TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 14, No. 3, June 20
15, pp. 500 ~ 5
0
7
DOI: 10.115
9
1
/telkomni
ka.
v
14i3.789
9
500
Re
cei
v
ed Fe
bru
r
y 1
2
, 201
5; Revi
se
d April 26 20
15; Acce
pted Ma
y 11, 201
5
Robust Control of Bench-top Helicopter Using
Quantitative Feedback Theory
Ameerul Hak
eem Mohd. Hairon, Has
m
ah Mansor
*, Tedd
y
Sury
a
Guna
w
a
n
,
Sheroz Kh
a
n
Dep
a
rtment of Electrical
and
Comp
uter
Engi
neer
ing, Ku
lli
yyah of Engi
ne
eri
ng,
Internatio
na
l Islamic Univ
ersit
y
Mala
ysi
a
(IIUM), 53100 Go
mbak, Kual
a L
u
mpur, Mal
a
ysi
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: hasmahm
@ii
u
m.edu.m
y
A
b
st
r
a
ct
A three de
gre
e
of freedo
m (
3
-DOF
) bench-
top hel
ic
o
p
ter i
s
a simplifi
ed
aeri
a
l veh
i
cl
e w
h
ich i
s
used to stu
d
y the b
e
h
a
viors
o
f
the hel
icopt
er
as w
e
ll as
tes
t
ing
mu
ltipl
e
fli
ght contro
l a
p
p
r
oach
e
s for the
i
r
efficiency. D
e
s
i
gni
ng
he
lico
p
t
e
r
’
s dy
na
mic
control
is
a c
hall
e
n
g
in
g tas
k
due
to the
prese
n
ce
of hi
gh
uncerta
inties
a
nd
non-
li
near
beh
avior. I
n
thi
s
study,
Qua
n
t
i
tative F
e
ed
ba
ck T
heory
(QF
T
)
is pro
pos
ed
to
achi
eve ro
bust
control ov
er the hel
icopt
er mode
l. It utili
z
e
s freque
ncy do
main
meth
od
olo
g
y w
h
ich ens
ur
e
s
pla
n
t
’
s stabi
lity
by cons
ider
in
g the
fe
edb
ack
of the syste
m
and th
us re
movi
n
g
the
effect of disturba
nc
es
and re
duci
ng s
ensitivity of
par
ameter
’
s
vari
ati
on. T
he prop
os
ed te
chn
i
q
ue is
tested agai
nst LQR-tune
d PID
control
l
er to d
e
monstrate its
proc
e
dures
as
w
e
ll as its performa
n
ce. Si
mulati
on resu
lts obtai
ne
d throu
g
h
MAT
L
AB Simul
i
nk softw
are sh
ow
n us that QF
T
algorit
h
m
ma
nag
ed to re
duc
e perc
entag
e o
f
oversho
o
t an
d
settling ti
me a
b
out 50% a
nd 3
0
% resp
ective
l
y
over the clas
sical PID contr
o
ller.
Ke
y
w
ords
: qu
antitative fe
edb
ack theory, be
nc
h-top h
e
lic
op
ter, robust controller
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Cou
n
tless n
u
m
ber
of real
-lif
e system
s
nowaday
s is cha
r
a
c
teri
ze
d by extrem
ely high
uncertainty which results i
n
great chall
enge
to exert
good stabilit
y tolerance a
nd perfo
rma
n
c
e
attribute
fo
r clo
s
ed
loo
p
system. To depi
ct
t
he case
of
a
system with hi
gh
u
n
certaint
y,
laboratory-scale ben
ch
-to
p
helico
p
ter which
e
m
p
l
oys three
-
d
egre
e
of freedom
(3-DOF)
dynamics i
s
u
s
ed
a
s
a
refe
ren
c
e
point
a
nd exp
e
ri
m
e
n
t
al model
for
verifying the
effectivene
ss of
variou
s flight control algo
rit
h
ms.
Achieving
hig
h
perfo
rma
n
ce co
ntrol ove
r
3
‐
DO
F heli
c
opter i
s
a diff
icult task du
e
to the
essen
c
e
of
a
few challe
ng
es. Fi
rstly, it is a
n
und
er a
c
tuated sy
ste
m
, which me
ans nu
mbe
r
of
control in
puts are
le
ss th
a
n
num
ber of
outputs to be
controlled; i
n
this
ca
se
it
ha
s t
w
o
c
o
n
t
rol
inputs
and
th
ree
output
s [1]. Secon
d
ly, there i
s
som
e
clo
s
e
rel
a
tionship b
e
twe
en movem
ent
of
pitch a
nd tra
v
el; the latter is o
u
r m
a
in
intere
st
in this
projec
t. Furthermo
re, multiple variabl
es
su
ch a
s
fligh
t
altitude, fuel con
s
um
ptio
n, ai
rspee
d a
nd amo
unt o
f
load co
uld
affect the pla
n
t
para
m
eters o
f
the aircrafts and co
nt
rol structu
r
e of the system [2].
Due to the fa
cts liste
d, so
me
gene
ral control algorithm
s
will find it hard to perform
well at the no
n
‐
equilibrium
points or under
model un
cert
ainties. He
nce,
esta
blishin
g
a rob
u
st
co
ntrol
al
go
rithm
is a chall
e
nging
task which
sho
u
ld
not
o
n
ly co
ntrol
the h
e
licopter’s th
ree
motions (elevation, pitc
h an
d tr
a
v
e
l
mo
tion
)
pre
c
isely, but
also
ca
pabl
e of ada
ptin
g to surroun
ding e
n
viron
m
ent an
d ha
s excellent a
n
ti-
disturban
ce p
r
ope
rtie
s.
Many works
has
bee
n do
ne on
dem
on
strating
the
d
i
fficulty to achieve eithe
r
robu
st or
adaptive
cont
rol ove
r
the h
e
lico
p
ter. Th
e
method
of
combinatio
n of
Linea
r Qu
ad
ratic
Reg
u
lat
o
r
-
Propo
rtional
Integral
Deriv
a
tive (LQ
R
-P
ID)
controlle
r wa
s p
r
op
ose
d
in [3]. Ho
wever, it is fo
u
n
d
out that thi
s
LQR-PID
ba
sed
controlle
r l
a
cks in te
r
m
s of ac
curac
y
(
h
igh s
t
eady-s
tate er
ror)
and
rapidity
(settling time
) [4]
.
Another m
e
thod
pr
opo
sed
is multi
p
le-su
r
face
sliding
co
ntrol
l
er
(MSSC) [5]. Although M
SSC wa
s p
r
oven to pe
rf
orm b
e
tter t
han PID
co
ntrolle
r, tedi
ous
mathemati
c
al
wo
rks are
need
ed
to a
ttain
t
he
de
sired equ
ation
and gain. Combi
nation
of
cla
ssi
cal PID
and fuzzy co
ntrolle
r wa
s a
l
so propo
se
d in [6] and [7]. It combin
es
the conveni
e
n
t
control of PID together with
flexible c
ontrol of fuzzy for 3DoF mo
del
helicopter.
In this proje
c
t, Quantitative Feedb
ack T
heory (QFT
) controlle
r
which wa
s
devel
oped by
Prof. Isaa
c M. Horo
witz i
n
the early 1
970
sis
inte
grated with the
existing LQ
R-PID
cont
ro
ller.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Rob
u
st Control of Bench
-
top He
li
co
pter Usin
g Qua
n
titative… (Am
e
erul Hakeem
Mohd. Hai
r
o
n
)
501
QFT de
als
with the un
certai
nty of plant’s
par
a
m
eters expli
c
itly to suit
the purpo
se of
perfo
rman
ce
and
stabilit
y
[8].
Thro
u
gh QFT ap
proa
ch, a combinatio
n of lineari
z
ati
on,
quanti
z
ation
and tra
n
sl
ation of de
sire
d perfo
rm
a
n
ce
su
ch a
s
robu
st sta
b
ility and rob
u
st
perfo
rman
ce
is carried
out on
set
of bou
nd
s i
n
Ni
chol
s cha
r
t; whil
e u
n
certaintie
s
(eit
her
stru
ctured o
r
unstructu
re
d
)
are
convert
ed into a
r
ea
s in
Nichol
s
cha
r
t call
ed t
e
mplate
s. Lo
op
sha
p
ing p
r
o
c
ess is then
carri
ed out to find the co
ntroller pa
ram
e
ters
by usin
g the Ni
chol
s ch
art
that illust
rates
stability,
performance, and di
sturbance rejectio
n bounds [9]. Thi
s
can be done by
fine-tunin
g
th
e gain
s
a
nd d
y
namic el
em
ents
su
ch a
s
pole
s
, ze
ro
s
and thei
r com
p
lex eleme
n
ts to
the fre
quen
cy re
spon
se
of nomin
al p
l
ant. The
proce
s
se
s
can
be
don
e th
roug
h inte
ra
ctive
environ
ment i
n
MATLAB software
whi
c
h
is
simple a
n
d
straightfo
rwa
r
d to use.
This p
ape
r is orga
nized a
s
follows. Se
ction 2 di
scu
s
sed the fun
damental
kn
owle
dge
about QF
T tech
niqu
e. Section 3 i
s
ab
out the
meth
odolo
g
y of the re
se
arch
while
se
ction
4
pre
s
ente
d
th
e results
of the
simul
a
tion a
s
well
as th
e
analy
s
is an
d
com
pari
s
on
of t
h
e
perfo
rman
ce
of
LQ
R-PID
a
nd
L
Q
R-PID based QFT (wit
h a
nd
with
out pre-filter i
n
stalle
d). Fi
n
a
lly,
se
ction 5 con
c
lud
ed the re
sea
r
ch findin
g
s.
2. QFT Fund
amentals
2.1. Plant Template
In QFT tech
nique
s, the plant’s dyna
mics i
s
rep
r
ese
n
ted in the form of frequ
en
cy
respon
se
wh
ich i
s
foun
d
ed on
the p
r
inci
ple
s
of f
r
equ
en
cy loo
p
sh
apin
g
mixed with t
he
plants’
un
cert
ainties [10]. B
y
con
s
id
erin
g
all
set of
pla
n
ts in
stea
d of
a
singl
e pl
an
t, the mag
n
itu
d
e
and pha
se
of the
pla
n
ts ge
nerate
set
of points
on
the
Nichol
s
cart
a
t
each frequ
e
n
cy
rathe
r
th
an
a single p
o
in
t. Hence a conne
cted reg
i
on or called
template is comp
osed at
each
sele
cted
freque
ncy, which
surro
und
s this set of points.
2.2. QFT Bo
unds
The majo
r step in QFT ap
proa
ch i
s
retri
e
ving domain
s
in the comp
lex plane (o
r Nichol
s
cha
r
t) by m
ean
s of con
v
erting fre
q
u
ency d
o
main
spe
c
ification
s
situ
ated o
n
the feed
b
a
ck
system. ‘Bo
u
nds’
is u
s
ed
to refe
r th
ese
domain
s
i
n
Q
FT’s li
st of te
rms.
Final
ste
p
of the
de
si
gn
is a
c
com
p
lish
ed
whe
n
a
n
o
minallo
op t
r
ansfe
r fu
nctio
n
is shap
ed
su
ch th
at it a
c
hieve
s
nomi
nal
clo
s
ed
-loo
p stability and lies within its b
o
und
s.
2.3. Loop Shaping
De
sign of th
e cont
rolle
r is ca
rri
ed out
by t
he process of loop shapin
g
in the
Nich
ols
cha
r
t. The
n
o
minal
ope
n-loop t
r
an
sfer functio
n
ch
ara
c
teri
stics
are
plotted
togethe
r
with
the
comp
osite
bo
und
whi
c
h i
s
evaluated
at the tria
l fre
q
uen
cie
s
. Basi
cally, the de
signing
pro
c
e
s
s
involves ad
di
tion of multiple elem
ents su
ch a
s
g
a
in, integrato
r
, pole a
nd
zero an
d th
eir
cou
n
terp
art
s
[
11]. By the o
peratio
ns do
n
e
, sh
ape
of th
e op
en-l
oop
tran
sfer fun
c
tion i
s
alte
re
d
so
that the boun
darie
s a
r
e co
mpen
sated
at
each of the trial freque
nci
e
s.
2.4. Pre-filter
Loop
shapi
ng
process gu
a
r
antee
s
that the clo
s
ed
-lo
o
p respon
se o
f
the system fulfills
the criteri
on
spe
c
ified
for
stability tolerances,
al
so f
o
r di
stu
r
ba
nces i
n
the
fre
quen
cy d
o
m
a
in.
Ho
wever, in orde
r to satisfy the
trackin
g
spe
c
if
icatio
ns, a pre
-
filter is need
ed to alter the sh
ap
e
of the system output according
to the desi
r
ed re
quire
ment
s.Introdu
cing the
pre-filter in
the
desi
gn
will
shift the frequency
response of the
closed-loop transfer func
tions, whi
c
h
contai
ns
plant’s
un
cert
ainties, into t
he spe
c
ificati
on ‘env
elo
pe’
or bo
und. T
h
is will
ensure
that the de
sired
tracking p
e
rfo
r
man
c
e of the
final system
can b
e
achie
v
ed.
3. Rese
arch
Metho
d
The th
ree
degree
-of-fre
edom
(3
-DO
F
) h
e
licopte
r
setup
for the
experi
m
ent i
s
manufa
c
tured
by Quan
ser
Con
s
ultin
g
Incorpo
r
ated.
T
he free b
ody diagram (FB
D
) of the sy
st
em
is sh
own in Figure 1 b
e
lo
w.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 14, No. 3, June 20
15 : 500 – 50
7
502
Figure 1. Fre
e
body diag
ra
m of
3-DO
F Heli
copte
r
System [12]
3.1. Modelling of 3-DOF
Bench
-top
Hel
i
copter
In this proje
c
t
,
our main intere
st is the c
ontrol of travel angle of the helico
p
ter.
Cha
nging
the travel direction i
s
quit
e
a ch
allengi
ng task
he
re
. This is b
e
cause travel a
ngle ha
s di
re
ct
relation
with
pitch axis; th
at is the only
way to co
ntro
l travel angle
is by
pitchi
ng
the body of the
helicopter. Fi
gure 2
sho
w
s the FBD for travel angl
e m
e
ch
ani
sm.
Figure 2. Fre
e
body diag
ra
m (FBD) for h
e
lico
p
ter’
s tra
v
el angle
Referrin
g to figure a
bove, the helicopte
r
’
s
body is a
s
sumed to be pi
tched up by a
n
angle
p. For small
angle
s
, the force re
quired
to keep t
he helicopter in
the air is ap
proximately
Fg.
Accel
e
ration
with re
spe
c
t to travel axis is t
he result due to torqu
e
prod
uced b
y
the horizo
n
t
al
comp
one
nt of Fg. The equ
ation asso
ciat
ed with
travel
angle is give
n in Equation
(1) b
e
lo
w.
Jt
r =
−
K
p
·
s
i
n
(
p
)
·
l
a
(
1
)
Whe
r
e
r i
s
t
r
avel
rate in
radi
an
per
se
con
d
,K
p isthe force
re
q
u
ired
to
kee
p
the
helico
p
ter
overhe
ad whi
c
h is
app
roxi
mately Fg an
d sin (p) i
s
the trigo
nome
t
ric si
n of the
pitch an
gle. In
addition, no f
o
rce is
send
along the trav
el axis for ze
ro pitch an
gle
ca
se.
3.2. QFT Co
ntroller Desi
gn
This sub-se
ct
ion will revie
w
the implem
ent
ation of QFT desi
gn techni
que an
d its basi
c
desi
gning
p
r
o
c
ed
ure. It p
r
e
s
ent
s a
detail
ed di
scus
sio
n
of the meth
o
d
and
ste
p
s
with the
aim to
establi
s
h a
solid und
ersta
nding of the
fundame
n
tal con
c
e
p
t of this app
roa
c
h.
A QFT desi
g
n
techni
que
co
mmonly com
p
rises the
s
e t
h
ree b
a
si
c st
eps:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Rob
u
st Control of Bench
-
top He
li
co
pter Usin
g Qua
n
titative… (Am
e
erul Hakeem
Mohd. Hai
r
o
n
)
503
a)
Cal
c
ulation of
QFT boun
ds
(ro
bu
st
stabili
ty, robust tracking, etc.
)
b)
De
signi
ng the
controll
er (or loop sh
apin
g
)
c)
Evaluating the desi
gn (o
r p
o
ssible p
r
e
-
filter desi
g
n
)
For the
syst
ems
with p
a
ram
e
tric
un
certai
nty models, pla
n
t template
s sh
ould be
gene
rated
be
fore
comm
en
cing
on th
e first
step
as i
n
Figu
re
3. A template i
s
the f
r
equ
e
n
cy
response
of the plant
at so
me fix
ed frequency. By utilizing the given plant templ
a
tes,
spe
c
ification
s
for a clo
s
e
d
-loop sy
stem i
s
co
nv
erte
d into magnitu
d
e
and p
h
a
s
e
con
s
trai
nts o
n
a
nominal
op
en
loop
fun
c
tion
thro
ugh
QFT
process. Te
rm ‘QFT
bo
un
ds’ i
s
used to
re
pre
s
e
n
t th
e
con
s
trai
nts m
entione
d abo
ve.
Figure 3. Plant templates
with different
freque
ncy respon
se
After the formation of the
plant’s te
mp
lates,
both
pl
ant’s tem
p
lates a
nd
spe
c
i
f
ication
s
are u
s
e
d
to develop b
o
u
nds
at the tri
a
l frequ
en
cie
s
in the freq
uen
cy-do
m
ai
n. There are
two
conditions for robust stabili
ty, or known as
Robust Stability Crit
eri
o
n 2 whi
c
h are:
a)
Nominal syst
em stability that corr
esponds to the nomi
nal plant, and
b)
The Ni
chol
s
envelop
e doe
s not
co
nverg
e
with criti
c
al
point
q
which is the (-180
°, 0
dB
) point in a
Nich
ols
cha
r
t or the (-1, 0) point in the complex plan
e
.
After stability bound
sho
w
n in Figu
re 4, the tracki
ng bo
und
s are b
e
ing
put into
con
s
id
eratio
n
next. The trackin
g
bo
un
ds (as i
n
Fi
gure
5) d
e
scriptio
ns
sh
o
u
ld follow th
e
requi
rem
ent
of the output plant
whi
c
h
fulfills t
he desired pl
ant output.In
tersection of bounds is
determi
ned
a
nd the
worst
ca
seof
all b
o
und
s i
s
sho
w
n in
Figu
re
6. The
compo
s
i
t
e orint
e
rse
c
tion
boun
d for e
a
ch valu
e of frequen
cy
ω
i iscom
p
o
s
ed of those
portion
s of
each
re
spe
c
tive
boun
d(trackin
g
and di
sturb
ance if
any) that are mo
st restri
ctive.
Whe
n
there
are inte
rsecti
ons
betwe
en two
boun
ds, the
o
u
tmost of the
two bo
und
ari
e
s b
e
come
s t
he pe
rimete
r.
If there a
r
e
no
intersectio
n
s,
then the b
o
u
nd with th
e l
a
rge
s
tvalue
o
r
with th
e out
ermo
st bo
un
dary do
minat
es.
This ist
he final boun
d take
n for the de
sign of the feed
backcomp
e
n
s
ator.
Figure 4. Rob
u
st margin or
stability
boun
ds
Figure 5. Rob
u
st tra
cki
ng b
ound
s
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7
504
Having comp
uted the stabi
lity and performan
ce
bo
un
ds, the next step in a QFT desi
g
n
is lo
op
shapi
ng p
r
o
c
e
s
s
whe
r
e
the
proce
s
s involv
es
de
signi
ng
a
nomin
a
l l
o
op fu
nctio
n
that
fulfills its b
o
und
s. The
n
o
minal l
oop i
s
the
re
sult
s from
com
b
i
n
ing n
o
min
a
l
plant a
nd t
o
be
desi
gne
d co
ntrolle
r which
has to
com
pen
sate the
worst
ca
se o
f
all boun
ds.
I
n gene
ral, t
h
e
pro
c
e
s
s of lo
op shapi
ng a
r
e
comp
osed
of addition
o
f
poles
and
zero
s a
s
well
as g
a
in
s so that
the nomin
al loop is
rep
o
sit
i
oned n
ear it
s bou
nd
s to
ensure
stabili
ty of the nominal clo
s
e
d
-lo
o
p
function.Th
e loop shapi
ng
usin
g Intera
ctiveDe
s
i
gn En
vironme
n
t (IDE) is sh
own in Figure 7.
Figure 6. Interse
c
tion of ro
bust
margi
n
(stabili
ty) and tracki
ng bou
nd
s
Figure 7. Loo
p sha
p
ing p
r
o
c
e
s
s
The final
step
in QFT ap
proach is d
e
si
g
n
ing th
e p
r
e
-
filterto gua
r
an
tee that outp
u
t of the
system
satisf
ies the tracking specifi
c
at
ions. A
dding pre-filter int
o
the system will shift the
freque
ncy
re
spon
se of the
clo
s
e lo
op tra
n
sfer fun
c
ti
on
that contai
ns plant un
ce
rtainties i
n
to th
e
spe
c
ification envelop
e
o
r
boun
ds. The
final
form
of
controlle
r G
(
s) a
nd
pre
-
filte
r
F
(
s) o
b
tain
ed
are sho
w
n in
the Equation
(2) a
nd (3
) be
low:
.
.
.
.
.
.
.
(
2
)
.
.
.
(
3
)
4. Results a
nd Analy
s
is
After finish
e
d
with
the
controlle
r
de
si
gn p
r
o
c
e
ss,
the pa
ram
e
ters of th
e
controlle
r
obtaine
d from
the previou
s
pro
c
e
s
s we
re
expor
ted into MATLAB Simulink
s
i
mulation s
o
ftware
to
fo
r
s
i
mu
la
tio
n
p
r
oc
ess
.
In
th
is
pr
oc
ess
,
th
r
e
e
different s
e
tups
were te
sted; th
e
first on
e b
e
i
n
g
LQR-tune
d P
I
D
controller
next is QFT
controlle
r
b
a
sed
o
n
PID a
nd the last one is PID-b
a
s
ed
QFT cont
roll
er with pre
-
f
ilter.
Figu
re
8
r
epresents the ove
r
all
blo
c
k dia
g
ram for te
sting
con
d
u
c
ted on
the controllers of ben
ch-to
p
helicopter’
s
travel angle.
Figure 8. Overall Simulin
k block dia
g
ra
m for ben
ch-t
op heli
c
opte
r travel angle
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TELKOM
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ISSN:
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046
Rob
u
st Control of Bench
-
top He
li
co
pter Usin
g Qua
n
titative… (Am
e
erul Hakeem
Mohd. Hai
r
o
n
)
505
In this
sim
u
la
tion, the o
u
tp
uts of th
e
sy
stem
s a
r
e
exported
to MA
TLAB Workspace
so
that graph
pl
otting can
be
done
ea
sie
r
a
nd in
mo
re
prese
n
table
ma
nner.
The
blo
c
k ‘Con
stant’
is
the set p
o
int for the
system
, in whi
c
h th
ree di
ffere
nt set points
had
been
sel
e
cte
d
. The rea
s
o
n
of
sele
cting th
e
s
e th
ree
different
ca
se
s is
to demon
st
ra
te the differe
nt travel an
gles d
e
si
red fo
r the
helicopter.
4.1. Simulati
on Results
As mention
e
d
earlie
r, three
different set
poi
nts h
ad be
en ch
osen th
at is 10º, 20º
and 30º
in which their value in radi
an is 0.52 ra
d, 0.
35 rad a
nd 0.17 rad resp
ectively. Four imp
o
rta
n
t
perfo
rman
ce
sp
ecifi
c
ation
s
which a
r
e
perce
ntage
of oversh
oo
t, settling time,perce
ntag
e of
steady-state
error
an
d control
efforts
are con
s
id
ered
h
e
re. The re
sults from simul
a
tions
con
d
u
c
ted
are tabul
ated in
Table
1
until
Table
3,
wh
ere th
e g
r
ap
h
s
o
b
taine
d
fo
r ea
ch
case
are
sho
w
n in Fig
u
re 9 until Fig
u
re 11.
Table 1. Re
sults for set po
int of 0.52 rad
Specifications
LQR
-
t
une
d
PID
PID-bas
e
d
QF
T
QF
T
w
i
th
Pre-fil
t
er
Overshoot
2.90%
11.89%
1.87%
Settling Time (s)
32.17
17.22
20.98
Stead
y
-
stat
e er
ro
r
50.53%
5.10%
0.65%
Control effo
rt ran
ge
-
0.445-1.0
9
4
0.450-0.9
4
6
Figure 9. Re
spon
se of the controlle
rs for
0.52 rad
set p
o
int
Figure 10. Co
ntrol efforts of
the controllers
for 0.52 ra
d set point
Table 2. Re
sults for set po
int of 0.35 rad
Specifications
LQR
-
t
une
d
PID
PID-bas
e
d
QF
T
QF
T
w
i
th
Pre-fil
t
er
Overshoot
2.89%
11.19%
2.18%
Settling Time (s)
31.52
16.75
20.37
Stead
y
-
stat
e er
ro
r
51.29%
1.94%
2.43%
Control effo
rt ran
ge
-
0.300-0.7
3
0
0.304-0.6
3
6
Figure 11. Re
spo
n
se of the controll
ers fo
r
0.35 rad
set p
o
int
Figure 12. Co
ntrol efforts of
the controllers for
0.35 rad
set p
o
int
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TELKOM
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KA
Vol. 14, No. 3, June 20
15 : 500 – 50
7
506
Table 3. Re
sults for set po
int of 0.17 rad
Specifications
LQR
-
t
une
d
PID
PID-bas
e
d
QF
T
QF
T
w
i
th
Pre-fil
t
er
Overshoot
2.90%
11.88%
1.71%
Settling Time (s)
31.27
16.39
20.10
Stead
y
-
stat
e er
ro
r
50.71%
5.12%
0.82%
Control effo
rt ran
ge
-
0.145-0.3
5
7
0.147-0.3
0
8
Figure 13. Re
spo
n
se of the controll
ers fo
r
0.17 rad
set p
o
int
Figure 14. Co
ntrol efforts of
the controllers
for 0.17 ra
d set point
4.2. Results Analy
s
is
The
LQ
R-tun
ed PID controller which
serves a
s
a b
enchma
r
k
for
this
proje
c
t exhibits a
uniform ch
aracteri
stics
th
rough
out
the three ca
se
s. Even
thou
g
h
its pe
rcenta
ge ove
r
shoot
is
better tha
n
P
I
D-ba
se
d Q
F
T co
ntroll
er, i
t
s ste
ady
-stat
e
erro
r
readi
ngs are q
u
ite
high
at ab
o
u
t
50% ran
ge. In addition, se
ttling time is also
the lon
g
e
s
t among all
at aroun
d 30
se
con
d
s rang
e.
For PID-ba
se
d QFT
contro
ller, simul
a
tio
n
sh
ow
n th
at it perform
s b
e
st at medi
u
m
ran
ge
of travel a
ngl
e, in thi
s
case 0.35
ra
d o
r
20º.
Comp
ared
with L
Q
R-tuned PID co
ntrolle
r a
nd
QFT
controlle
r
with p
r
e-filte
r
, it
has faste
s
t
settling
time with
lowest
pe
rcenta
ge of steady-state error
whi
c
h is 1
6
.7
5 se
con
d
s a
n
d
0.68% re
sp
ectively.
On the other
han
d, its
percent
age of oversh
oot
is the
hig
h
e
s
t in all
three
case
s
(1
1.19
% as op
po
se
d to
2.89% a
nd 2.1
8
%)
as a trade
-off
with
that fastest settling time. This i
s
also
unde
si
rable
since hi
gh am
ount of
overshoot ca
n cau
s
e
‘clippin
g
’ of the control sig
n
a
l.
Addition of pre-filter to the
PID-ba
se
d Q
FT cont
rolle
r manag
ed to redu
ce the ov
ershoot
percenta
ge d
r
amati
c
ally (d
own to
1.71
% from 11.
8
8
%
in the case of 0.17
rad
)
, perfo
rmin
g
the
best am
ong a
ll controllers t
e
sted. R
edu
ci
ng the oversh
oot cam
e
wit
h
the co
st of delay in settli
ng
time, but the delay is still within acceptable range.
Another imp
o
r
tant asp
e
ct that
wa
s bein
g
put into test is range of
control effort. Control
effort is
defin
ed a
s
the
a
m
ount of
co
n
t
rol si
gnal
ge
nerate
d
by
controlle
r a
s
t
he result of
error
sign
al fro
m
sensor. F
o
r all
thre
e
ca
se
s
of travel
angl
e,
the pre
-
filter wo
rked
we
ll by redu
cing
the
control effort
range to a
b
out 22-2
5
% lesser
co
m
p
a
r
ed with
QF
T controller
with no pre-f
ilter
installe
d. He
nce, le
ss
am
ount of co
ntrol sign
al
ne
e
d
s to be
gen
erated to
ach
i
eve the de
si
red
res
u
lts.
5. Conclusio
n
From th
e sim
u
lation d
one
via MATLAB Simulink
soft
ware, it ca
n
be con
c
lud
e
d
that the
controlle
r de
sign
fulfills t
he d
e
si
red
robu
st st
a
b
ility and
rob
u
st
trackin
g
p
e
rforman
c
e. T
h
is
transl
a
tes to
robu
st
control over the
uncertainty
a
nd di
sturb
a
n
c
e
s
which prese
n
t in re
al
life
situation, i
n
t
h
is
ca
se
heli
c
opter
flig
ht dy
namics
wh
ere it is gove
r
n
ed by m
any u
n
ce
rtaintie
s
such
as ai
r sp
eed,
humidity and
amount of lo
ad ca
rri
ed.
To
prove the si
mulation resu
lts, these three
types of
cont
rolle
rs
sh
all
be impl
emen
ted on th
e
a
c
tual m
odel
of the be
nch
-
top h
e
licopt
er in
whi
c
h fine-tu
ning of the de
sign may be
required late
r on.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Rob
u
st Control of Bench
-
top He
li
co
pter Usin
g Qua
n
titative… (Am
e
erul Hakeem
Mohd. Hai
r
o
n
)
507
Referen
ces
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Z, Shi H.
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ontr
o
l Strate
gy D
e
sign B
a
se
d o
n
F
u
zz
y
Lo
gic
an
d LQR for
3-D
O
F
Helico
p
ter
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l.
Internat
ion
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l Co
nfere
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ig
en
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a
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r
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ip F
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op H
e
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ter S
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chno
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ang Q, Lee T
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r
o
c
e
e
d
i
ng
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o
f
th
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h
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mp
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252
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[5]
Mostafa A, Rin
i A, Ari L.
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ntrol for 3DOF
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opter
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i
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COM). Kuala Lump
u
r. 201
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[6]
Arbab N
K
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i Y, S
y
e
d
AA, Xu
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o
F
Model H
e
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w
i
t
h
H
y
brid C
ontro
l.
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K
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i
MR, H
a
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emi S, Sana
ei D. D
e
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ng
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i
m
u
lati
on for Vert
ical Mov
i
ng
Co
ntrol of UA
V
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y
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zz
y Lo
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e
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o
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ot C.
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e
e
d
b
a
ck
Contro
ll
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Using
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ne
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Progra
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l
gorit
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eed
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ntrol C
onfer
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