In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
2, June
2
01
9, pp.
768~
7
7
6
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
2.pp
7
68-
77
6
768
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
The line
a
r quadr
a
tic regular al
gor
ithm-based contr
ol system
of
th
e direct current
m
otor
Tr
on
g-Th
an
g N
g
u
y
en
F
acul
t
y
o
f
E
nergy
E
ngin
e
e
r
i
n
g
,
T
huy
lo
i
U
n
i
v
ers
i
ty,
V
iet
n
am
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Oct
1
0
,
2
018
Re
vise
d Jan
2
6
, 2019
Ac
ce
p
t
ed
M
ar 2
, 2
0
19
Th
is
r
es
earch
a
i
m
s
to
p
ropose
a
n
o
p
tim
al
c
ont
ro
l
l
er
f
or
c
ont
rol
ling
t
h
e
speed
of
t
he
D
i
r
ect
C
urren
t
(
D
C
)
m
o
tor.
B
ased
o
n
the
m
a
th
em
a
tical
e
qu
ati
o
n
s
o
f
DC
M
oto
r
,
th
e
aut
h
o
r
b
u
i
l
d
s
the
equ
a
t
i
o
n
s
o
f
t
he
s
tat
e
s
p
ace
m
o
del
and
bu
il
d
s
t
h
e
l
i
n
ear
q
uadrat
ic
r
eg
ula
t
or
(
L
Q
R)
c
o
n
troll
e
r
to
m
inim
ize
th
e
erro
r
bet
w
een th
e
s
et
s
p
eed and th
e
r
e
sp
ons
e
s
p
eed of
D
C
m
o
t
or. The r
esu
l
ts
o
f
th
e
p
r
op
ose
d
c
on
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le
r
a
r
e
c
o
mpa
r
ed
w
ith
t
h
e
t
ra
di
tio
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l
c
o
ntrol
l
e
rs
a
s
the
PID
,
the
f
eed-f
or
ward
c
ont
roller.
T
he
s
imula
t
ion
result
s
show
t
hat
t
he
q
ual
i
t
y
o
f
th
e
co
nt
rol
s
y
stem
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n
t
h
e
case
of
L
Q
R
c
o
n
t
r
oller
is
m
u
c
h
hi
gher
t
h
a
n
t
h
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trad
it
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l
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t
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s.
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h
e
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es
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n
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e
sp
eed
a
lw
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y
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f
o
llo
w
s
t
he
set
speed
w
ith
th
e
s
hort
co
nv
ers
i
o
n
t
ime,
t
h
e
re
i
sn'
t
o
v
e
rsh
oot.
The
resp
ons
e
speed
is
a
l
m
os
t
un
af
f
e
c
t
ed
w
hen
th
e to
rqu
e
im
p
a
c
t
o
n
t
he
s
ha
ft
is ch
a
n
ged
.
K
eyw
ord
s
:
D
C
m
ot
or
LQR control
Op
ti
mal
con
t
rol
PID co
n
t
rol
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Tron
g-Tha
ng
N
g
u
y
en,
F
a
cult
y
o
f
E
ne
rgy
Engi
nee
r
i
n
g,
T
huyl
o
i
U
ni
ver
s
ity,
17
5 Ta
y S
on,
D
on
g
D
a
, H
anoi,
V
i
et
nam
Em
ail:
ngu
ye
n
t
r
o
n
g
t
h
a
n
g
@
t
l
u
.e
du.vn
1.
I
N
TR
OD
U
C
TI
O
N
The
D
C
m
ot
o
r
i
s
a
tra
d
iti
o
n
a
l
ele
c
t
ric
m
o
tor
.
I
n
com
p
a
r
ison
to
t
h
e
o
t
h
e
r
elec
tric
m
otor
s
uch
a
s
brus
hle
ss
D
C
m
otors
[
1
-3],
i
nd
uc
t
i
o
n
m
ac
hi
ne
[
4-6]
,
the
D
C
m
oto
r
ha
s
t
h
e
intr
ins
i
c
a
d
van
t
a
g
es
s
uc
h
as
t
he
ea
se
o
f
ma
int
e
na
nce,
t
he
l
a
r
g
e
e
lec
t
rom
a
g
n
e
t
i
c
t
o
r
q
ue,
the
simp
l
e
c
on
t
r
ol
s
t
r
u
c
t
u
re
a
nd
th
e
ad
ju
st
a
bi
li
ty
o
f
t
h
e
s
p
e
e
d
i
n
a
w
i
d
e
r
a
n
g
e
.
T
h
u
s
,
t
h
e
D
C
m
o
t
o
r
i
s
s
t
i
l
l
v
e
r
y
p
o
p
u
l
ar
i
n
t
h
e
ap
pl
ica
t
i
on
of
i
n
d
u
str
i
a
l
a
re
as
requ
ire
d
t
he
h
igh-
qua
lit
y
mot
i
o
n
,
suc
h
a
s
m
i
nin
g
,
t
r
ans
port
a
tio
n,
s
t
e
el
r
o
l
lin
g,
e
t
c
.
S
o
,
it
is
v
er
y
im
p
o
rt
ant
to
enha
nc
e
the
pe
rform
a
nc
e
of
t
he
D
C
mo
tor
c
o
n
t
ro
l
s
y
stem
.
Ther
e
a
re
m
a
n
y
stud
i
e
s
on
t
he
D
C
mo
to
r
co
n
t
ro
l
such
a
s
[7-
1
0
]
.
Most
o
f
thes
e
st
ud
ies
use
a
sim
p
l
e
c
o
n
t
ro
lle
r
s
uch
a
s
P
ro
por
ti
ona
l
–
In
t
e
gral
–D
e
r
iva
t
i
v
e
(PI
D
)
con
t
ro
l
l
ers.
T
he
a
dv
a
n
ta
ge
o
f
the
P
I
D
control
i
s
a
s
imp
l
e
struc
ture
,
bu
t
t
h
e
draw
ba
ck
i
s
t
h
at
t
he
qua
l
i
t
y
o
f
t
h
e
con
t
ro
l
s
y
stem
i
s
no
t
h
i
g
h
.
The
r
e
sear
ch
[
11]
h
a
v
e
prop
ose
d
a
s
o
l
u
t
i
o
n
t
o
c
o
n
t
r
o
l
t
h
e
D
C
m
o
t
or
t
hat
has
ac
hi
e
v
e
d
h
ig
h-
qua
l
ity,
it
is
t
he
c
o
n
tr
ol
m
eth
o
d
b
a
s
e
d
o
n
the
f
l
a
t
nes
s
p
rinc
ip
l
e
,
but
t
he
l
i
m
it
a
t
ion
of
t
h
i
s
met
h
od
i
s th
at
t
h
e
c
ont
rol
a
l
go
rit
h
m i
s
c
o
m
pl
e
x
.
To
over
c
om
e
all
t
h
e
lim
ita
t
i
o
n
s
of
t
h
e
p
re
vi
ous
m
eth
o
d
,
i
n
t
his
s
tud
y
,
t
h
e
a
ut
ho
r
p
r
opo
ses
a
solu
ti
on
to
b
uil
d
a
c
o
n
t
r
ol
s
y
s
t
e
m
bas
e
d
o
n
t
he
l
i
n
ea
r
quadr
a
tic
r
e
g
ul
a
t
o
r
c
o
n
t
r
o
l
l
e
r
.
T
h
e
c
o
n
t
r
o
l
a
l
g
o
r
i
t
h
m
i
s
s
i
m
p
l
e
and
the
qua
l
i
t
y
i
s
o
p
timize
d
.
By
u
si
ng
LQ
R
co
ntro
l
l
e
r
,
the
de
vi
a
t
i
o
n
of
t
he
D
C
Mo
t
o
r
speed
c
an
b
e
minim
i
z
e
d,
an
d
t
he
re
s
p
onse
spee
d is no
t
c
ha
nge
d w
h
en t
h
e
d
istu
rb
a
n
c
e
su
ch
as
sh
af
t
t
o
rq
u
e
is ch
a
n
g
e
d.
The
LQ
R
c
ont
rol
m
e
th
o
d
i
s
use
d
t
o
c
o
ntr
o
l
a
lo
t
of
o
bj
e
c
t
s
in
p
ra
ct
i
c
e
as
t
wo-whe
el
s
se
l
f-ba
l
a
n
c
i
n
g
mobi
le
r
o
b
o
t
[12-
14],
con
v
e
r
ter
[1
5-1
7
],
quad-
ro
t
o
r
[1
8-20]
,
w
i
nd
power
g
en
e
r
at
o
r
[
21
,
2
2
]
.
Th
e
Li
n
e
a
r
Q
u
adr
a
t
i
c
Re
gula
t
or
m
etho
d
is
s
et
t
i
ng
the
c
ontr
o
l
l
er
by
us
in
g
a
m
a
t
he
ma
ti
c
a
l
a
lg
ori
t
hm
t
o
m
i
ni
m
i
ze
t
he
c
ost
fu
nc
ti
o
n
w
i
t
h
w
e
ig
ht
ing
fac
t
or
s
de
fi
ne
d
b
y
t
h
e
d
es
i
g
n
e
r.
T
he
c
o
s
t
-
f
u
n
c
t
i
o
n
i
s
o
f
t
e
n
d
e
f
i
n
e
d
a
s
a
s
u
m
o
f
t
h
e
dev
i
a
t
i
o
ns
o
f
resp
onse
ou
tp
u
t
and
the
i
r de
s
i
r
e
d va
lue
s
[23,
24]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
The li
ne
ar
quadr
a
tic regular
algo
r
i
thm-based cont
r
o
l sys
t
em
of
the
di
rect … (
T
rong-T
hang
N
g
uyen)
76
9
2.
T
H
E L
Q
R
CONTROL S
Y
STEM
C
ons
ide
r
i
ng t
h
e obje
c
t
w
i
t
h st
ate
equa
t
i
o
n
:
)
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.
)
(
.
)
(
t
u
B
t
x
A
t
x
(1)
wher
e:
)]
(
),...,
(
),
(
[
)
(
2
1
t
x
t
x
t
x
t
x
n
is the
v
ector
o
f
state
s
i
gn
a
l
,
)]
(
),...,
(
),
(
[
)
(
2
1
t
u
t
u
t
u
t
u
m
is the
vec
t
or
o
f
con
t
ro
l si
gna
l
.
The
r
e
q
u
irem
ent
of
t
he
c
o
n
tr
ol
s
ys
tem
is
t
o
fi
nd
the
c
o
n
t
r
o
l
s
i
gna
l
)
(
t
u
i
n
o
r
der
for
the
c
ontr
o
l
ob
jec
t
f
rom
t
h
e
in
itia
l
sta
t
e
)
0
(
)
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0
x
t
x
go
to
t
he
e
n
d
s
tate
0
)
(
f
t
x
a
n
d
s
a
t
i
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f
y
t
h
e
f
o
l
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o
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o
n
d
i
t
i
o
n
(cost f
unc
t
i
ona
l
)
:
f
t
t
T
T
f
f
T
dt
t
u
R
t
u
t
x
Q
t
x
t
x
M
t
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J
0
min
)]
(
.
).
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)
(
.
).
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[
2
1
)
(
.
).
(
2
1
(2)
Where
Q
a
n
d
M
a
re
t
he
s
y
m
me
t
r
i
c
,
posi
tive
sem
i
-def
in
ite
w
ei
gh
t
m
a
tri
x
.
R
i
s
the
sym
m
et
r
i
c,
pos
it
ive
de
fin
i
te
w
e
i
gh
t m
a
trix.
To
sol
v
e
th
e
p
ro
bl
em, we
es
t
ab
l
i
s
h
th
e
Ha
mi
l
t
on
fun
ct
i
o
n
:
)]
(
.
)
(
.
[
)]
(
.
).
(
)
(
.
).
(
[
2
1
t
u
B
t
x
A
t
u
R
t
u
t
x
Q
t
x
H
T
T
T
(3)
The
o
p
t
i
ma
l
ex
per
i
m
e
n
t
i
s
the
sol
u
ti
on o
f
the
f
ol
low
i
ng e
q
u
a
tio
ns
:
-
The
st
a
t
e e
q
u
a
ti
on:
)
(
.
)
(
.
)
(
t
u
B
t
x
A
t
x
(
4
)
-
The
equi
l
i
br
ium
e
quat
i
o
n
:
)
(
.
)
(
.
)
(
t
A
t
x
Q
x
H
t
T
(5)
-
The
opt
i
m
al
c
on
d
i
t
i
on
:
0
)
(
.
)
(
.
t
B
t
u
R
u
H
T
T
(6)
F
r
om e
q
u
a
t
ion
(6), w
e have
:
)
(
.
.
)
(
1
t
B
R
t
u
T
T
(7)
Re
plac
e
)
(
t
u
int
o
(4),
w
e
ha
ve:
)
(
.
.
.
)
(
.
)
(
1
t
B
R
B
t
x
A
t
x
T
T
(8)
Com
b
ining (8)
and
(5)
we
h
ave:
)
(
)
(
.
.
)
(
)
(
1
t
t
x
A
Q
B
R
B
A
t
t
x
T
T
(9)
S
o
lvi
ng
the
ab
ove
eq
u
a
t
i
o
ns,
w
e
h
ave
the o
p
tima
l
c
on
tro
l
si
gna
l
:
)
(
).
(
)
(
*
t
x
t
K
t
u
(10)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
768
–
7
76
77
0
Where
)
(
.
.
)
(
1
t
P
B
R
t
K
T
)
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t
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e
p
o
si
tiv
e
sem
i
-
d
efin
i
t
e sol
u
tio
n
of t
he
R
ic
cat
i e
qua
t
i
o
n
:
P
B
R
B
P
Q
P
A
A
P
P
T
T
.
.
.
.
.
.
1
(11)
I
n
the
case
of
t
he
in
f
in
i
t
e
time
∞
,
the
c
ost func
tio
n is a
s fo
l
l
ow
s:
f
t
T
T
dt
t
u
R
t
u
t
x
Q
t
x
J
0
min
)]
(
.
).
(
)
(
.
).
(
[
2
1
(
12)
Th
e op
ti
mal
c
o
n
t
ro
l
sign
a
l
:
)
(
.
)
(
*
t
x
K
t
u
(13)
W
h
e
re
P
B
R
K
T
.
.
1
P
i
s
the p
o
si
t
i
v
e
sem
i-def
i
n
i
te
s
ol
u
t
i
on
of
t
he
R
i
c
ca
ti
eq
uat
i
o
n
:
0
.
.
.
.
.
.
1
P
B
R
B
P
Q
P
A
A
P
T
T
(14)
(
K
a
nd
P
do n
o
t
de
p
e
n
d on
the
time
)
3.
T
H
E DIAGRAM AND
T
HE EQ
U
TION
S OF
T
HE DC
MOT
O
R
The diagram
o
f
a
s
epar
atel
y e
x
ci
te
d DC Mo
t
or
i
s
presente
d as
F
igure
1 [2
5
]
it inc
l
u
d
es
:
-
The
fie
l
d w
i
n
d
i
n
g
s ar
e
i
n
t
h
e
sta
tor,
they
are
used
t
o
exci
te
t
he
fie
l
d
f
l
ux.
-
The
ar
ma
t
u
r
e
coi
l
s
a
re
on th
e
rot
o
r,
t
hey a
r
e sup
p
lied
curr
ent
v
i
a
brus
h a
nd
the c
o
mm
u
t
a
t
or.
F
i
gur
e 1.
The
dia
gra
m
of
a
s
epar
ate
l
y e
x
c
i
te
d D
C
Mo
t
or
The
m
a
them
at
i
c
a
l
e
qua
t
i
ons o
f
t
h
e
D
C
M
o
t
o
r
inc
lude
:
-
Th
e
vo
lt
a
g
e
equ
a
ti
o
n
:
E
dt
di
L
i
R
V
a
a
a
a
a
(V
)
(
15)
Where
a
V
is
t
he
a
rm
ature
vol
ta
ge
,
w
h
ic
h
i
s
f
e
d
i
n
t
o
t
h
e
ar
ma
t
u
r
e
c
o
i
l;
a
a
L
R
,
i
s
t
h
e
a
r
m
a
t
u
r
e
resista
n
ce
a
nd
in
duc
ta
nce
,
E
is the
elec
trom
o
tive
.
-
The
elec
tromo
t
ive
eq
ua
t
i
o
n
:
).
.
(
f
af
E
i
L
K
E
(V)
(16)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
The li
ne
ar
quadr
a
tic regular
algo
r
i
thm-based cont
r
o
l sys
t
em
of
the
di
rect … (
T
rong-T
hang
N
g
uyen)
77
1
Where
ω
i
s
t
h
e
spee
d
of
t
he
r
otor
,
K
E
i
s
th
e
coe
f
fic
i
e
n
t
of
v
o
lta
ge,
f
i
is
t
h
e
w
in
din
g
f
iel
d
c
urr
e
nt,
af
L
i
s
t
he
fie
l
d
a
rm
ature
m
u
t
u
a
l
i
n
duc
ta
nce
.
-
The
m
o
tio
n e
q
uat
i
on
:
f
m
L
e
T
B
T
T
dt
d
J
(N.
m
)
(
17)
Where
J
is
t
he
i
ne
rt
ia,
e
T
i
s
t
h
e
e
l
ectr
o
m
e
c
h
an
i
cal
t
or
q
u
e,
L
T
i
s
the
t
o
rq
ue
w
h
i
ch
i
m
p
ac
t
to
t
he
shaft,
m
B
i
s
the c
o
eff
i
c
i
e
n
t of
t
he
vi
s
co
us fric
tio
n,
f
T
i
s t
h
e
c
oul
omb
f
r
i
c
t
i
on
to
r
q
u
e
.
-
The
elec
trome
c
ha
nic
a
l
t
orque
e
quat
i
o
n
:
a
f
af
a
T
e
i
i
L
i
K
T
).
.
(
(N
.
m
)
(
18)
Where
T
K
is t
he c
oeffic
i
e
n
t of
t
h
e
torq
u
e.
Ba
se
d on
the
e
qua
t
i
o
n
s
of the
D
C
Motor
, w
e
bui
l
d
the
m
o
d
e
l
dia
g
ram
o
f
D
C Mo
t
o
r a
s
show
n in
F
ig
ure
2.
F
i
gure
2.
T
he
m
ode
l
d
i
a
g
ram
of D
C Mo
t
o
r
The
pa
ram
e
ter
s
o
f
t
h
e
D
C
M
ot
or in
th
is st
u
dy ar
e show
n
in
T
ab
le
1
.
Tab
l
e
1.
T
he D
C
Mot
o
r
para
me
ters
Ra
(
)
L
a
(
H
)
K
t
K
e
J(
k
g
.
m^
2
)
B
m(
N
.
m
.
s
)
T
f
(
N
.
m)
0.
5
0.
011
0
.
2
0
.
1
0
.
2
0
.
1
V
a
r
To
i
n
v
es
t
i
ga
te
t
he
d
e
p
e
n
d
e
n
c
e
of
t
he
M
otor
s
pe
e
d
o
n
t
h
e
ar
ma
t
u
r
e
v
o
l
t
a
g
e,
w
e
se
t
t
h
e
a
r
ma
ture
vo
lta
ge
c
ha
n
g
e
from
Va
= 75V
t
o
Va
=
1
00V
.
To
i
nve
sti
g
a
t
e
t
h
e
dep
e
n
d
e
n
ce
o
f
the
M
o
tor
spe
e
d
o
n
th
e
shaft
tor
que,
w
e
s
e
t
t
he
s
ha
ft
t
or
qu
e
cha
n
ge
f
r
o
m
T
L
= 10(
N.M
)
to
T
L
= 20
(N
.M
)
.
Ru
nni
ng
t
he
s
im
u
l
a
t
i
o
n
m
odel,
w
e
obt
a
i
n t
h
e t
i
m
e
c
hara
cter
i
s
tic o
f t
h
e
spe
e
d
show
n
in
F
ig
u
r
e
3.
F
i
gure
3.
The
t
i
m
e
cha
r
ac
t
e
ris
t
ic
o
f
the
spee
d
w
h
en
c
ha
ngi
n
g
th
e
ar
ma
t
u
r
e
vo
l
tage
an
d
t
he
shaft
t
orq
u
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
768
–
7
76
77
2
The
m
i
ssi
o
n
o
f
t
he
s
ys
tem
is
t
o
c
ontr
o
l
the
speed
o
f
t
h
e
D
C
m
ot
or
f
ol
l
o
w
i
ng
t
h
e
de
si
re
d
val
u
e.
I
t
als
o
m
in
imize
s
t
he
c
ha
ng
e
in
s
pee
d
w
hen
c
h
a
n
g
i
ng
t
h
e
torq
ue
i
m
p
ac
te
d
o
n
t
he
s
ha
ft
o
f
t
h
e
D
C
M
o
t
or.
In
t
h
i
s
stud
y,
t
he
a
uth
o
r
pro
pose
s
a
n
op
t
i
ma
l
co
n
t
rol
l
e
r
L
Q
R
t
o
c
o
n
t
ro
l
t
he
r
esp
ons
e
spee
d
fo
l
l
o
w
i
n
g
the
se
t
spee
d
w
ith
t
he s
horte
st
c
o
nvers
io
n t
i
m
e
.
4.
B
U
I
L
DING TH
E
C
O
N
TROL
S
Y
S
T
E
M
FOR TH
E D
C
M
OTO
R
4.1.
The
PI c
o
ntr
o
ll
e
r
an
d
fee
d-forwar
d
cont
rol
l
er
Base
d
o
n
t
he
d
epe
n
de
nce
of
t
he
M
o
t
or
s
p
e
e
d
o
n
t
h
e
ar
ma
t
u
r
e
v
o
l
t
age
and
t
h
e
sh
aft
to
rq
u
e
,
th
e
aut
h
or
b
ui
lt
a
n
d
tes
t
e
d
t
he
t
rad
i
t
i
ona
l
c
o
n
t
r
o
ller
s
f
or
D
C
m
o
to
r
s
a
s
a
b
a
si
s
f
o
r
comp
a
r
i
s
on
w
it
h
L
Q
R
con
t
ro
l
l
ers.
T
he
f
i
r
st
c
o
n
tro
l
l
e
r
is
a
F
ee
d-fo
rw
a
r
d
contro
l
l
e
r
wit
h
t
he
g
ai
n
coe
ffic
i
en
t
K=
2.
1
4
.
The
s
econ
d
con
t
ro
l
l
er
i
s
t
h
e
P
I
c
ont
r
o
lle
r,
t
he
c
ontro
l
sys
t
em
m
odel
sh
o
w
n
i
n
F
i
gu
r
e
4
.
F
i
gure
4.
The
c
on
tro
l
sys
tem
m
odel w
i
th
t
he
P
I
con
t
rol
l
er
The
para
me
t
e
rs
o
f
t
h
e
PI
c
on
t
r
o
ller
are
de
term
i
n
ed
e
x
p
er
i
m
en
tal
ly
.
We
d
e
f
in
e
th
e
ap
p
r
op
ri
at
e
para
me
ters
i
n
order
t
h
a
t
t
he
q
ua
lit
y
of
t
he
c
on
t
r
o
l
s
yste
m
i
s
g
ood.
F
i
n
a
l
l
y
,
the
P
I
c
o
n
t
rol
l
e
r
p
a
r
am
et
e
r
s
ar
e
d
e
fin
e
d
as
f
oll
o
ws:
Kp=
1
,
Kp=
5
R
u
n
n
i
n
g
t
he
s
ys
tem
in
t
w
o
c
ases
o
f
the
c
o
n
t
r
o
lle
r
(
P
I
a
n
d
Fe
ed-
forw
a
r
d),
the
s
i
m
u
la
ti
on
re
sul
t
i
s
show
n as
F
igure
5.
F
i
gure
5.
T
he
s
i
m
ula
t
ion
resu
l
t
in t
h
e
ca
se
s o
f
F
e
e
d-for
w
ard
an
d
P
I
c
ontro
l
l
e
r
Th
e
si
mul
a
tion
re
su
lt
s
sho
w
t
h
a
t
th
e
Fe
e
d
-fo
r
ward
c
on
t
r
o
l
l
e
r
h
a
s
m
e
t
the
c
o
nt
r
o
l
re
qu
ir
em
ent.
T
he
respo
n
se
s
pee
d
o
f
t
h
e
D
C
m
otor
h
as
b
ee
n
fo
l
l
ow
i
n
g
the
set
spe
e
d
.
H
o
w
e
v
e
r
,
t
h
e
q
u
a
l
i
t
y
o
f
c
o
n
t
r
o
l
s
y
s
t
e
m
i
s
low
.
I
n
partic
u
l
ar
,
t
h
e
res
p
o
n
s
e
s
pee
d
o
f
t
h
e
D
C
M
o
t
or
i
s
n
o
t
m
ain
t
a
i
n
e
d
w
h
en
c
ha
ng
i
n
g
t
h
e
t
o
rq
ue
i
mpa
c
t
e
d
on
t
h
e
sha
f
t.
T
hi
s
w
ill
ha
ve
a
v
e
r
y
n
e
ga
t
i
v
e
e
ffec
t
w
h
e
n
a
pp
l
y
i
n
g
i
n
th
e
elec
t
r
i
c
m
ot
ion
of
t
h
e
p
r
o
d
u
c
t
io
n
proce
s
s.
I
n
t
h
e
ca
se
o
f
the
P
I
c
on
t
r
ol
ler
,
t
he
c
on
tro
l
q
ual
ity
has
bee
n
i
m
p
r
ove
d
a
lo
t.
T
he
r
espo
nse
s
p
e
e
d
h
as
bee
n
f
o
l
low
e
d
the
se
t
s
p
ee
d
w
i
t
h
t
he
s
h
o
rt
t
rans
iti
on
t
i
m
e
,
a
n
d
it
is
m
a
i
nt
a
i
ne
d
w
h
e
n
c
han
g
i
n
g
t
he
t
orq
u
e
impa
ct
ed
on
t
h
e
shaf
t
.
H
ow
eve
r
,
the
lim
i
t
a
tio
ns
a
r
e
t
ha
t
t
h
ere
i
s
t
he
o
ve
rsho
t,
a
n
d
t
her
e
i
s
osc
i
lla
ti
on
bef
o
r
e
the r
e
sponse speed is stable.
Th
us,
t
h
e
a
u
th
or
p
r
o
pose
s
a
n
opt
im
al
c
o
n
tr
ol
l
e
r
(LQ
R
)
t
o
a
d
d
res
s
t
h
ese
limi
t
a
t
io
ns
a
n
d
i
m
p
ro
ve
t
he
qua
l
ity
o
f the
c
o
n
t
ro
l sys
t
em
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
The li
ne
ar
quadr
a
tic regular
algo
r
i
thm-based cont
r
o
l sys
t
em
of
the
di
rect … (
T
rong-T
hang
N
g
uyen)
77
3
4.2.
Th
e
opt
i
m
a
l
L
QR
c
on
t
r
ol
ler
F
r
om
t
h
e
e
q
u
a
t
i
ons
o
f
D
C
M
otor
s,
c
han
g
i
n
g
i
n
t
o
th
e
sta
t
e
equa
t
i
on
s
with
t
h
e
s
t
a
t
e
v
ari
a
b
l
es
t
h
a
t
are
the a
r
m
a
ture
c
urr
e
nt a
n
d
the
r
otor
spee
d
:
a
a
a
a
a
a
E
a
f
L
a
T
m
V
L
i
L
R
L
K
dt
di
T
J
T
J
i
J
K
J
B
dt
d
1
1
1
(19)
To
i
n
c
re
as
e
the
e
ffi
ci
e
n
c
y
o
f
th
e
co
nt
rol
pro
c
e
ss,
w
e
a
d
d
t
h
e
s
ta
te
v
ar
iab
l
e
)
/
(
s
t
o
t
h
e
s
t
ate
equa
t
i
o
n
s
:
a
a
a
a
a
a
E
a
f
L
a
T
m
V
L
i
L
R
L
K
dt
di
T
J
T
J
i
J
K
J
B
dt
d
dt
s
d
1
1
1
)
/
(
(20)
In
t
h
e
a
b
o
v
e
s
t
a
t
e
e
qu
at
ion
s
,
t
h
e
st
at
e
v
a
ria
b
l
e
s
a
r
e
)
,
,
/
(
)
,
,
(
3
2
1
a
i
s
x
x
x
x
,
t
h
e
c
o
n
t
r
o
l
signa
l
is
a
V
.
T
h
e
t
o
r
q
u
e
f
L
T
J
T
J
T
1
1
is the
noi
se.
We de
s
i
g
n
the
c
ontr
o
l
si
gna
l
)
(
.
)
(
t
x
K
t
u
LQR
i
n
or
der
for
0
)
(
lim
set
response
t
x
x
.
Named
e
x
i
s
t
he
e
rror
betw
ee
n
response
x
a
nd
set
x
.
)
,
,
(
_
3
_
3
3
_
2
_
2
2
_
1
_
1
1
set
response
set
response
set
response
e
x
x
x
x
x
x
x
x
x
x
x
.
The
sta
t
e
eq
uat
i
o
n
(20)
is re
writ
t
e
n a
s
f
o
l
low
s
:
u
B
x
A
x
e
e
.
.
(21)
Where
45
.
45
1
.
9
0
2
5
.
0
0
0
1
0
0
0
0
1
0
a
a
a
E
T
m
L
R
L
K
J
K
J
B
A
;
9
.
90
0
0
1
0
0
a
L
B
I
n
o
r
d
er
f
o
r
t
h
e
r
esponse
s
p
e
e
d
f
o
llow
i
n
g
t
he
s
et
s
pe
ed
w
it
h
t
h
e
sh
ort
tr
ans
i
t
i
on
time
,
w
e
defi
ne
t
h
e
o
p
t
i
m
a
l
c
o
n
tr
o
l
s
ig
n
a
l
L
Q
R
t
o
m
i
n
im
i
z
e
t
h
e
g
o
a
l
f
u
n
c
t
i
o
n
:
min
)]
(
.
).
(
)
(
..
).
(
[
2
1
dt
t
u
R
t
u
t
x
Q
t
x
J
T
T
(22)
With
0
0
0
0
30
0
0
0
2
Q
,
02
.
0
R
.
Th
e op
ti
mal
c
o
n
t
ro
l
sign
a
l
:
)
(
.
)
(
*
t
x
K
t
u
LQR
(23)
Where
:
P
B
R
K
T
LQR
.
.
1
(24)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
768
–
7
76
77
4
P
i
s
the p
o
si
t
i
v
e
sem
i-def
i
n
i
te
s
ol
u
t
i
on
of
t
he
R
i
c
ca
ti
eq
uat
i
o
n
:
0
.
.
.
A
P.A
1
T
P
B
PBR
Q
P
T
(25)
S
o
lvi
ng
the
eq
ua
ti
on (
2
5) w
e ha
ve
:
0002
.
0
0085
.
0
0022
.
0
0085
.
0
5380
.
0
1394
.
0
0022
.
0
1394
.
0
7821
.
7
P
(26)
Re
plac
e
P int
o
(
24),
we
h
ave:
0.8937]
38.4622
10.0000
[
K
LQR
(27)
The
c
ontro
l
sy
stem
dia
gr
am
is show
n i
n
F
ig
ure
6.
F
i
gure
6. The
c
on
t
r
ol
s
y
s
tem
dia
g
ram
in the
c
a
s
e
of LQ
R
c
ontro
l
ler
5.
RESULT
S
A
N
D
ANALY
S
IS
We
r
un
t
h
e
s
imu
l
at
io
n
mode
l
i
n
t
h
e
f
ol
l
o
wi
ng
c
ase
s
:
t
h
e
Fee
d
-f
o
rw
a
r
d
co
nt
rol
l
e
r
,
P
I
C
ont
rol
l
e
r
,
op
tim
al LQ
R
c
on
tro
l
l
e
r.
T
he
s
i
m
ula
t
ion
resu
l
t
s ar
e show
n
in
F
ig
ure
7.
Th
e
si
mul
a
t
i
on
res
u
lt
s
sho
w
t
h
a
t
th
e
qu
al
ity
o
f
t
h
e
c
ont
ro
l
sy
s
t
e
m
i
n
t
h
e
c
a
s
e
o
f
u
s
i
n
g
t
h
e
o
p
t
i
m
a
l
con
t
ro
l
l
er
L
QR
i
s
e
x
t
r
em
el
y
b
e
t
t
e
r
t
ha
n
t
h
a
t
o
f
t
h
e
Fe
ed-for
w
ar
d
c
ontr
o
l
l
er
a
nd
the
P
I
c
on
t
r
o
ller
.
I
n
the
ca
se
of
t
he
s
yste
m
w
i
t
h
L
Q
R
c
o
n
t
ro
ller,
t
he
r
es
po
nse
s
p
ee
d
a
l
w
a
ys
f
o
ll
ow
s
t
o
t
he
s
e
t
s
pee
d
w
ith
a
v
er
y
shor
t
trans
i
t
i
on
tim
e,
there
is no
t ov
e
r
sho
t
.
Whe
n
c
ha
ng
i
n
g
the
d
i
s
t
urba
nce
(sha
ft
t
or
que)
,
t
he
s
pee
d
i
n
ca
se
t
he
F
e
e
d-for
w
ard
con
t
ro
l
l
e
r
i
s
cha
nge
d
a
nd
i
s
unrec
overa
bl
e
,
t
he
s
peed
i
n
t
h
e
c
a
se
o
f
P
I
c
on
tr
o
lle
r
i
s
c
ha
nge
d
a
n
d
osc
i
ll
ate
d
,
afte
r
a
t
i
m
e
o
f
abo
u
t
4
s
,
the
r
e
sp
onse
s
p
e
e
d
i
s
r
e
st
o
r
ed.
E
s
pe
cia
l
l
y
i
n
the
ca
se
o
f
t
h
e
LQ
R
c
o
n
t
ro
ller,
t
he
r
esp
o
n
s
e
sp
ee
d
is
alm
o
st
u
na
ffe
c
t
ed
b
y
t
h
e
c
h
a
nge
o
f
the
sh
a
f
t
tor
que.
To
m
ore
c
l
ear
l
y
s
how
t
he
d
i
f
fer
e
nt
q
ual
itie
s
i
n
t
he
di
ffe
re
nt c
ases,
the
sim
u
l
a
t
i
on
r
esults
a
r
e
z
oo
m
and show
n
in
F
igure
8.
F
i
gure
7.
T
he sim
ul
a
t
i
on
resu
l
t
s
in
t
he d
iffere
nt
c
a
s
e
s
:
F
e
ed-f
or
w
a
rd,
P
I
,
LQ
R c
ontro
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
The li
ne
ar
quadr
a
tic regular
algo
r
i
thm-based cont
r
o
l sys
t
em
of
the
di
rect … (
T
rong-T
hang
N
g
uyen)
77
5
F
i
gure
8. The
simula
t
i
on r
e
su
lts i
n
t
h
e
z
oom
vie
w
6.
CONCL
U
S
ION
I
n
t
h
i
s
s
t
ud
y,
t
he
a
ut
h
o
r
ha
s
succe
e
d
ed
i
n
b
u
i
l
di
n
g
t
he
o
p
tim
al
c
on
t
r
ol
l
e
r
LQR
fo
r
th
e
DC
M
oto
r
.
The
c
o
nt
r
o
l
qua
li
ty
o
f
t
h
e
pro
pose
d
c
o
n
t
r
ol
ler
LQ
R
i
s
c
ompa
red
w
i
th
t
he
t
ra
d
iti
o
n
al
c
o
n
t
ro
llers
.
The
si
m
u
lat
i
on
res
u
l
t
s
s
how
t
ha
t
the
sys
t
em
w
i
t
h
LQ
R
c
o
n
t
r
o
lle
r
off
ers
su
pe
r
i
or
q
ual
i
t
y
co
m
p
a
r
ed
t
o
t
r
a
d
iti
ona
l
con
t
ro
l
l
ers.
T
h
e
r
e
s
ponse
sp
ee
d
a
l
w
a
ys
f
o
l
l
o
w
s
t
o
t
h
e
s
e
t
s
p
e
e
d
w
ith
a
v
ery
sh
ort
tra
n
sit
i
on
t
ime
.
T
he
respo
n
se s
pee
d
is alm
o
s
t
u
naffecte
d
w
hen
ch
ang
i
ng
the
sha
ft to
r
que. F
i
nal
l
y
, t
h
e pr
o
p
o
s
e
d
c
ontro
l
l
er ha
s
ver
y
si
m
p
le
c
o
n
t
r
o
l
alg
o
ri
thm
s
,
but
t
he
q
ua
lit
y
i
s
o
p
t
i
m
al.
Th
is
i
s
a
good
b
asis
f
o
r
a
pply
i
n
g
c
o
nt
rol
al
go
rith
m
t
o
elec
tr
ic m
otio
n
usi
ng
the
D
C
Mo
t
or.
REFE
RENCES
[1]
Park
, J.
S
.,
&
L
ee,
K
.
D
.
“
Desi
gn an
d Im
pl
em
ent
a
tio
n
o
f
BL
D
C Mo
to
r
w
i
th
I
n
t
e
g
r
a
t
e
d
D
r
iv
e
C
i
r
c
u
i
t
”
.
International
Jou
r
n
a
l
o
f
Po
we
r Electr
onics
and D
r
i
ve Sys
t
ems
(
I
JPE
D
S)
,
vol.
8
(3
),
p
p
.
1
10
9-1116
;
2
0
1
7
.
[2]
Tro
ng,
T
.
N
.
,
&
D
u
c,
M
.
N.
“
The
sp
ee
d
co
nt
rol
syst
em
o
f
BLD
C
u
s
i
ng
PID
controller
w
i
th
P
WM
m
odula
t
i
on
tech
niq
u
e”.
Int
e
rna
t
i
o
n
a
l Jou
r
na
l
of Ad
v
a
nced
an
d A
ppied
Sci
e
nces,
vol.
2(12
),
p
p
.
4
7-5
1
;
20
15.
[3]
S
e
kh
ar,
G
.
R
.,
&
B
an
ak
ara,
B
.
“
A
n
Intern
a
l
C
urrent
C
o
n
t
r
olled
B
LDC
Motor
Drive
Suppl
i
ed
w
it
h
P
V
F
ed
H
igh”,
Int
e
rna
t
i
o
n
a
l
Jo
u
r
n
a
l of El
ectrical
an
d
Co
mp
u
t
er
E
ngineer
in
g
(
I
J
E
CE),
v
o
l
8
(2
),
p
p.
1
26
2-1
272;
2
0
1
8
[4]
Ab
delh
ak,
B.
,
&
Bach
ir,
B.
“
A
Hig
h
g
ain
o
b
s
e
rver
b
as
ed
s
e
n
so
rle
ss
n
on
lin
e
a
r
c
on
trol
o
f
in
du
c
t
io
n
ma
c
h
in
e
.
”
Int
e
rna
t
i
o
n
a
l
Jo
u
r
n
a
l of Po
wer
E
l
ectr
onics an
d
D
r
i
ve Systems
(
I
JPE
D
S)
,
5
(3
),
305
-314
,
2
01
5.
[5]
Gu
nab
a
l
a
n,
R
.,
&
S
ubb
iah
,
V
.
“
S
peed
S
ens
o
rl
e
s
s
V
e
c
t
or
C
on
tro
l
o
f
Induc
t
i
on
Motor
Drive
with
P
I
and
Fuzzy
Controller.
”
In
t
e
rna
t
i
o
n
a
l Jou
r
nal
o
f
Po
wer
Electr
o
n
i
cs
an
d
Dri
ve
Syst
ems
(
I
JPE
D
S
)
, v
o
l
.
5
(3
),
pp.
3
15
-325
,
2
01
5.
[6]
A.
R
am
es
h
,
O
.
Chan
dra
S
e
kh
ar,
M
.
S
iv
a
K
u
m
a
r,
“
A
Nov
e
l
T
h
re
e
P
h
a
se
M
ulti
l
e
vel
Inve
rt
er
w
it
h
Si
ngle
Dc
L
ink
F
o
r
Ind
u
cti
o
n
Mo
to
r
D
r
ive
Ap
plicat
ion
s
”.
Intern
at
io
na
l
Jo
ur
nal
of E
l
ectrica
l
an
d Comp
ut
er En
gi
n
eeri
n
g
(
I
JECE)
,
v
o
l.
8
(2
), p
p.
76
3
-
7
7
0
. 20
1
8
.
[7]
Bos
c
o,
M
aycon
Ch
imi
n
i
,
e
t
a
l
,"Estim
a
t
io
n
o
f
p
aram
eters
and
t
uni
n
g
o
f
a
s
p
eed
P
I
o
f
p
erm
a
nent
m
ag
net
DC
M
o
t
or
us
in
g
diff
erential
evo
l
utio
n",
E
l
e
c
t
r
i
c
M
a
chin
es a
n
d
Drives
Conferen
ce (
I
EM
D
C
)
,
IE
EE Inter
n
a
t
i
onal,
pp
.
1
-6;
20
17
.
[8]
Yao
,
J
i
a
ny
on
g,
Z
on
gx
ia
J
iao,
a
nd
D
aw
e
i
M
a,
"Ad
a
pti
v
e
ro
bu
st
c
on
t
r
o
l
o
f
D
C
M
o
to
r
s
w
it
h
e
x
te
n
d
e
d
s
t
a
t
e
observe
r
",
IE
EE
T
r
a
n
s
a
cti
o
n
s
o
n
Indu
st
ri
a
l
El
ectroni
cs
V
o
l 61(7)
,
pp.
3
6
3
0
-
363
7,
20
1
4
.
[9]
Xu
e,
D
in
gy
u
,
C
hu
nn
a
Zh
ao,
and
Y
a
ng
Qu
a
n
C
h
e
n,
"
F
r
ac
t
i
o
n
al
o
rder
P
I
D
c
o
n
t
r
o
l
o
f
a
D
C
-
M
o
t
o
r
w
i
t
h
e
l
a
s
t
i
c
s
h
a
f
t
:
a case
stu
d
y
"
,
Am
erica
n
Co
n
t
rol
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erence,
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T
h
o
m
a
s
,
N
e
e
n
u
,
a
n
d
D
r
P
.
P
o
o
n
g
o
d
i
,
"
P
o
s
i
t
i
o
n
c
o
n
t
r
o
l
o
f
D
C
M
o
t
o
r
u
s
in
g
ge
n
e
tic
a
l
go
rith
m
ba
se
d
PID
con
t
ro
ller",
P
r
o
c
eedin
gs
of
t
h
e
W
o
rl
d
Cong
res
s
on E
ngin
eerin
g,
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o
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2
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“
Th
e
Con
t
ro
l
S
t
ruc
t
ure
f
o
r
DC
M
oto
r
b
ased
o
n
the
F
lat
n
ess
Con
t
rol”.
I
n
te
r
n
a
t
i
o
na
l J
o
u
r
n
a
l
of
P
o
w
e
r
El
ectro
n
i
cs
a
n
d
Dr
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y
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t
ems (
I
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g
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a
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d
L
Q
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o
l
o
f
a
t
w
o
-
whee
l
s
s
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a
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a
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e-K
e
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g,
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R
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o
f
LQ
R
con
t
ro
ll
er
b
as
ed
o
n
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h
eel
e
d
s
elf-b
alanci
ng
r
o
bot.
In
Co
ntro
l a
n
d
Deci
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n
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09
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«
D
ig
i
t
al
L
QR
s
t
eady
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stat
e
o
p
tim
a
l
con
t
ro
l
w
i
th
f
eedf
o
rward
for
no
nm
inim
u
m
p
h
a
s
e
b
oo
st
D
C-DC
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onv
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In
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l an
d De
ci
si
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e
r
f
o
r
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u
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n
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D
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13
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ob
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s
t
L
Q
R
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l
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M
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v
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n
L
MI
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r
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r
ans
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e
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a,
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n
r
i
qu
ez-Caldera,
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ama
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-L
ara,
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u
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J.
“
LQR
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f
o
r a q
u
adro
to
r us
in
g uni
t
qu
aterni
on
s:
M
odel
i
ng
a
nd
s
i
m
u
lati
on
”.
I
n
Ele
c
t
ro
nic
s
, Commu
n
ic
a
t
ion
s
an
d Co
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t
in
g (C
ONI
E
L
E
COM
P
), 20
13
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n
te
r
n
at
io
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l C
o
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e
r
e
n
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Liu
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C
.,
Pa
n,
J
.,
&
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ha
ng
,
Y.
“
PID
a
n
d
LQR
tr
a
j
e
c
t
ory
tra
c
k
in
g
c
o
ntrol
for
a
n
u
nma
n
ne
d
quadr
otor
h
e
lic
op
te
r:
Ex
perim
e
ntal
s
t
u
d
i
es
”. In
Co
ntro
l Co
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erence (
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r
a
q
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t
or:
M
o
d
e
li
ng
a
nd
s
i
m
u
l
ati
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In
20
14
I
n
te
r
n
at
io
na
l C
o
n
f
e
r
e
n
c
e
on
A
d
v
a
n
c
e
s
in
C
o
mp
u
t
in
g
,
C
o
m
m
u
n
i
c
a
ti
on
s an
d I
n
f
o
r
m
a
t
ic
s
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C
A
C
C
I
)
.
I
E
E
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,
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6
-
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4
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16
S
l
avo
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,
T.
P.
T
.
“
LQ
R
p
o
wer
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e
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In
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s &
In
for
m
at
ic
s
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&
I
)
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IE
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.,
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u
,
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h
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,
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,
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u
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.
“
D
i
s
t
urb
a
nce
acco
m
m
o
d
at
in
g
L
Q
R
m
e
t
h
o
d
b
ased
p
i
t
ch
c
on
tro
l
s
trat
egy f
o
r
w
i
nd
tu
rbi
n
es”.
In
20
0
8
Seco
nd
In
tern
at
ion
a
l
S
y
mp
o
s
ium
o
n
In
t
e
ll
i
g
ent In
f
o
rma
tion T
e
ch
no
lo
gy App
l
i
c
at
ion
.
I
E
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E
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r
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l
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,
B.
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n
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uctio
n t
o
stat
e
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s
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Lewi
s, Fran
k
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.,
Dra
gu
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as
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Opti
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.
Jo
hn
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i
l
ey
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0
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[25]
Tron
g-
Th
a
n
g
N
g
u
y
e
n
,
“The
n
e
u
ra
l
ne
twork
-
ba
se
d
c
o
n
t
r
o
l
sys
t
e
m
o
f
d
irect
c
urrent
m
o
t
o
r
d
river”
.
Internat
ion
a
l
Jou
r
n
a
l
o
f
El
ectri
cal
an
d
Comp
u
t
er E
n
g
i
neerin
g (
I
JE
CE)
,
9
(
2),
p
p
.
14
45
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2,
2
0
1
9
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Evaluation Warning : The document was created with Spire.PDF for Python.