Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 1, No. 2,
February 20
1
6
, pp. 310 ~
318
DOI: 10.115
9
1
/ijeecs.v1.i2.pp31
0-3
1
8
310
Re
cei
v
ed Au
gust 11, 20
15
; Revi
sed
No
vem
ber 2
4
, 2015; Accepte
d
De
cem
ber
15, 2015
Travel Angle Control of Quanser Bench-top Helicopter
based o
n
Quantitative F
eedback Theory Techn
i
que
A.H. Mohd Hairon, H. Mansor*, T.S. Guna
w
a
n, S. Khan
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 n
on-l
i
n
ear b
ehav
ior. T
he
main
obj
ective
of this rese
arch i
s
to achi
eve r
o
bust contro
l ov
e
r
the h
e
lic
opter
mo
de
l re
gard
l
ess p
a
ra
meter
variati
o
n
an
d
distur
banc
es
usin
g ro
bust c
ontrol
techn
i
q
u
e
,
Quantitative F
eed
back T
h
e
o
r
y
(QF
T
).
QF
T
utili
z
e
s fre
que
n
cy domai
n method
olo
g
y w
h
ic
h ensur
es pl
an
t
’
s
stability
by considering th
e feedback
of the system
and thus remo
ving the
effect of
disturbanc
es
and
reduc
ing
se
nsi
t
ivity of p
a
ra
meter
’
s var
i
ati
o
n
.
T
he pr
opos
e
d
tech
niq
u
e
is
testeda
gai
nst
LQR-tun
ed P
I
D
control
l
er i
n
bo
th simulati
on
a
nd re
al h
a
rdw
a
re envir
on
ment
to verify its pe
rfor
m
a
n
c
e
.
Th
e re
su
l
t
s o
b
t
ai
ne
d
shown us
that
QFT algorithm man
aged to r
educ
e settling
tim
e
and st
eady state err
o
r of
about
80% and
33% res
pectiv
e
ly over the cl
a
ssical PID cont
roller.
Ke
y
w
ords
: Quantitative F
e
e
d
back T
heory, b
ench-
to
p he
lico
p
ter, robust co
ntroll
er
Copy
right
©
2016 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
Bench
-
top
h
e
lico
p
ter i
s
an exam
ple
of syst
em
w
i
th
h
i
gh
un
c
e
r
t
a
i
n
t
y. It is
ver
y
chall
engin
g
to engin
eers as well as resear
ch
ers to exert good sta
b
ility toleran
c
e a
n
d
perfo
rman
ce
attribute for
clo
s
ed
-loo
p system. A three-d
e
g
r
ee of
freedo
m (3
-DOF
) lab
o
rat
o
ry
scale
ben
ch
top h
e
licopt
er
usually b
een
used
by engi
nee
rs a
nd
re
sea
r
che
r
s to
study t
he
dynamic
beh
avior of the
aerial vehi
cles an
d se
t
as expe
rime
ntal model f
o
r verifying t
h
e
effectivene
ss
of various flig
ht control alg
o
rithm
s
.
Achieving
hi
gh p
e
rfo
r
ma
n
c
e
co
ntrol
ov
er
3
‐
DOF
h
e
li
copte
r
i
s
a
difficult task du
e to th
e
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 contro
l
structu
r
e of the
system [2].
Many works has be
en d
one to
achie
v
e either
ro
b
u
st o
r
a
dapti
v
e cont
rol o
v
er the
helicopter. T
he meth
od
of com
b
inati
on of Li
nea
r Qua
d
rati
c
Reg
u
lator-Proportio
nal Int
egral
Derivative
(L
QR-PID) co
ntrolle
r
wa
s p
r
o
posed i
n
[3
].
Ho
wever, it i
s
found
out th
at this
LQ
R-P
I
D
based
co
ntrol
l
er l
a
cks in
te
rms of
accu
racy
(hig
h
ste
ady-state
e
r
ror) an
d
rapi
di
ty (settling
time)
[4]. Another
method
pro
p
o
se
d is multi
p
le-su
r
face
sl
iding
cont
roll
er
(MSSC) [5
]. Although M
SSC
wa
s p
r
oven t
o
pe
rform
be
tter than PID cont
rolle
r,
te
diou
s math
e
m
atical
wo
rks a
r
e n
eed
ed
to
attain the de
sired e
quatio
n
and g
a
in. Co
mbination
of cla
ssi
cal PID
and fu
zzy
co
ntrolle
r was
a
l
so
prop
osed in [6] and [7]. It combine
s
the
conve
n
ient
control of PID togethe
r wi
th flexible co
ntrol
of
fuzzy for 3
-
DOF model h
e
l
i
copte
r
.
In gene
ral, th
e problem
s f
a
ce
d by the
previou
s
re
se
rch
e
rsto
cont
rol a
e
rial
veh
i
cle a
r
e
lack of accu
racy, slo
w
re
spo
n
se and
slo
w
co
mput
ational time
due to co
mpl
e
x mathemat
ical
equatio
ns. I
n
this
re
se
arch, Qu
anti
t
ative Feedb
ack Th
eory
(QFT
) i
s
prop
osed a
s
the
interg
rated
c
o
n
trolle
r
fo
r
tra
v
el
angl
e con
t
rol. QFT wa
s develop
ed by Prof. Isaac M. Horo
wit
z
in
the early 19
7
0
s, de
sign
ed
to deal with t
he un
ce
rtaint
y of plant’s p
a
ram
e
ters ex
plicitly to suit
th
e
purpose
of perform
a
nce and stability
[8].
During
the design, the plant
uncert
ainty is
defined
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Tra
v
el Angle
Control of Qu
anser Ben
c
h
-
top Heli
copte
r
based on
… (A.H. Mohd
Hairon
)
311
upfront; as well as
pe
rf
orma
nce spe
c
ificatio
ns
. A
s
a
result,
a robu
st
co
ntrolle
r
with
high
accuracy an
d
fast respon
se coul
d be a
c
hieved.
In this research, Qu
an
se
r
ben
ch-to
p
hel
icopt
e
r
h
a
s b
een cho
s
e
n
a
s
the ca
se st
udy.
The
existing
controller p
r
ovide
d
by the man
u
facturer
i
s
L
Q
R-PID where the pe
rformance is
set
as
the ben
chm
a
rk. Th
e QFT
is propo
se
d to be inte
rgra
ted with PID
controlle
r na
med PID-ba
sed
QFT. In o
r
de
r to validate
the re
sult
s, perfo
rman
ce
comp
ari
s
o
n
has
bee
ncon
ducte
d on
b
o
th
simulatio
n
an
d actual b
e
n
c
h-top heli
c
o
p
ter environme
n
t.
Thro
ugh
QFT
approa
ch, a
combi
nation
of linear
i
z
ati
on, quanti
z
ati
on and t
r
an
sl
ation of
desi
r
ed performance such as r
obust
st
ability and robus
t
perform
ance i
s
carri
ed out on
set of
boun
ds
in Ni
chol
s ch
art; while
un
ce
rta
i
nties are co
nverted
into area
s
in Ni
chols
cha
r
t
ca
lled
templates.
Lo
op shapi
ng p
r
ocess i
s
the
n
ca
rri
ed o
u
t
to find the
co
ntrolle
r pa
ra
meters by u
s
i
ng
the Ni
chol
s
chart that illustrate
s
stabilit
y, perform
ance, and di
sturbance rej
e
ct
ion bounds [
9
].
This can be d
one by fine-tu
ning the gain
s
and dyn
a
mi
c eleme
n
ts such a
s
pole
s
,
zero
s an
d their
compl
e
x ele
m
ents to the frequ
en
cy re
spon
se of nom
inal plant.
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
the
re
sults
and
a
nalysi
s
of the
simulatio
n
a
s
well a
s
the
re
sults
on the
a
c
tual b
e
ch-to
p
helicopter. Compa
r
ison of
the perform
ance of
LQ
R-PID a
nd L
Q
R-PID ba
sed QFT i
s
a
l
so
discu
s
sed in
this cha
p
te
r. Finally, se
ction 5 con
c
luded the re
sea
r
ch findin
g
s with
some
recomme
ndat
ions for futu
re
work.
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 st
ep in QFT a
ppro
a
ch is re
trieving dom
ains in
Nich
o
l
s ch
art by mean
s of
conve
r
ting
f
r
eque
ncy dom
ain spe
c
ifications
situ
ated
on the
feed
b
a
ck
system. ‘
B
ound
s’ i
s
u
s
ed
to refer these
domain
s
in QFT’s li
st of term
s.
Final step of the design is a
c
co
mplish
ed wh
en a
nominall
oop t
r
an
sfer fu
ncti
on is
sh
ape
d
su
ch that
it achi
eves no
minal
cl
osed
-loop stability
and
lies withi
n
its boun
ds.
2.3. Loop Shaping
De
sign of th
e cont
rolle
r is ca
rri
ed out
by
the 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.
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.
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 310 – 318
312
Figure 1. Fre
e
body diag
ra
m of 3-DO
F
Heli
copte
r
System [12]
Figure 2. Fre
e
body diag
ra
m (FBD) for
helicopter’
s
travel 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:
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
g
n
Figure 3. Plant templates
with different
freque
ncy respon
se
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
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Tra
v
el Angle
Control of Qu
anser Ben
c
h
-
t
op Heli
copte
r
based on
… (A.H. Mohd
Hairon
)
313
con
s
trai
nts m
entione
d ab
o
v
e. After the formatio
n of
th
e plant’
s
tem
p
lates, b
o
th p
l
ant’s tem
p
lat
e
s
and spe
c
ificat
ions a
r
e u
s
ed
to develop b
ound
s at
the trial freq
uen
c
i
e
s in the freq
uen
cy-do
m
ai
n.
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
s
c
riptio
ns
should follow the
requi
rem
ent
of the output plant
whi
c
h
fulfills the
desired pl
ant output.Inte
rsection 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
h
e 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
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
r
al, 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. The
loop shapin
g
usin
g Intera
ctiveDe
s
ign 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 form
of controlle
r
G(s) obtai
ned
is sho
w
n in t
h
e Equation
(2) belo
w
:
.
.
.
.
.
.
.
(
2
)
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314
3.3. Implementa
tion of PID-b
ased
QF
T Controller to Quan
ser 3
-
DOF Be
nch
-
top Helicopter
Simulation
Before a
c
tual
run
co
uld b
e
con
d
u
c
ted o
n
t
he real b
e
n
ch
-top
helicopter m
o
del
as
sho
w
n
in Figu
re
8, t
he d
e
si
gne
d
controlle
r
sho
u
ld b
e
te
sted
on the
si
mula
tion file first.
This is to e
n
sure
that the co
ntroller
wo
rks
well with the
h
e
lico
p
ter
syst
em alon
g wit
h
its ha
rd
wa
re. The
simula
tio
n
file, namely ‘s_heli3
d’ is
su
pplied
by Qu
anser In
c
., where it d
e
pi
cts the ove
r
all
helicopter
system
in Simulink test environment.
Figure 8. Qua
n
se
r 3-DO
F b
ench-top
helicopter
Figure 9. Main Simulink bl
ock diag
ram f
o
r
Quan
se
r 3-DOF Bench-to
p Heli
copte
r
Simulation
In the Figure
9, the simul
a
tion file con
s
ist
s
of seve
ral blocks. Th
e first one i
s
‘De
s
ire
d
Angle from P
r
og
ram’,
wh
e
r
e th
e u
s
e
r
can in
put the
desi
red
an
gle
to b
e
simula
ted. Next i
s
t
he
controlle
r blo
ck
whe
r
e th
e previou
s
ly
design
ed
QFT co
ntroll
er is imple
m
ented an
d
it
is
responsibl
e in controlling the movement of t
he helicopter. The controller is fed with the
summ
ation of
error
sig
nal
from the
heli
c
opte
r
a
nd th
e de
sired a
n
g
le from
the
use
r
in
put.From
the controller,
the voltag
e i
s
sent to
the
helicopt
er mo
del. Fin
a
lly, the ‘S
cope
s’
b
l
ock
contai
ns a
set of oscilloscope that is used to di
spla
y
the results of
the simulation process.
3.4. Implementa
tion o
f
PID-ba
sed
QFT Cont
roller to
Actua
l
Quanse
r 3
-
DOF Bench
-
top
Helicopter
The final
pa
rt of this
proj
ect is the im
ple
m
entation
of the PID-ba
se
d QFT
co
ntro
ller o
n
to
the actual be
nch
-
top heli
c
opter. The Q
uan
ser 3
D
O
F
bench-top
helicopter
sy
st
em co
nsi
s
t
s
of
several comp
onent
s, whi
c
h are th
e hel
icopte
r
mod
e
l
,
powe
r
ampl
ifier, data a
c
quisitio
n
(DAQ)
board a
nd
re
al time
cont
ro
l software
in
stalled o
n
a
de
skto
p
comp
ut
er. Th
e
cont
rol software al
so
utilizes MATLAB Simulink environment
whi
c
h is t
he
same as in simulation carried out before,
except few bl
ocks that were inte
rfaced d
i
rectly with th
e hard
w
a
r
e o
f
the helicopt
e
r. Among th
em
are Analo
g
O
u
tput block which fed the
comp
uted vol
t
age by controller to DAQ
board and the
Encod
e
r Inp
u
t
block that pi
cked up the e
n
co
der m
e
a
s
urem
ents for
data monito
ri
ng purpo
se.
4. Results a
nd Analy
s
is
This
cha
p
ter
discu
s
ses the
results obtai
ned from the
simulatio
n
do
ne in Simulin
k as
well
as test cond
u
c
ted on a
c
tua
l
bench-top h
e
lico
p
ter mo
d
e
l. It is divide
d into two parts, in which the
first
will em
phasi
z
es
on t
he impl
ementation of
the
controller onto Qu
anser 3-DOF Bench-top
Heli
copte
r
si
mulation. Fin
a
lly, the resul
t
s obtai
ne
d from impleme
n
t
ation of the PID-ba
se
d Q
F
T
controlle
r ont
o actual b
e
n
c
h-top heli
c
o
p
ter are sh
own and di
scusse
d in detail.
4.1. Quanse
r
3-DOF Helic
opter Simula
tion Re
sults
As mention
e
d
earli
er, three differe
nt set points h
a
d
been
cho
s
e
n
that is 10º,
20º and
30º. Three i
m
porta
nt perf
o
rma
n
ce sp
e
c
ificatio
ns
wh
ich a
r
e pe
rcentage of ov
ershoot, settling
time and percenta
ge of st
eady-state error a
r
e co
n
s
i
d
ere
d
here. The re
sult
s from sim
u
latio
n
s
con
d
u
c
ted a
r
e tabulated i
n
Table 1 to
Table 3,
whe
r
e the g
r
ap
h
s
obtain
e
d fo
r ea
ch
ca
se
are
sho
w
n in Fig
u
re 10 to Fig
u
re 12.
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IJEECS
ISSN:
2502-4
752
Tra
v
el Angle
Control of Qu
anser Ben
c
h
-
top Heli
copte
r
based on
… (A.H. Mohd
Hairon
)
315
Table 1. Re
sults for 30 de
gree
set point
Figure 10. Re
spo
n
se of the controll
ers fo
r 30
degree set po
int
Specifications
LQR
-
t
une
d
PID
PID-bas
e
d
Q
FT
Overshoot
16.49%
5.62%
Settling Time (s)
49.86
9.03
Stead
y
-
stat
e er
ro
r
3.29%
2.18%
Table 2. Re
sults for 20 de
gree
set point
Figure 11. Re
spo
n
se of the controll
ers fo
r 20
degree set po
int
Specifications
LQR
-
t
une
d
PID
PID-bas
e
d
Q
FT
Overshoot
16.54%
5.62%
Settling Time (s)
48.08
9.05
Stead
y
-
stat
e er
ro
r
3.29%
2.18%
Table 3. Re
sults for 10 de
gree
set point
Figure 12. Re
spo
n
se of the controll
ers fo
r 10
degree set po
int
Specifications
LQR
-
t
une
d
PID
PID-bas
e
d
Q
FT
Overshoot
16.49%
5.63%
Settling Time (s)
46.36
9.17
Stead
y
-
stat
e er
ro
r
3.29%
2.18%
4.2. Quanse
r
3-DOF Helic
opter
Hard
w
a
re Tes
t
Re
s
u
lts
The final
part of the proj
e
c
t is im
plem
ent
ation of b
o
th LQ
R-PID and PID-ba
sed
QF
T
controlle
r o
n
to the
actu
al
Quan
se
r b
e
n
c
h-to
p
helico
p
ter. Sin
c
e th
e test i
s
co
nd
ucted
in
real
t
i
me
environ
ment,
the re
sults
of the te
st are rep
r
e
s
ente
d
in set
s
of
grap
h, ea
ch
with 10
-seco
nds
timeframe.
Re
spo
n
se of
PID-ba
se
d Q
FT controll
er
is
sho
w
n i
n
F
i
gure
13
to Fi
gure
15
belo
w
. Th
e
yellow lin
e re
pre
s
ent
s the
desi
r
ed
an
gle
whi
c
h i
s
10,
20 o
r
30 d
e
g
ree
s
. T
he d
e
sired
angl
e
is
assume
d to
be inp
u
t at in
stantan
eou
s t
i
me, whi
c
h
e
x
plains th
e sudde
n spike
of the value.
On
the other ha
n
d
, the purple l
i
ne rep
r
e
s
e
n
ts the re
spo
n
se of the respe
c
tive cont
rolle
r.
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IJEECS
Vol.
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6 : 310 – 318
316
Tra
v
el Angle
(deg
re
e)
Time
(s
)
(a)
Time (s
)
(b)
Figure 13. Re
spo
n
se of PID-b
a
sed QF
T
contro
ll
er at
0-10
se
con
d
s (a) an
d 10-2
0
se
con
d
s
(b) fo
r 10 deg
ree set point
Tra
v
el Angle
(deg
re
e)
Time
(s
)
(a)
Time (s
)
(b)
Figure 14. Re
spo
n
se of PID-b
a
sed QF
T
contro
ll
er at
0-10
se
con
d
s (a) an
d 10-2
0
se
con
d
s
(b) fo
r 20 deg
ree set point
Tra
v
el Angle
(deg
re
e)
Time
(s
)
(a)
Time (s
)
(b)
Figure 15. Re
spo
n
se of PID-b
a
sed QF
T
contro
ll
er at
0-10
se
con
d
s (a) an
d 10-2
0
se
con
d
s
(b) fo
r 30 deg
ree set point
Next is the re
spo
n
se of LQ
R-PID
cont
rol
l
er
, sho
w
n in
Figure 16 to Figure 18. Since the
respon
se
is
quite
slo
w
which
is mo
re
t
han 20 se
con
d
s,
th
e
g
r
aph
s are shown
in
thre
e
timeframe
s
,
each in 1
0
-seco
n
d
s
pe
rio
d
. The te
ste
d
LQ
R-PID
controlle
r is
the default fi
le
sup
p
lied by Q
uan
ser In
c., the manufa
c
tu
rer of the be
n
c
h-to
p heli
c
o
p
ter.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Tra
v
el Angle
Control of Qu
anser Ben
c
h
-
top Heli
copte
r
based on
… (A.H. Mohd
Hairon
)
317
4.3. Results Analy
s
is
Two different
modes of te
sting have b
een c
ond
ucte
d to demon
strate the ca
pa
bility of
Quantitative Feedb
ack Th
eory (QFT)
controlle
r a
s
well a
s
comp
aring it
s pe
rforma
nce aga
inst
Linea
r Qua
d
ratic Re
gulato
r
– Prop
ortio
nal Integr
al
Deriv
a
tiv
e
(
L
QR
-PID)
con
t
roller. Th
e tests
cover
simul
a
tion mode in M
A
TLAB Simulink environm
ent only up to actual ru
n on
real ben
ch
-to
p
helicopter m
o
del.
From
the th
ree m
ode
s
of
test, it can
b
e
seen
th
a
t
Q
F
T
pe
r
f
or
ms
be
s
t
in
r
e
du
c
i
ng
th
e
time taken to
re
ach
stead
y state
or
cal
l
ed
se
ttling ti
me. The
imp
r
ovements a
c
hieved
are
m
o
re
than 80% i
n
both si
mulati
on mo
de
(Ta
b
le 1 to
Tabl
e 3)
and
also
on real h
a
rd
ware te
st (Fi
gure
13 to Figure 15).
Tra
v
el Angle
(deg
re
e)
Time
(s
)
(a)
Time (s
)
(b)
Time (s
)
(c
)
Figure 16. Re
spo
n
se of LQ
R-PID
cont
rol
l
er at
0-1
0
se
con
d
s (a), 10
-20 second
s (b) and 2
0
-30
se
con
d
s (c) for 10 de
gree
set point
Tra
v
el Angle
(deg
re
e)
Time
(s
)
(a)
Time (s
)
(b)
Time (s
)
(c
)
Figure 17. Re
spo
n
se of LQ
R-PID
cont
rol
l
er at
0-1
0
se
con
d
s (a), 10
-20 second
s (b) and 2
0
-30
se
con
d
s (c) for 20 de
gree
set point
Tra
v
el Angle
(deg
re
e)
Time
(s
)
(a)
Time (s
)
(b)
Time (s
)
(c
)
Figure 18. Re
spo
n
se of LQ
R-PID
cont
rol
l
er at
0-1
0
se
con
d
s (a), 10
-20 second
s (b) and 2
0
-30
se
con
d
s (c) for 30 de
gree
set point
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 310 – 318
318
W
i
th
th
e gre
a
t
impr
o
v
eme
n
t
in r
edu
c
i
ng
s
e
ttling
time
, it is
e
x
pe
c
t
ed
th
a
t
th
e
achi
evement
woul
d com
e
with the co
st of higher
ove
r
sh
oot. Ho
we
ver it is prove
n
to be not true
for this p
r
oje
c
t. From the
Quan
se
r be
n
c
h-to
p heli
c
o
p
ter sim
u
latio
n
, PID-ba
sed
QFT co
ntroll
er
score
d
10%
lesser
oversh
oot as
well a
s
mu
ch
better s
e
ttling time c
o
mpared
with LQR-PI
D.
More
over, te
st con
d
u
c
ted
on actual b
ench-top h
e
li
copte
r
al
so revealed g
r
ea
t perform
an
ce of
PID-ba
se
d Q
FT cont
rolle
r where no o
v
ersh
oot wa
s reco
rd
ed ev
en thoug
h it has mu
ch lo
wer
settling time than LQ
R-PI
D controll
er (Fi
gure 1
6
to Figure 1
8
).
5. Conclusio
n
From the
sim
u
lation do
ne
via MATLAB Simulink
software a
s
well
as test
con
d
u
c
ted on
actual
be
nch
-
top
heli
c
opt
er m
odel,
it
can
be
co
n
c
l
uded
that th
e controller
desi
gn fulfill
s
th
e
desi
r
ed robust stability an
d robust tracking
perform
ance. Thi
s
transl
a
te
s to
robust control over
the uncertaint
y
and distu
r
b
ances
whi
c
h
pre
s
ent in re
al
life situatio
n, in this ca
se helicopter fl
igh
t
dynamics wh
ere it is gove
r
ned by many uncertain
tie
s
su
ch a
s
air speed, humi
d
ity and amount
of
load carried.
For future improvem
ents,
addition of p
r
e-filt
er to th
e PID-ba
se
d
QFT co
ntrol
l
er onto
Quan
se
r be
n
c
h-to
p heli
c
o
p
ter is
su
gge
sted in o
r
d
e
r to achieve f
a
ster
settling
time with a
nd
redu
ce
d stea
dy state error.
Referen
ces
[1]
Liu Z, Choukri
Z, Shi H.
C
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
Mode
l.
Internat
ion
a
l Co
nfere
n
c
e on Intell
ig
en
t Control an
d Informatio
n
Pro
c
essin
g
. Dali
an
. 2010.
[2]
Mansor
H, Zae
r
i AH, Moh
d
N
oor SB, R
a
ja
A
h
mad
RK, T
a
ip FS, Ali HI
.
De
sign Of QF
T
C
ontrol
l
er F
o
r
A Bench-T
op Helic
opter S
y
s
t
em Model
. In
ternatio
nal J
o
urna
l of Si
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