
r
e
c
om
m
onl
y
us
e
d
in
c
ont
r
ol
pr
oc
e
s
s
e
s
a
nd
s
ys
te
m
s
.
T
he
e
qua
ti
ons
f
or
a
P
I
D
c
on
tr
ol
le
r
a
r
e
pr
ovi
de
d,
a
nd
F
ig
ur
e
12
s
how
s
th
e
bl
oc
k di
a
gr
a
m
of
t
he
P
I
D
c
ont
r
ol
le
r
[
18
]
.
u
(
t
)
=
Kp
e
(
t
)
+
Ki
∫
0
e
(
t
)
d
(
t
)
(
4)
E
xpl
a
na
ti
on:
u(
t)
:
P
I
D
c
ont
r
ol
le
r
out
put
s
ig
na
l
K
p:
pr
opor
ti
ona
l
c
ons
ta
nt
K
i:
i
nt
e
gr
a
l
c
ons
ta
nt
K
d:
de
r
iv
a
ti
ve
c
ons
ta
nt
e
(
t)
:
e
r
r
or
s
ig
na
l
d(
t)
:
di
s
tu
r
ba
nc
e
T
he
c
r
e
a
ti
on of
t
he
P
I
D
c
ont
r
ol
le
r
s
ys
te
m
c
ons
i
s
ts
of
s
e
ve
r
a
l
s
u
bs
ys
te
m
s
,
i
nc
lu
di
ng t
he
m
ot
or
a
nd t
he
c
ont
r
ol
pa
ne
l,
a
s
s
how
n
in
F
ig
ur
e
13.
I
ni
ti
a
ll
y,
th
e
r
e
s
e
a
r
c
he
r
d
e
s
ig
ns
th
e
m
ot
or
m
ove
m
e
nt
s
ys
te
m
.
N
e
xt
,
th
e
r
e
s
e
a
r
c
he
r
de
ve
lo
ps
th
e
c
ont
r
ol
pa
ne
l.
F
in
a
ll
y,
th
e
s
e
two
s
ubs
ys
t
e
m
s
a
r
e
in
te
gr
a
te
d
in
to
a
s
in
gl
e
P
I
D
c
ont
r
ol
le
r
s
ol
a
r
t
r
a
c
ke
r
s
ys
te
m
.
i
nput
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
, V
ol
. 13, No. 4, D
e
c
e
m
be
r
2024:
4003
-
4018
4012
F
ig
ur
e
12. B
lo
c
k di
a
gr
a
m
of
de
r
iv
a
ti
ve
c
ont
r
ol
P
I
D
F
ig
ur
e
13. C
ont
r
ol
m
ot
or
T
he
f
ir
s
t
s
ubs
y
s
te
m
de
s
ig
ne
d
is
th
e
m
ot
or
c
ont
r
ol
,
a
s
il
lu
s
tr
a
te
d
i
n
F
ig
ur
e
14.
T
hi
s
s
ub
s
ys
te
m
in
c
lu
de
s
th
e
e
qua
ti
ons
f
or
th
e
m
ot
or
th
a
t
ge
ne
r
a
te
s
to
r
que
to
r
o
ta
te
th
e
s
ol
a
r
pa
ne
l.
T
he
s
e
e
qua
ti
ons
de
s
c
r
ib
e
th
e
e
le
c
tr
om
a
gne
ti
c
m
ot
io
n ne
c
e
s
s
a
r
y f
or
t
he
s
ys
te
m
'
s
op
e
r
a
ti
on
[
18]
.
di
dt
=
1
L
(
V
–
K
g
K
f
d
θ
dt
–
R
i
)
(
5)
E
xpl
a
na
ti
on:
di
/d
t:
de
r
iv
a
ti
ve
of
c
ur
r
e
nt
w
it
h r
e
s
pe
c
t
to
t
im
e
, de
pi
c
ti
ng t
he
c
ha
nge
i
n e
le
c
tr
ic
c
ur
r
e
nt
i
n t
he
m
ot
or
L
:
m
ot
or
in
duc
ta
nc
e
V
:
m
ot
or
in
put
vol
ta
ge
K
g:
ge
a
r
r
a
ti
o c
ons
ta
nt
K
f
:
f
r
ic
ti
on
c
ons
ta
nt
dθ
/d
t:
de
r
iv
a
ti
ve
of
r
ot
a
ti
on a
ngl
e
w
it
h r
e
s
pe
c
t
to
t
im
e
, de
pi
c
ti
ng t
he
a
ngul
a
r
ve
lo
c
it
y of
t
he
m
ot
or
R
:
m
ot
or
r
e
s
is
ta
nc
e
.
F
ig
ur
e
14. C
ont
r
ol
m
ot
or
s
ub
s
ys
te
m
Evaluation Warning : The document was created with Spire.PDF for Python.